# Decision models for on-premises parcel lockers service revenue management

Seyed Sina Mohri, Hadi Ghaderi, Reza Zanjirani Farahani, Neema Nassir, Russell G Thompson

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Seyed Sina Mohri, Hadi Ghaderi, Reza Zanjirani Farahani, Neema Nassir, Russell G Thompson. Decision models for on-premises parcel lockers service revenue management. International Journal of Production Economics, 2026, 294, 10.1016/j.ijpe.2025.109894. hal-05440881

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# Decision models for on-premises parcel lockers service revenue management

Seyed Sina Mohri<sup>a,b</sup>, Hadi Ghaderi<sup>a,b</sup>, Reza Zanjirani Farahani<sup>c,d</sup>, Neema Nassir<sup>b</sup>,
Russell G. Thompson<sup>b,*</sup>

## ARTICLE INFO

Keywords:

City logistics

Revenue models

Contract design

Apartment parcel lockers

## ABSTRACT

On-premises parcel lockers (OPLs) have recently garnered attention as a convenient, safe, and secure parcel delivery solution in urban areas. Companies like Amazon Hub, GroundFloor, and My Parcel Locker have adopted basic Service Revenue Models (SRMs), providing OPLs in buildings under different contract arrangements, such as subscription models and annual partnership fees. However, high capital and ongoing costs impede the adoption of OPLs in small buildings. This study aims to develop advanced decision models for the revenue management of on-premises parcel lockers by developing extensions to the basic SRM. The extensions function by incorporating the concept of carriers paying a service fee and buildings receiving services through partnership agreements. Two distinct partnership scenarios are evaluated: (i) a building hosts the OPL while serving neighbouring buildings, and (ii) collaboration with the local government, where authorities establish shared OPLs in public space near designated buildings, promoting sustainable urban delivery. Alternative SRMs are formulated using novel optimisation techniques, and equilibrium points are identified and analytically evaluated to determine optimal service fees and contract durations. Using real-life data from Melbourne, this study compares the performance of these models under different scenarios. Using real-life data from Melbourne, this study compares the performance of the proposed models under various scenarios. While partnerships involving shared public OPLs supported by local governments remain the most cost-effective overall, incorporating modest land costs slightly reduces their advantage, though they continue to offer the most feasible and widely accepted solution.

## 1. Introduction

The e-commerce industry was valued at USD 18.98 trillion in 2022 and projected to reach USD 47.73 trillion by 2030 (Research and Markets, 2023). Remote work is reshaping consumer behaviour and rising expectations for fast, reliable, and hassle-free delivery services has become a strategic challenge for the industry (Pan et al., 2021; Vazquez-Noguerol and Prado-Prado, 2025). In the United States, nearly 50 % of consumers now expect two-day delivery as the standard (Statista, 2021). However, such short delivery models pose operational challenges, including incompatible delivery windows against carriers' working hours, leading to high rates of first-delivery failure that undermine customer satisfaction, damage brand reputation, and create risks for online-only retailers (Kandula et al., 2021). Failed deliveries not

only create additional cost to carriers for handling and redelivery of parcels but also induce additional traffic and transport externalities to the wider community (Rai et al., 2021).

To address these challenges, delivery networks with Alternative Delivery Points (ADPs), such as Parcel Lockers (PLs) have gained popularity in academia and industry (He et al., 2022; Mohri et al., 2024a). Initially introduced as shared delivery points in high-traffic public areas like transport hubs and shopping centres, lockers serve as alternatives to the doorsteps of customers (Mohri et al., 2023, 2025a). In this study, they are referred to as community-access PLs (CAPLs). CAPLs, as shown in Fig. 1, are typically located within 250 to 2000 m of a receiver's delivery point. They are often free to use and may even offer incentives for self-collection (Mohri et al., 2025b). Provided by carriers or governments, CAPLs facilitate consolidation of deliveries and reduce

<footnote><sup>a</sup> Department of Management and Marketing, School of Business, Law and Entrepreneurship, Swinburne University of Technology, Victoria, Australia</footnote>

<footnote><sup>b</sup> Department of Infrastructure Engineering, University of Melbourne, Victoria, Australia</footnote>

<footnote><sup>c</sup> Rennes School of Business, 2 rue Robert d'Arbrissel, Rennes, 35065, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: rgthom@unimelb.edu.au (R.G. Thompson).</footnote>
service time and vehicle kilometres travelled (VKT) for carriers (Mohri et al., 2022; Ghaderi et al., 2022). Moreover, CAPLs offer a great degree of convenience, including collection flexibility, reliability, safety, and security to receivers (Peng et al., 2023).

However, compared to home delivery, CAPLs can create inconvenience for parcel receivers due to the extra trips required to collect parcels (Mohri et al., 2024b). This inconvenience is significant enough that, despite substantial investments by major carriers, CAPL usage and its associated benefits for carriers and receivers remain low, with home delivery still dominating (Hasija et al., 2020). For instance, Australia Post's network of over 1000 CAPLs accounted for only 14% and 8.5% of total deliveries in 2019 and 2020, respectively (Australia Post, 2021). Challenges for adopting CAPL are quite different in low and high-density areas. In low-density areas, where properties are typically single-household homes, delivery points are widely dispersed, requiring receivers to make longer collection trips that impact their convenience and acceptance. This results in low utilisation rates and poor financial viability for carriers to invest in such facilities. In high-density areas, dominated by apartments, multiple deliveries to different households are often consolidated at a single delivery point. For CAPLs to eliminate these delivery stops, a collective agreement from all households is required—a scenario with low probability. Consequently, only few delivery points are removed, offering minimal reductions in carrier routing costs.

In response to the abovementioned challenges associated with CAPLs, companies like Amazon Hub, Luxer One, and GroundFloor have introduced a new concept called “On-Premises PLs” (OPLs) (Amazon Hub, 2022; Luxer One, 2022). Unlike CAPLs, OPLs are installed inside buildings, eliminating the need for parcel receivers to make collection trips while retaining the benefits of CAPLs. This makes OPLs a highly convenient parcel delivery solution for receivers. However, while OPLs offer significant operational benefits, their adoption has been hindered by limitations in current Service Revenue Models (SRMs). These models primarily recover costs from building owners or residents, overlooking the interests of other key stakeholders, such as carriers and local government (Ranjbari et al., 2023a). The limited, yet emerging literature on OPLs highlights considerable benefits for carriers, including shorter delivery times, elimination of failed deliveries, and streamlined parcel handling (Mohri et al., 2024c). Other beneficiaries include the wider community and local government through reduced vehicle activity and associated externalities (Mohri et al., 2024c). However, while OPLs generate value for these stakeholders, they are often used for free in some buildings and are not included in SRMs, preventing them from contributing to the service fees. This exclusion hinders the ability of OPLs to assist other buildings access these facilities at lower, more attractive fees, thus limiting their scalability and widespread adoption in diverse urban environments.

Additionally, the cost structure of these SRMs, particularly the need for high upfront investment, is more appropriate for large buildings due to economies of scale, while small and medium-sized buildings face significant financial barriers for adoption (Mohri et al., 2024c). The

acceptance of such facilities among medium to small-sized buildings remains very low due to the high capital or service fees that are difficult to justify in these contexts. While the prevalence of medium to small buildings is much higher than that of large buildings, their reluctance to adopt OPLs further limits the scalability and widespread benefits of these facilities (Mohri et al., 2024c). Therefore, wider adoption of OPLs requires more inclusive, modern and flexible SRMs, capable of embracing a diverse range of buildings, spatial considerations and market configurations.

This study aims to address these gaps by introducing a new generation of OPL SRM models capable of incorporating the interests of all stakeholders, including OPL providers, carriers, local government, and residents. By leveraging a hybrid analytical-optimisation approach, the proposed models act as powerful decision support instrument for OPL providers, aiding the determination of optimal service fees and contract durations that could enhance the financial viability of such systems and deliver stakeholder value in urban freight systems. This study seeks to address two key research questions. First, it will explore how new SRMs for OPLs can be developed to incorporate a broader range of buyers and beneficiaries, fostering increased OPL adoption, and create value for all stakeholders involved. Second, the research will assess how the adoption of OPLs can be enhanced through the implementation of these new SRMs. Drawing on a case study from Melbourne, Australia, we provide a comparative evaluation of the proposed models, examining their implications across different delivery volumes, building sizes, and partnership structures. The findings highlight the potential of these advanced SRMs to drive the broader adoption of OPLs in diverse urban settings.

This paper is organised as follows. Section 2 reviews relevant literature, followed by Section 3 describing extensions of the basic SRM problem. Section 4 provides the experimental setting based on a Melbourne case study, followed by the results in Section 5. Finally, conclusions are drawn in Section 6.

## 2. Literature review

PLs are the most popular form of ADPs. The applications of PLs are well-known in city logistics research, with most of the literature centred around CAPLs. Successful deployment of CAPL systems requires inclusive consideration of all stakeholders. Specifically, for successful adoption, the perceived value of such systems must outstrip traditional delivery systems for customers, carriers, and other stakeholders involved in the last-mile delivery ecosystem (Mohri et al., 2024c).

The literature places a special focus on the benefits of ADPs for customers. Giuffrida et al. (2012) emphasise that CAPLs could eliminate the likelihood of failed deliveries as the result of the not-at-home problem, while Iwan et al. (2016) and Oliveira et al. (2017) point to the benefits associated with greater collection flexibility (e.g., 24/7 access) and improved delivery time windows. Zenezini et al. (2018) and Calabrò et al. (2023) highlight that CAPLs could lower customer delivery costs. More recently, improved parcel security and ease of returns

<figure><img src="image_3.png" /><figcaption>Fig. 1. A comparison between types of PLs.</figcaption></figure>
were examined by Lee et al. (2019), van Duin et al. (2020), and An et al. (2022). Specifically, An et al. (2022) observed a positive correlation between consumers' CAPL adoption and their delivery experience considering personal information loss. On the other hand, few studies highlight the shortcomings of CAPLs for customers. For example, Zenezini et al. (2018) stress the need for additional collection trips by customers. As noted by Iannaccone et al. (2021), customers are willing to pay to reduce the distance required for parcel collection. Vakulenko et al. (2018) emphasise the loss of human contact, additional retrieval complexity, and waiting time associated with system failure. Faugère and Montreuil (2020) point to the limitations of CAPLs in handling large and odd-shaped parcels, while Tsai and Tiwasing (2021) and An et al. (2022) reflect on privacy issues as the result of sharing personal information with CAPL providers and other third parties.

From a carrier's point of view, Zenezini et al. (2018), Lemardelé et al. (2021), and Seghezzi et al. (2022) highlight that CAPLs could lower operational costs through reductions in routing and parcel dropping costs. Consequently, such outcomes could reduce the size of carriers' fleets and workforce in the long term (Milewski and Milewska, 2021; Carotenuto et al., 2022). Furthermore, CAPLs could facilitate locating addresses and prevent incorrect deliveries in large residential complexes (Zenezini et al., 2018). Shortened delivery time, elimination of re-delivery, and increased efficiency as the result of fewer drops per delivery tour have been identified as other benefits for carriers (Mohri et al., 2024c). Some studies have also noted that less interaction with residents and the public improves overall delivery productivity (An et al., 2022). On the other hand, high fixed and operational costs of running CAPLs or over-priced access fees to third party CAPL networks (Xu et al., 2021), inadequate functionality for certain parcel configurations (Choi et al., 2021) and security issues (Quan et al., 2022) have been reported in the literature as disadvantages for carriers.

Besides customers and carriers, indirectly, CAPLs could benefit other stakeholders such as local government and the public. In particular, reduced commercial vehicle activity could lower environmental and social externalities in dense urban areas (Carotenuto et al., 2018; Carotenuto et al., 2022; Pinchasik et al., 2025). Other benefits explored in the literature include improved network efficiency (Milewski and Milewska, 2021) and enhanced urban infrastructure utilisation (Mohri et al., 2024c). At the same time, the literature highlights that poor harmonisation and compatibility of CAPL systems with urban design (González-Varona et al., 2020), along with increased transport activity associated with customers' pick-up trips to CAPLs leads to environmental and social externalities from host locations (Zhang et al., 2018; Liu et al., 2019; Schwerdfeger and Boysen, 2020).

Although CAPL facilities present a theoretically attractive solution, the limitations discussed above have been negatively impacting their adoption globally (Hasija et al., 2020; Lim et al., 2022). To address these limitations, the concept of OPL located within residential buildings, has garnered increasing attention in both academia and industry. Unlike CAPLs, OPLs are installed within the property boundaries to provide exclusive access to residents, thereby enhancing privacy and convenience by offering flexible delivery times and reducing parcel collection costs. The academic discourse on OPLs is new, yet the limited body of knowledge underscores their advantages for a diverse range of stakeholders. Lee et al. (2019) developed a decision support system for optimising the placement and sizing of OPLs in residential settings. Ranjbari et al. (2023b) conducted an empirical assessment of OPL utilisation and carrier behaviour in downtown Seattle, determining the optimal facility size. Authors emphasised the need to understand residents' online shopping behaviour when configuring lockers. In a subsequent study, Ranjbari et al. (2023a) examined the effects of OPL deployment on delivery times, revealing potential reductions in carrier dwell times within buildings. Mohri et al. (2024c) further demonstrated that OPLs yield significant operational and external cost savings, benefiting not only residents but also carriers and local government.

Conventionally, OPL providers adopt a basic SRM model, charging

buildings for installation, management, and maintenance through either one-time fees or ongoing monthly or yearly rental payments (My Parcel Locker, 2024). However, such models come with two main shortcomings. First, due to high initial costs, this model may not be financially feasible for buildings smaller than a certain size. Second, buildings are responsible for absorbing all the costs, while other stakeholders such as carriers and the wider community may benefit from the installation of OPLs, leading to an inequitable setting. Mohri et al. (2024c) highlighted the issue of cost-effectiveness of OPLs for smaller buildings and advocated for more sophisticated SRMs to facilitate wider adoption. However, current SRM approaches for OPLs remain simplistic and fail to account for the interdependencies between stakeholders' interests, thereby limiting their scalability and effectiveness. The academic literature around SRMs for CAPLs and OPLs is limited. While studies on CAPLs discuss some pricing models (Yu et al., 2021), SRM frameworks are almost entirely absent in the literature. This gap in the literature is particularly striking given the growing complexity of last-mile delivery ecosystems, where multiple stakeholders must balance costs, access, and service levels. To the best of our knowledge, Yu et al. (2021) is the only study investigating the pricing of CAPLs for both carriers and parcel receivers. This study is motivated by the fact that in China, most CAPL facilities are operated by independent companies, in contrast to other regions where CAPLs are mainly managed by carriers or local government. The pricing model for CAPLs follows the “beneficiary-pay principle,” which allocates the costs of using CAPLs to either carriers or parcel receivers, depending on the availability at the delivery address and the delivery time. This approach allows for optimisation of last-mile delivery costs and improved efficiency by reducing the need for multiple delivery attempts, particularly when parcel receivers are unavailable. The study of Yu et al. (2021) utilises a Travel Salesman Problem (TSP) to optimise delivery routes and costs, accounting for the availability of parcel receivers. If all parcel receivers are available, the carrier fully bears the locker service cost. However, if a receiver is unavailable, the costs are shared between the carrier and the receiver.

Compared to CAPLs, designing alternative SRMs for OPLs is more critical, primarily because, in all real-world implementations, OPLs are provided by private companies that charge buildings based on the benefits they receive. Given the profit-driven nature of OPL provision and operation, the lack of comprehensive SRM models creates a gap in existing research. This study contributes to the literature on ADPs and city logistics by refining the basic OPL SRM, defining modern alternatives, and evaluating their implications within a last-mile delivery ecosystem. Specifically, we go beyond assessing OPLs for individual buildings and their residents, exploring the potential benefits of such systems for carriers and local government. We suggest that these stakeholders should be incorporated into SRM as key actors, providing decision support for OPL providers. Accordingly, we introduce two underlying partnership strategies.

1. **Centralised OPL Services:** This strategy involves a building hosting OPL services for neighbouring buildings, thereby facilitating centralised service provision and benefiting multiple small buildings nearby.

2. **Government Collaboration:** This approach entails collaboration with local government authorities to establish shared OPLs in public areas near designated buildings, eliminating the need for individual collection trips and associated costs.

### 3. Problem definition

The research problem in this study is informed by a collaborative industry-based project with a OPL solution provider in Australia to address the challenges associated with expanding the adoption of OPLs. Without revealing the commercial arrangements, the OPL provider adopts an existing SRM – the “Basic SRM” discussed in Subsection 3.2– where the contract is set between the OPL provider and a single
building. Under this model, the building is responsible for covering the fixed costs associated with the installation of OPLs, as well as the operational costs related to customer service and maintenance. Additionally, the contract must ensure profitability for the OPL provider while offering perceived value (e.g., cost savings for the building's residents) to the building.

In the current SRM model, payments from buildings are structured as instalments, similar to a loan agreement, with the building paying for the provision and maintenance of the OPL facilities over time. The key decisions for the OPL provider in this model include determining the optimal contract duration (in years) and setting an appropriate annual service fee to be charged to the building. These decisions are vital to ensure the OPL provider meets its financial objectives while offering a competitive and viable service to the buildings. While profitability is essential, the price is not maximised in the objective functions of the SRMs, as excessively high service fees would undermine competitiveness and limit market adoption. This approach aligns with the concept of penetration pricing, where firms accept lower margins in the short term to encourage adoption and build market share (Spann et al., 2015). It

also reflects the well-recognised trade-off between profit margin and market share, in which prioritising affordability and adoption can strengthen long-term competitive positioning. This is consistent with findings by Waller et al. (2010), who showed that shorter contract durations motivate service providers to exert greater effort, leading to improved performance and efficiency. Similarly, in a dynamic market such as the parcel locker sector, where technologies and consumer behaviours evolve rapidly, shorter contracts enable providers to remain responsive, manage risk, and achieve quicker returns on investment. Accordingly, the model guarantees an acceptable Net Profit Margin (NPM) while prioritising shorter loan durations. As discussed in Sub-section 3.1, this emphasis reflects the provider's strategic considerations: quicker investment recovery, reinvestment for growth, and effective risk management, all while maintaining competitive and affordable service terms for buildings.

This study aims to enhance the basic SRM by incorporating the additional beneficiaries of OPL services, such as carriers and local government, and considering different partnership mechanisms. We introduce five alternative SRM models based on two key features: 'service

<figure><img src="image_4.png" /><figcaption>Fig. 2. Schematic representation of the proposed SRMs.</figcaption></figure>
buyer' and 'partnership strategy'. In the basic SRM, the host building is the sole service buyer. However, recognising carriers as key beneficiaries (Mohri et al., 2024c), we propose three alternatives—SRM1, SRM2, and SRM3—that include carriers as secondary service buyers. In terms of the partnership model, we extend the basic SRM by proposing SRM2 and SRM3, which consider partnerships among neighbouring buildings, and SRM4 and SRM5, which include local government as additional beneficiaries of OPL services. Fig. 2 illustrates a schematic representation of the proposed SRMs.

### 3.1. Key considerations and assumptions

In this section, a set of key considerations and assumptions are outlined to provide clarity on the structure and objectives of the proposed SRMs. The key considerations primarily justify the contract as a loan agreement, with a focus on minimising contract duration and ensuring profitability for the OPL provider and other parties. These considerations reflect the operational goals of the OPL provider in recovering its investment efficiently, while also maintaining competitive terms. The assumptions, which apply uniformly across all proposed SRMs, provide further details on the model's operational and financial aspects.

#### 3.1.1. Key considerations

1. **Market Competition and Strategic Positioning:** The OPL provider operates in a competitive landscape, with several other companies providing similar services. Given that OPL services are a relatively new market offering, the company's primary goal is to gain market share rather than to maximise immediate profits. By offering attractive loan contracts with manageable durations, the company can position itself as a viable and competitive alternative in the market. The strategy is to secure as many partnerships as possible, even if the initial profit margins are lower, as long as long-term profitability and sustainability are guaranteed through an acceptable NPM. The focus on minimising contract duration helps the company to quickly recover investments, thereby allowing it to scale faster in a competitive environment. This approach is aligned with established concepts in business strategy, such as penetration pricing, where firms deliberately accept lower margins to stimulate adoption and capture market share (Spann et al., 2015; Sije and Oloko, 2013)

2. **Attractiveness of the SRMs and Financial Flexibility for Clients:** The OPL provider aims to make its service offerings more attractive to buildings by adopting a loan contract model, where clients pay for OPL services over a defined period rather than bearing all upfront costs. This model reduces the financial burden on buildings, making the service more accessible, particularly for smaller buildings with limited budgets. However, the OPL provider has to ensure its investments are recouped in a short period of time, with a guaranteed profit margin. Thus, it is essential to shorten the contract duration, while maintaining an affordable annual service fee. By minimising contract duration, the company ensures that its capital is efficiently reinvested into acquiring new clients and expanding its market presence.

While long-term contracts provide stability, they also prolong the payback period, delay investment recovery, and increase exposure to long-term demand and market risks. In contrast, shorter contracts accelerate the payback period, reduce the financing horizon, and enable the OPL provider to recycle capital into new sites more rapidly, a critical factor in the early expansion phase of a competitive and still-maturing market. For OPL providers, this is particularly relevant: capital tied up in one long contract cannot be redeployed quickly to new sites, limiting opportunities for scale and reducing strategic flexibility.

3. **Balancing Profitability and Risk Management:** Minimising contract duration is critical not just for recovering investments quickly, but also for managing risk. By shortening the contract, the OPL provider reduces its exposure to long-term financial uncertainties, such as fluctuations in demand or changes in the competitive landscape. While profit maximisation remains important, the OPL provider prioritises contract duration minimisation to create a more agile business model that can better adapt to changing market conditions.

4. **Long-Term Strategy for Industry Growth:** The OPL provider is not solely focused on short-term profits; instead, it views this approach as part of a long-term strategy for industry growth and market expansion. By offering flexible, short-duration contracts that are attractive to building owners, the company can rapidly increase its market share. The quick return on investment allows for reinvestment into technology upgrades, expansion of service offerings, and improvement of customer service – all of which contribute to long-term industry leadership. This approach is aligned with the strategic trade-off between profit margin and market share, in which firms sacrifice short-term profitability to secure a stronger long-term competitive position (Buzzell et al., 1975).

The decision to minimise contract duration in the SRM model is grounded in the practical realities of the OPL provider's business strategy. In a competitive market, the company prioritises securing market share and ensuring financial sustainability over maximising immediate profits. By offering loan contracts with a focus on minimising duration, the company can recover its investments more quickly, manage risks effectively, and maintain a competitive edge. As long as the NPM is met, the OPL provider is positioned to expand its market presence, ensuring long-term growth and success within the industry. Thus, minimising the contract duration is a strategic choice that aligns with both the company's financial objectives and the broader goal of expanding the adoption of OPL services.

#### 3.1.2. Assumptions

1. The service quality provided by the OPL provider remains consistent across contract models. It is fixed at a satisfactory level and covers maintenance and customer service throughout the contract duration. This assumption is essential for maintaining simplicity and consistency across the SRM models. By fixing service quality, we focus on the financial and contractual aspects of the SRM, avoiding complications from varying service levels. This uniformity enables clearer comparison of contract structures without introducing distracting variables. Similar assumptions have been made in studies such as Habli et al. (2023), who considered fixed service quality in ride-sharing models for passengers.

2. Buildings are considered key stakeholders in the model, and the value created by the installed OPL in each building is estimated as the aggregated value of the facility for all residing households. This assumption simplifies the model by treating the entire building as a single entity. The aggregated value model assumes that each household benefits equally from the OPL services, which is a reasonable approximation in many cases, particularly in high-rise urban environments where services like parcel lockers are shared (Pham and Lee, 2019).

3. For simplicity, the NPM for OPL companies, carriers, and buildings are assumed to be equal. This assumption is made to streamline the comparison of contract structures without introducing excessive complexity due to variations in profit margins. However, to evaluate the influence of this assumption, a sensitivity analysis is conducted in Appendix A3, where different NPM ratios among stakeholders are tested to examine their impact on model outcomes.

4. The acceptance behaviour of entities involved in SRMs is assumed to be homogeneous. This assumption simplifies the model by assuming homogeneous acceptance behaviour across buildings, which may
vary based on factors such as size or tenant preferences. This approach is common in several acceptance models, such as those utilising the multinomial logit (MNL) model, as demonstrated in studies by Lyu and Teo (2022) and Mohri and Haghshenas (2017).

5. Buyers pay a fixed service fee for the duration of the contract. This fixed-fee structure suits urban environments with high-rise buildings, offering predictability and financial visibility to both OPL providers and buyers. It ensures a steady revenue stream for providers and cost consistency for buyers, enhancing trust and simplifying financial arrangements. Similar to the findings in supply chain risk management studies, such as Kremer and Van Wassenhove (2014), firms prefer fixed-fee contracts to mitigate overpayment tendencies and inventory risks. In this context, the fixed-fee structure reduces the tendency for buyers to overpay for service mismatches, providing both cost stability and improved financial planning.

6. The payment by the OPL provider to the government for land provision is disregarded, as it is likely to be minimal. Local governments frequently support initiatives that promote shared services, such as parcel lockers, car-sharing, and scooter-sharing systems, due to their positive impact on reducing emissions, alleviating traffic congestion, and enhancing urban mobility (Mohri et al., 2024c). For instance, the City of Melbourne and the City of Port Phillip have both publicly supported car-sharing systems by allocating public spaces for these platforms (City of Melbourne, 2025; City of Port Phillip, 2025). Furthermore, the LockerNYC initiative in New York City, launched in 2024, demonstrates the potential benefits for local government when facilitating such partnerships (New York City, 2025). However, to examine the possible impact of nominal land leasing costs, a sensitivity analysis is presented in Appendix A3, testing a range of annual fees to confirm the robustness of the results.

It is worth highlighting that by changing these assumptions, several new contract structures can be generated. While these assumptions are designed to keep the model practical and manageable, relaxing them would provide more nuanced insights into how variability in behaviour and financial objectives could impact outcomes. This paper covers a set of such contracts with realistic yet simplistic assumptions, paving the way for future studies that can explore these dimensions in more detail. Table 1 summarises the proposed SRM extensions along with their key features and assumptions discussed in Subsection 3.1.

The subsequent subsections detail the formulated SRMs presented in Table 1. The notation utilised in the formulations and their respective definitions are presented in Table 2.

## 3.2. Formulating basic SRM

The basic SRM presents the most common form of a revenue man-

agement model adopted in recent years (My Parcel Locker, 2024), in which the OPL provider is the seller of service and building *i* is the buyer. To make the service offering attractive to the buyer and maximise its own profitability, the seller aims to optimise both the duration of the contract (*T*₀) and the annual service fee (*τ*ᵢ) charged to building *i*. Fig. 3 depicts the basic SRM model.

**Value of OPLs for buildings:** Primarily, OPLs provide a solution for missed deliveries. Depending on carriers' methods of managing missed deliveries, OPLs could provide different benefits for residents. Some carriers arrange for redelivery in a few days, causing inconvenience and delays to parcel receivers. Other carriers drop missed deliveries to a nearby public ADP or post office, requiring additional travel to retrieve parcels, incurring both time and monetary expenses. In both cases, OPLs address these issues. Here, we formulate the value of OPLs in terms of time, cost and delayed delivery savings for residential building *i* with *D*ᵢ households. The annual number of parcel deliveries to each household is indicated by *n*. Studies show that household income is correlated with the frequency of online shops and can be used a proxy to estimate average number of parcel deliveries (Spurlock et al., 2020; Unnikrishnan and Figliozzi, 2021). Considering *h* as the hourly income ($/hour) of a household, the number of parcel deliveries can be estimated as *n* = *αh*<sup>β</sup>, where *α* and *β* are coefficients. Function *f*ᵢ(*h*) represents the PDF of the hourly income of households in building *i*. Thus, the annual number of deliveries for building *i* can be estimated as *D*ᵢ ∫<sub>0</sub><sup>∞</sup> *αh*<sup>β</sup>*f*ᵢ(*h*)*dh*. To simplify, it is assumed that a fraction *ξ*, where *ξ* ∈ [0, 1], of the annual deliveries to buildings without OPLs are considered as failed deliveries. Therefore, households in building *i* miss *ξD*ᵢ ∫<sub>0</sub><sup>∞</sup> *αh*<sup>β</sup>*f*ᵢ(*h*)*dh* deliveries annually. The urban freight market consists of a set of |*M*| carriers (*m* ∈ *M*). Each carrier follows a specific approach for managing failed deliveries. Assume that *M*₁ includes all carriers that arrange redelivery for the customers, while *M*₂ includes those carriers who leave failed deliveries at ADPs for collection by households (*M*₁ ∪ *M*₂ = *M*). The market shares of carriers are shown by *q*<sub>m</sub> (∀*m* ∈ *M*). Accordingly, the annual number of failed parcel deliveries for building *i* (*F*ᵢ) is calculated by (1) and (2), respectively.

$$ \mathbb{E}F_{1i} = \sum_{m \in M_1} q_m \xi D_i \int_0^{\infty} \alpha h^\beta f_i(h) dh \quad (1) $$

$$ \mathbb{E}F_{2i} = \sum_{m \in M_2} q_m \xi D_i \int_0^{\infty} \alpha h^\beta f_i(h) dh \quad (2) $$

Eliminating parcel collection trips leads to both time and cost savings for residents. When collecting parcels from ADPs, residents must allocate time and resources, particularly for heavy and large parcels which may require driving. To capture this effect, let *θ* ∈ [0, 1] denote the fraction of heavy and large parcels relative to the total number of failed

<table><caption>**Table 1**
Summary of SRM variants and key assumptions.</caption><thead><tr><th>Model</th><th>Service Buyer(s)</th><th>Partnership Type</th><th>Key Distinguishing Features</th><th>Main Assumptions</th></tr></thead><tbody><tr><td>Basic SRM</td><td>Building only</td><td>None</td><td>Contract between OPL provider and a single building; building covers installation and operational costs through fixed annual instalments.</td><td>Service quality fixed; Homogeneous acceptance behaviour; Equal NPMs; Fixed annual service fee; No government land cost.</td></tr><tr><td>SRM1</td><td>Building + Carrier</td><td>None</td><td>Extends Basic SRM by including carriers as secondary beneficiaries contributing to service fees.</td><td>Same as Basic SRM</td></tr><tr><td>SRM2</td><td>Building only</td><td>With neighbouring buildings</td><td>Enables cooperative contracts among adjacent buildings sharing OPL facilities to reduce individual costs.</td><td>Same as Basic SRM</td></tr><tr><td>SRM3</td><td>Building + Carrier</td><td>With neighbouring buildings</td><td>Same as SRM2, but with carriers added as additional contributors to service fees.</td><td>Same as Basic SRM</td></tr><tr><td>SRM4</td><td>Building only</td><td>With local government</td><td>Introduces government support (i.e., land provision) to remove the host building and reduce cost burdens for partnered buildings.</td><td>Same as Basic SRM</td></tr><tr><td>SRM5</td><td>Building + Carrier</td><td>With local government</td><td>Same as SRM4, but with carriers added as additional contributors to service fees.</td><td>Same as Basic SRM; land cost included via sensitivity analysis in Appendix A3; NPMs varied via sensitivity analysis in Appendix A3.</td></tr></tbody></table>
<table><caption>**Table 2**
Notations.</caption><thead><tr><th>Type</th><th>Notation</th><th>Definition</th></tr></thead><tbody><tr><td rowspan="7">Sets and indices</td><td><i>m</i></td><td>Index of carriers</td></tr><tr><td><i>i,j</i></td><td>Index of buildings</td></tr><tr><td><i>J<sub>i</sub></i></td><td>Set of partnered buildings to building <i>i</i></td></tr><tr><td><b>M<sub>1</sub></b></td><td>Set of carriers arranging redelivery for failed parcels</td></tr><tr><td><b>M<sub>2</sub></b></td><td>Set of carriers leaving failed deliveries at ADPs</td></tr><tr><td><b>M</b></td><td>Set of carriers, <i>M</i> = <i>M<sub>1</sub></i> ∪ <i>M<sub>2</sub></i></td></tr><tr><td rowspan="10">Decision variables</td><td><i>τ<sub>i</sub></i></td><td>Annual service fee charged to building <i>i</i> ($)</td></tr><tr><td><i>τ'<sub>i</sub></i></td><td>Annual service fee charged to carriers for OPL services and facilities in building <i>i</i> ($)</td></tr><tr><td><i>β<sub>j</sub></i></td><td>The fee imposed to partnered building <i>j</i></td></tr><tr><td><i>T<sub>0</sub></i>, ..., <i>T<sub>5</sub></i></td><td>Contract duration based on the basic SRM, SRM1, ..., and SRM5 (years)</td></tr><tr><td rowspan="17">Parameters</td><td><i>n</i></td><td>Annual number of parcel deliveries to a household</td></tr><tr><td>α and β</td><td>Coefficients, <i>n</i> = <i>ah<sup>β</sup></i></td></tr><tr><td><i>h</i></td><td>Hourly income of a household ($/hour)</td></tr><tr><td><i>h'</i></td><td>The hourly operating cost of delivery vehicles</td></tr><tr><td><i>f<sub>i</sub>(h)</i></td><td>Probability Density Function (PDF) of the hourly income of households in building <i>i</i></td></tr><tr><td><i>D<sub>i</sub></i></td><td>Number of households in building <i>i</i></td></tr><tr><td><i>ξ</i></td><td>Failure delivery rate, ξ ∈ [0, 1]</td></tr><tr><td><i>q<sub>m</sub></i></td><td>Market share of carrier <i>m</i></td></tr><tr><td><i>E<sup> walk</sup><sub>1i</sub></i></td><td>Expected yearly failed parcel count in building <i>i</i> for carrier redelivery</td></tr><tr><td><i>E<sup> drive</sup><sub>1i</sub></i></td><td>Expected yearly failed parcel count in building <i>i</i> for customer pickup from ADPs.</td></tr><tr><td><i>θ</i></td><td>Fraction of heavy and large parcels relative to total parcels, θ ∈ [0, 1]</td></tr><tr><td><i>s<sub>walk</sub></i></td><td>Walking speed (km/hour)</td></tr><tr><td><i>s<sub>drive</sub></i></td><td>Driving speed (km/hour)</td></tr><tr><td><i>d<sub>i</sub></i></td><td>The distance between building <i>i</i> and the nearest ADP</td></tr><tr><td><i>E<sup> walk</sup><sub>1i</sub></i></td><td>Expected yearly cost for households of building <i>i</i> to retrieve missed parcels from ADPs by walking ($)</td></tr><tr><td><i>E<sup> drive</sup><sub>1i</sub></i></td><td>Expected yearly cost for households of building <i>i</i> to retrieve missed parcels from ADPs by driving ($)</td></tr><tr><td><i>E<sup> walk</sup><sub>1i</sub></i></td><td>The yearly value of OPLs in building <i>i</i> and is associated with collecting failed parcels by households ($)</td></tr><tr><td>λ<sub>i</sub>, λ ≥ 1</td><td>Hourly operating cost of a personal vehicle, accounting for the driver's time value ($)</td></tr><tr><td><i>e</i></td><td>Expected delay for households with failed parcels awaiting redelivery (hour).</td></tr><tr><td>γ<sup>+</sup><i>h</i></td><td>Hourly detrimental values of redelivering small parcels for households ($)</td></tr><tr><td>γ<sup>-</sup><i>h</i></td><td>Hourly detrimental values of redelivering large parcels for households, γ' < γ ($)</td></tr><tr><td><i>E<sup> walk</sup><sub>1i</sub></i></td><td>Total perceived value of OPLs for building <i>i</i>, <i>E<sup> walk</sup><sub>1i</sub></i> = <i>E<sup> walk</sup><sub>1i</sub></i> + <i>E<sup> walk</sup><sub>2i</sub></i> ($)</td></tr><tr><td>ρ<sub>1</sub></td><td>Delivery peak month factor, ρ<sub>1</sub> > 1</td></tr><tr><td>ρ<sub>2</sub></td><td>Delivery peak day factor, ρ<sub>2</sub> > 1</td></tr><tr><td><i>N<sub>i</sub></i></td><td>Maximum expected number of daily deliveries to building <i>i</i></td></tr><tr><td>σ</td><td>A factor adjusting space requirements for large parcels in OPLs compared to small parcels</td></tr><tr><td><i>B</i></td><td>Number of small locker compartments in a locker bank</td></tr><tr><td><i>b<sub>i</sub></i></td><td>The required number of locker banks in building <i>i</i></td></tr><tr><td>ω</td><td>Fixed cost of a locker bank ($)</td></tr><tr><td>φ</td><td>Annual operational cost of a locker bank ($)</td></tr><tr><td><i>r</i></td><td>Interest rate</td></tr><tr><td><i>E<sup> c</sup><sub>i</sub></i></td><td>Expected costs of providing OPL facilities and services in building <i>i</i> ($)</td></tr><tr><td><i>NPM</i></td><td>Net profit margin for OPL provider, carriers, and host buildings</td></tr><tr><td><i>t</i></td><td>Time taken from delivery workers to fulfil a parcel delivery in buildings with OPLs (hour)</td></tr><tr><td><i>t'</i></td><td>Time taken from delivery workers to fulfil a parcel delivery in buildings without OPLs (hour)</td></tr><tr><td><i>g<sub>i</sub>(t)</i></td><td>PDF associated with the distribution of <i>t</i></td></tr><tr><td><i>g<sub>i</sub>(t')</i></td><td>PDF associated with the distribution of <i>t'</i></td></tr><tr><td><i>e</i></td><td>Time taken from delivery workers to load a failed parcel onto a delivery vehicle (hour)</td></tr><tr><td><i>E<sup> walk</sup><sub>1i</sub></i></td><td>OPLs' creating values in carriers' first-attempt parcel deliveries to building <i>i</i> ($)</td></tr></tbody></table>

<table><caption>**Table 2 (continued)**</caption><thead><tr><th>Type</th><th>Notation</th><th>Definition</th></tr></thead><tbody><tr><td><i>E<sup> walk</sup><sub>2i</sub></i></td><td>OPLs' creating values in carriers' second-attempt parcel deliveries to building <i>i</i> ($)</td><td></td></tr><tr><td><i>E<sup> walk</sup><sub>1i</sub></i></td><td>Total creating values of OPL services in building <i>i</i> for carriers, <i>E<sup> walk</sup><sub>1i</sub></i> = <i>E<sup> walk</sup><sub>1i</sub></i> + <i>E<sup> walk</sup><sub>2i</sub></i> ($)</td><td></td></tr><tr><td><i>E<sup> walk</sup><sub>1i</sub></i></td><td>The total perceived value of PLs for building <i>i</i> when <i>i</i> is also a host building</td><td></td></tr><tr><td><i>N<sub>i</sub></i></td><td>Maximum number of daily deliveries to building <i>i</i> and its partners (i.e., partnered buildings)</td><td></td></tr><tr><td><i>b<sub>i</sub></i></td><td>Required number of locker banks in building <i>i</i> when <i>i</i> is also a host building</td><td></td></tr><tr><td><i>E<sup> walk</sup><sub>1i</sub></i></td><td>Expected costs of providing OPL facilities and services in building <i>i</i> when <i>i</i> is also a host building ($)</td><td></td></tr></tbody></table>

parcels. Without loss of generality, assume that walking and driving distances to each ADP are equal, while travel speeds on these two modes are different, and represented by $s_{walk}$ and $s_{drive}$, respectively. Additionally, assume that walking falls within a range of acceptable distances for residents, thus incurring only time costs. The conversion of time to monetary value, using the hourly income ($h$), results in a generalised monetary cost (EC) associated with collecting missed parcels. Given that the closest ADP is situated $d_i$ kilometres away from building $i$, the expected annual monetary cost incurred by households of building $i$ by walking ($E<sup> walk</sup><sub>1i</sub>$) can be expressed using Equation (3).

$$E<sup> walk</sup><sub>1i</sub> = D_i \int_{0}^{\infty} (1 - \theta) \frac{2hd_i}{s_{walk}} \left( \sum_{m \in M_2} q_m \right) \xi \alpha h^{\beta} f_i(h) dh = (1 - \theta) \frac{2d_i}{s_{walk}} \xi \alpha D_i \sum_{m \in M_2} q_m \int_{0}^{\infty} h^{\beta+1} f_i(h) dh \quad (3)$$

In this equation, $\frac{2hd_i}{s_{walk}}$ represents the total cost borne by a household to collect a single parcel from the nearest ADP, where travel distance and time are calculated for a round trip. Similarly, the cost incurred by driving to ADPs is evaluated using Equation (4), which incorporates additional expenses associated with fuel and parking costs.

$$ \begin{aligned} E<sup> drive</sup><sub>1i</sub> &= D_i \int_{0}^{\infty} \theta \frac{2\lambda dh}{s_{drive}} \sum_{m \in M_2} q_m \xi \alpha h^{\beta} f_i(h) dh \\ &= (1 + \lambda) \theta \frac{2d_i}{s_{drive}} \xi \alpha D_i \sum_{m \in M_2} q_m \int_{0}^{\infty} h^{\beta+1} f_i(h) dh \end{aligned} \quad (4) $$

Here, $\lambda h, \lambda \ge 1$ denotes the hourly operating cost of a personal vehicle, accounting for the driver's time. The sum of $E<sup> walk</sup><sub>1i</sub>$ and $E<sup> drive</sup><sub>1i</sub>$ yields the total annual cost borne by all households in building $i$ to retrieve failed deliveries from ADPs. Since OPLs eliminate ADP collection trips, the value created by utilising OPLs, which can be quantified for building $i$ as $E<sup> walk</sup><sub>1i</sub>$, using Equation (5).

$$E<sup> walk</sup><sub>1i</sub> = E<sup> walk</sup><sub>1i</sub> + E<sup> drive</sup><sub>1i</sub> \quad (5)$$

Redelivery is also associated with delays in receiving parcels, causing inconvenience to customers. On average, each failed delivery imposes a delay of $\bar{e}$ hours on the receiving customer. Furthermore, the disutility associated with each hour of delay is positively correlated with the customer's hourly income (Hsu and Li, 2006). Furthermore, the disutility is assumed to be higher for light and small parcels compared to heavy and large parcels (Mohri et al., 2024c). As a result, the hourly (delay) cost of redelivery for small and large parcels are denoted by $\gamma'h$ and $\gamma''h$, respectively, where $\gamma'' < \gamma'$. With OPLs, these costs are eliminated, resulting in a secondary value creation for residents, which can be calculated using Equation (6). The total perceived value of OPLs for building $i$ is therefore equal to $E<sup> walk</sup><sub>1i</sub> + $E<sup> walk</sup><sub>2i</sub>$, as described in Equation (7).
<figure><img src="image_5.png" /><figcaption>Fig. 3. The basic SRM.</figcaption></figure>

$$ \mathbb{E}v_{2i} = D_i \int_0^\infty (\gamma'(1-\theta) + \gamma''\theta)h \sum_{m \in M_1} q_m \xi \alpha h^{\beta} f_i(h) dh = (\gamma'(1-\theta) + \gamma''\theta) \xi \alpha D_i \sum_{m \in M_1} q_m \int_0^\infty h^{\beta+1} f_i(h) dh \quad (6) $$

$$ \mathbb{E}v_i = \mathbb{E}v_{1i} + \mathbb{E}v_{2i} \quad (7) $$

**OPL costs for providers:** The provision of OPL services and facilities in a building involves both fixed (upfront) and operational costs for the provider. Fixed cost pertains to acquiring OPL systems from a manufacturer and installation costs. On the other hand, operational costs are associated with maintenance and customer services, which are correlated with the size of the OPL system. At the broadest level, these costs are determined by the number of locker banks. A locker bank comprises a set of locker compartments of varying sizes. Hence, accurate estimation of required size of locker banks for a building is essential. Given that building *i* receives $D_i \int_0^\infty \alpha h^{\beta} f_i(h) dh$ deliveries per year, the expected daily deliveries can be calculated as $\frac{D_i}{365} \int_0^\infty \alpha h^{\beta} f_i(h) dh$. The peak delivery factors $\rho_1$ and $\rho_2$, which represent the delivery peak month and peak day, respectively, are then multiplied by the expected daily demand. This allows the maximum expected number of daily deliveries ($N_i$) to building *i* to be estimated, which is determined by equation (8). The two types of parcels, namely, large and small, require different locker compartment sizes, with the former requiring $\sigma$ times more space than the latter. Moreover, each locker bank can accommodate a maximum of *B* small locker compartments. The required number of locker banks in building *i* ($b_i$) can then be determined by Equation (9). The OPL provider incurs a fixed cost of $\omega$ for each locker bank and an annual operational cost of $\varphi$. To calculate the yearly average cost for the company, we need to consider both the fixed costs and annual costs incurred over a period of *T* years, with an interest rate *r* applied. Accordingly, the present value of the total costs incurred by the OPL provider is calculated using Equation (10). Next, this present value cost is converted into a yearly annual cost for the company over a period of *T* years, as shown in Equation (11). Since OPLs are suitable options for developed countries with low interest rates, the first-order approximation for the term $(1+r)^{-T}$, which is $1-T\cdot r$, can be substituted into Equation (11). By simplifying Equation (11), the total annual cost of OPLs for the company can be approximated by Equation (12).

$$ N_i = \rho_1 \rho_2 \frac{D_i}{365} \int_0^\infty \alpha h^{\beta} f_i(h) dh \quad (8) $$

$$ b_i = \left[ \frac{(\sigma\theta + (1-\theta))N_i}{B} \right]^+ = \left[ \frac{(1-\theta)(\sigma-1))N_i}{B} \right]^+ \quad (9) $$

$$ \text{Present Value of } \mathbb{E}c_i = \left( \omega + \varphi \left( \frac{1 - (1 + r)^{-T}}{r} \right) \right) b_i \quad (10) $$

$$ \mathbb{E}c_i = \frac{\left( \omega + \varphi \left( \frac{1 - (1 + r)^{-T}}{r} \right) \right)}{T} b_i \quad (11) $$

$$ \mathbb{E}c_i = \left( \frac{\omega}{T} + \varphi \right) b_i \quad (12) $$

**The equilibrium point:** Naturally, the OPL provider aims to generate a NPM through the annual service fees charged to the building. Conversely, building *i* only enters a contract if the annual value of the OPL service ($\mathbb{E}v_i$) exceeds the annual fee ($\tau_i$). Thus, the OPL provider must determine the optimal contract duration ($T_0$) and annual fee ($\tau_i$) that would simultaneously satisfy its own NPM and the value perceived by building *i*. Accordingly, the following optimisation model should be solved by the OPL provider to determine the optimal values for contract duration and service fee.

$$ \text{Min } T_0 \quad (13) $$

Subject to:

$$ \text{NPM}(\tau_i) \le \tau_i - \mathbb{E}c_i \quad \tau_i \ge \frac{\mathbb{E}c_i}{1 - \text{NPM}} \quad \tau_i \ge \frac{\left(\frac{\omega}{T_0} + \varphi\right) b_i}{(1 - \text{NPM})} \quad (14) $$

$$ \tau_i \le \mathbb{E}v_i \quad (15) $$

**Lemma 1.** The optimal solution to the optimisation model is achieved by setting $\tau_i$ equal to $\mathbb{E}v_i$ and $T_0$ to $\frac{\omega b_i}{\mathbb{E}v_i(1 - \text{NPM}) - \varphi b_i}$. The detailed proof is presented in Appendix A1.

The parametric formulation and solution of the optimisation model enables the calculation of the sensitivity of the model's decisions to key parameters, such as the delivery failure rate ($\xi$). To conduct sensitivity analysis, we compute the derivatives of $\tau_i$ and $T_0$ with respect to $\xi$, as shown in Equations (16) and (17), respectively. Both derivations depend on the partial derivative of $\mathbb{E}v_i$ with respect to $\xi$, which is calculated by Equation (18).

$$ \frac{\partial \tau_i}{\partial \xi} = \frac{\partial \mathbb{E}v_i}{\partial \xi} \quad (16) $$

$$ \frac{\partial T_0}{\partial \xi} = \frac{\frac{\partial \mathbb{E}v_i}{\partial \xi} (1 - \text{NPM}) \omega b_i}{(\mathbb{E}v_i (1 - \text{NPM}) - \varphi b_i)^2} \quad (17) $$

$$ \frac{\partial \mathbb{E}v_i}{\partial \xi} = \int_0^\infty h^{\beta+1} f_i(h) dh \left[ \alpha D_i \sum_{m \in M_2} q_m \left( (1-\theta) \frac{2d_i}{s_{\text{walk}}} \right) + (1+\lambda)\theta \frac{2d_i}{s_{\text{drive}}} + \alpha D_i \sum_{m \in M_1} q_m (\gamma'(1-\theta) + \gamma''\theta) \right] \quad (18) $$

The results show that for $\tau_i$, since $\tau_i = \mathbb{E}v_i$, the service fee is directly proportional to $\mathbb{E}v_i$. As $\xi$ increases, $\mathbb{E}v_i$ increases, leading to an increase in $\tau_i$. This implies that the service fee will rise with a higher delivery failure rate because the perceived value of OPLs for the building increases, allowing the provider to set higher fees for its services. For $T_0$, $\frac{\partial T_0}{\partial \xi}$ is negative, which means an increase in the delivery failure rate leads to a reduction in the contract duration. This is consistent with the idea that a
higher failure rate is associated with higher service fees, resulting in shorter contracts and higher cost savings. This type of sensitivity analysis can be extended to other SRMs for different parameters, providing OPL providers with valuable insights into the impacts of key factors on their primary decisions.

### 3.3. Formulating SRM1

The first extension of the basic contract (SRM1) designates the OPL provider as the seller and both buildings and carriers as buyers. The cost of supplying OPL facilities and services and associated values for building $i$ ($E\nu_i$) remains equal to the basic SRM, formulated in sub-sections 3.1.1 and 3.1.2. To identify the contractual equilibrium point, it is necessary first to estimate the annual value generated by the OPLs for carriers ($E\nu'_i$). Once these values are known, the OPL provider can strategically determine the optimal annual service fees to be charged to building $i$ ($\tau_i$) and carriers ($\tau'_i$), as well as the contract duration ($T_1$). Fig. 4 demonstrates SRM1.

**Estimating the value for carriers:** OPLs offer major cost savings for carriers, which are deemed as 'value for carriers' and quantified in this subsection. The first value for carriers using OPL services is in the initial delivery attempt. The use of OPLs can be attributed to reduced delivery time as workers can load parcels directly into lockers, eliminating the need to hand over goods to customers. Direct handover involves sub-activities such as contacting customers, waiting time, and obtaining signatures. Shortened drop-off time in buildings allows carriers to fulfil deliveries more efficiently. The second value is linked to the redelivery of parcels when the first attempt fails, which is associated with additional loading and unloading of failed deliveries from vans to depots or ADPs and sorting tasks. Moreover, by using OPLs, carriers who arrange redelivery will no longer need to spend extra time at the entrance of buildings to hand out missed parcels to customers. This section quantifies the potential cost savings associated with first and second delivery attempts.

During the initial delivery, it takes delivery worker $t$ hours to fulfill each parcel when OPLs are in place, while this figure is denoted by $t'$ for buildings without OPLs. Both $t$ and $t'$ are considered as random variables, and their variations are defined by PDFs denoted as $g_i(t)$ and $g'_i(t')$, respectively. In buildings with OPLs, the failed delivery rate is zero; therefore, no parcels are returned to the delivery vehicle. In the absence of OPLs, loading failed parcels onto the delivery vehicles is expected to take a relatively short amount of time with low variation, which is denoted as $\bar{\epsilon}$. The cost savings for carriers resulting from the use of OPLs in building $i$ are estimated using Equation (19).

$$E\nu'_{1i} = \bar{h} \sum_{m \in M} q_m D_i \int_0^\infty \alpha h^\theta f_i(h) dh \left[ \int_0^\infty t' g'_i(t') dt' - \int_0^\infty t g_i(t) dt + \bar{\epsilon} \bar{\epsilon} \right] \quad (19)$$

In Equation (19), $\int_0^\infty t' g'_i(t') dt' + \bar{\epsilon} \bar{\epsilon}$ and $\int_0^\infty t g_i(t) dt$ represents the expected time taken to deliver a parcel without and with an OPL, respectively. The difference between these two times indicates the time saved per parcel. Multiplying this by the annual parcel deliveries to building $i$, $\sum_{m \in M} q_m D_i \int_0^\infty \alpha h^\theta f_i(h) dh$, we estimate the total annual service time saved by carriers. To convert the time saving to a monetary value, we use the hourly operating cost of delivery vehicles ($\bar{h}$). This leads to the annual cost associated with deliveries to building $i$ ($E\nu'_{1i}$).

To estimate the cost of failed deliveries and the potential savings, it is crucial to identify the key strategies carriers use for handling failed deliveries, such as redelivery attempts or requiring customers to collect their parcels from ADPs. For redelivery, carriers perform activities such as unloading failed deliveries from delivery vehicles, sorting at the depot and reloading onto the vehicle for the next delivery round. Additionally, carriers spend time at the entrance of the building ($i$) during the next delivery round, which involves contacting customers, handing over parcels and receiving signatures. For carriers, this translates to three loading/unloading activities, one sorting activity at the depot and a delivery service for each failed delivery. In this study, we assume the sorting cost at depots is equal to the cost of loading/unloading parcels to/from vehicles. Therefore, the additional cost for additional loading/unloading each failed delivery is equal to $4\bar{h} \bar{\epsilon}$. Furthermore, the service cost at the doorstep of building $i$ for handing out parcels to customers is denoted by $\bar{h} \int_0^\infty t' g'_i(t') dt'$. On the other hand, parcel collection from ADPs requires the carrier to unload parcels from delivery vehicles and sort them at a nearby ADP. Therefore, the only additional cost incurred by carriers is $2\bar{h} \bar{\epsilon}$. These costs are eliminated after placing OPLs in building $i$, hence, the perceived value for carriers is $E\nu'_{2i}$, which can be calculated using Equation (20).

$$E\nu'_{2i} = \bar{h} \bar{\epsilon} D_i \int_0^\infty \alpha h^\theta f_i(h) dh \left[ \sum_{m \in M_1} q_m \left( 4\bar{\epsilon} + \int_0^\infty t' g'_i(t') dt' \right) + \sum_{m \in M_2} q_m (2\bar{\epsilon}) \right] \quad (20)$$

Overall, the total value of OPL services in building $i$ for carriers is computed by (21).

$$E\nu'_{i} = E\nu'_{1i} + E\nu'_{2i} \quad (21)$$

**The equilibrium point:** The OPL provider and carrier are profit-seeking entities, requiring a reasonable NPM. Hence, the provider determines the appropriate annual service fees ($\tau_i$ and $\tau'_i$) for building $i$ and carrier. The OPL provider, as the seller of service, seeks to identify the optimal fees and minimum contract duration ($T_1$) that meet the expectations of all parties. Accordingly, the following optimisation model can assist the OPL provider in determining the optimal decision values for this revenue model.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Arrangement of SRM1.</figcaption></figure>
$$ \text{Min } T_1 \qquad (22) $$

Subject to: Constraint (15) and

$$ \text{NPM}(\tau_i + \tau'_i) \le \tau_i + \tau'_i - \mathbb{E}c_i \rightarrow \tau_i + \tau'_i \ge \frac{\mathbb{E}c_i}{1 - \text{NPM}} \qquad (23) $$

$$ \text{NPM}(\mathbb{E}v_i) \le \mathbb{E}v'_i - \tau'_i \rightarrow \tau'_i \le \mathbb{E}v'_i(1 - \text{NPM}) \qquad (24) $$

**Lemma 2.** The optimal solution of the model is as follows: Building i is charged an annual service fee of $\tau_i = \mathbb{E}v_i$, consequently, the carrier is charged an annual service fee of $\tau'_i = \mathbb{E}v'_i(1 - \text{NPM})$. The duration of the contract ($T_1$) is then set by $\frac{\omega b_i}{\mathbb{E}v_i(1-\text{NPM})+\mathbb{E}v'_i(1-\text{NPM})^2-\omega b_i}$. The detailed proof is presented in Appendix A1.

## 3.4. Formulating SRM2

SRM2 outlines a revenue model in which the OPL system is installed in building i, allowing for partnership with neighbouring buildings. The system's installation in the host building is indexed by i and access to the system by neighbouring residents forming partnered set indexed buildings by $J_i$ ($j \in J_i$). This proposed partnership scenario is inspired by sharing economy models for limited facilities in urban areas, such as parking spaces and storage spaces. Many cities around the world have already implemented shared facilities and amenities between neighbouring residential buildings, with examples including shared storage spaces and parking. Platforms such as Spacer (2025) and Neighbor (2025) illustrate the practicality of such shared-access systems. In this OPL partnerships, security can be ensured through architectural design and technology integration, for example, by embedding lockers into the building façade or window wall to enable controlled dual access, or by creating semi-public ground-floor zones separated from residential entrances.

The OPL provider sells the service to the host building, which may have capacity exceeding the building needs for sharing with neighbouring buildings. In exchange, the partnering buildings pay an annual fee ($\theta_j$) to the host building. For simplicity, we consider a neighbouring radius of 50 m from the host. Although the proximity of the partnered buildings to the host building may have a minor impact on the perceived value of the OPL services, the partnered buildings expect to pay less for the services in this situation. Therefore, it is assumed that each partnered building also expects to achieve the NPM. Fig. 5 presents an outline of SRM2.

The hosting building must also receive benefit from the partnership. Therefore, the total fees received from the neighbouring partnered buildings ($\sum_{j \in J_i} \theta_j$) should justify the host building's NPM. The costs of providing OPL services and facilities by the host building and the value of OPL service for both host and partnered buildings are formulated in the contract. Finally, the contract's decisions ($\tau_i, \theta_j, \forall j \in J_i$, and $T_2$) are optimised based on the equilibrium constraints.

**Value Measurement:** The annual value of the OPL service for households of the host building i is equal to $\mathbb{E}v_i$ calculated by (7). In addition to $\mathbb{E}v_i$, building i will take a fee from each partnered building $\theta_j, \forall j \in J_i$. Therefore, the total perceived value of OPL services for the host building i is equal to $\mathbb{E}v_{i,i=\text{host}}$ and is calculated by Equation (25).

$$ \mathbb{E}v_{i,i=\text{host}} = \mathbb{E}v_i + \sum_{j \in J_i} \theta_j \qquad (25) $$

OPL services for partnered building j is equal to $\mathbb{E}v_j$ calculated by Equation (7). However, in exchange for the use of the OPL system, each partnered building pays a fee ($\theta_j$) to the host. Therefore, $\theta_j$ is the cost of OPL services and facilities for partnered building j.

**Measuring the Cost of OPL Provision:** Equations (26)–(28) estimate the cost of providing OPL facilities to all households of the host and partnered buildings. Equation (26) defines $N_{i,i=\text{host}}$ as the maximum number of daily deliveries to building i and its partners. The OPL installed in building i support the daily deliveries of its own households and those of partnered buildings. Therefore, instead of using equation (8) to calculate $N_i$, $N_{i,i=\text{host}}$ is computed using Equation (26). In Equation (26), $\sum_{j \in J_i} N_j = \sum_{j \in J_i} \rho_1 \rho_2 \frac{D_i}{365} \int_0^\infty \alpha h^\theta f_j(h) dh$ represents the maximum number of daily deliveries to building i from all partnered buildings. The required number of locker banks in host building i ($b_{i,i=\text{host}}$) is then calculated using Equation (27). Finally, similar to Equation (12), Equation (28) uses $b_{i,i=\text{host}}$ to calculate the total annual cost of providing OPL system and services for the host building i ($\mathbb{E}c_{i,i=\text{host}}$).

$$ N_{i,i=\text{host}} = \rho_1 \rho_2 \frac{D_i}{365} \int_0^\infty \alpha h^\theta f_j(h) dh + \sum_{j \in J_i} N_j \qquad (26) $$

$$ b_{i,i=\text{host}} = \left[ \frac{(1 - \theta(\sigma - 1))N_{i,i=\text{host}}}{B} \right] \qquad (27) $$

$$ \mathbb{E}c_{i,i=\text{host}} = \left(\frac{\omega}{T} + \varphi\right) b_{i,i=\text{host}} \qquad (28) $$

**The equilibrium point:** The OPL provider is responsible for establishing the partnership, including all contract decisions. The OPL provider charges an annual service fee ($\tau_i$) to the host building (i), which includes the partnership details, such as fees and service duration. The host building in turn charges partnered buildings ($\theta_j, \forall j \in J_i$). Given the security and access concerns for the host building, it is assumed that the host would accept the contract only if the value created by the OPLs ($\mathbb{E}v_{i,i=\text{host}}$) exceeds their costs and generates the NPM. Accordingly, the partnered buildings also expect the NPM, agreeing to share their residents' information with the host and collect their parcels from the shared OPL. Therefore, the decisions that the OPL provider makes include the annual service fee for host building i ($\tau_i$), the fees advised to the host building to charge partnered buildings ($\theta_j$) and the duration of the contract ($T_2$). The decisions can be optimised by solving the following optimisation model.

<figure><img src="image_7.png" /><figcaption>Fig. 5. Arrangement of SRM2.</figcaption></figure>
$$ \text{Min } T_2 \qquad (29) $$

Subject to:

$$ \text{NPM}(\tau_i) \le \tau_i - \mathbb{E}_{c_{i,l=\text{host}}} \qquad (30) $$

$$ \text{NPM}(\mathbb{E}_{v_{i,l=\text{host}}}) \le \mathbb{E}_{v_{i,l=\text{host}}} - \tau_i \rightarrow \tau_i \le \mathbb{E}_{v_{i,l=\text{host}}}(1 - \text{NPM}) \rightarrow $$

$$ \tau_i \le \left( \mathbb{E}v_i + \sum_{j \in J_i} \theta_j \right) (1 - \text{NPM}) \qquad (31) $$

$$ \text{NPM}(\mathbb{E}v_j) \le \mathbb{E}v_j - \theta_j $$

$$ \theta_j \le \mathbb{E}v_j(1 - \text{NPM}) \qquad (32) $$

**Lemma 3.** The annual service fee for host building i is given by $\mathbb{E}v_i(1 - \text{NPM}) + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^2$, and the fee for partnered building j is $\mathbb{E}v_j(1 - \text{NPM})$. The minimum duration of the contract ($T_2$) is calculated as $\frac{\mathbb{E}v_i(1 - \text{NPM})^2 + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^3 - \varphi b_{i,l=\text{host}}}{\mathbb{E}v_i(1 - \text{NPM})^2 + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^3 - \varphi b_{i,l=\text{host}}^2}$. The detailed proof is presented in Appendix A1.

### 3.5. Formulating SRM3

In this SRM configuration, the OPL provider sells its services to carriers and host building i and charges an annual service fee $\tau_i$ and $\tau'_i$, respectively. Host building i installs an OPL system with the capacity to serve its residents and those of partnering buildings for a fee ($\theta_j$) to partnered buildings. SRM3 also considers a NPM for carriers and OPL provider. Hence, the OPL provider undertakes decisions related to the annual service fee of host building i ($\tau_i$) and carrier ($\tau'_i$), the fees charged by the host to partnered buildings ($\theta_j$), and finally, the duration of the contract ($T_3$). Consequently, the following optimisation model is formulated to assist the OPL provider in optimising these decisions.

$$ \text{Min } T_3 \qquad (33) $$

Subject to:

$$ \text{NPM}(\tau_i + \tau'_i) \le \tau_i + \tau'_i - \mathbb{E}_{c_{i,l=\text{host}}} \rightarrow \tau_i + \tau'_i \ge \frac{\mathbb{E}_{c_{i,l=\text{host}}}}{1 - \text{NPM}} \qquad (34) $$

$$ \text{NPM} \left( \mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j \right) \le \mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j - \tau'_i \rightarrow $$

$$ \tau'_i \le \left( \mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j \right) (1 - \text{NPM}) \qquad (35) $$

$$ \text{NPM}(\mathbb{E}_{v_{i,l=\text{host}}}) \le \mathbb{E}_{v_{i,l=\text{host}}} - \tau_i \rightarrow \tau_i \le \mathbb{E}_{v_{i,l=\text{host}}}(1 - \text{NPM}) \rightarrow $$

$$ \tau_i \le \left( \mathbb{E}v_i + \sum_{j \in J_i} \theta_j \right) (1 - \text{NPM}) \qquad (36) $$

$$ \text{NPM}(\mathbb{E}v_j) \le \mathbb{E}v_j - \theta_j \rightarrow \theta_j \le \mathbb{E}v_j(1 - \text{NPM}) \qquad (37) $$

**Lemma 4.** The maximum applicable $\theta_j$ is $\mathbb{E}v_j(1 - \text{NPM})$. $\tau_i$ is equal to $\mathbb{E}v_i(1 - \text{NPM}) + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^2$. $\tau'_i$ should be set to $\mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j(1 - \text{NPM})$ and finally $T_3$ equals to $\frac{\omega b_{i,l=\text{host}}}{\mathbb{E}v_i(1 - \text{NPM})^2 + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^3 + (\mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j)(1 - \text{NPM})^2 - \varphi b_{i,l=\text{host}}^2}$. The detailed proof is presented in Appendix A1.

### 3.6. Formulating SRM4 and SRM5

SRM4 and SRM5 are similar to SRM2 and SRM3, respectively, with the difference that OPL systems will be placed outside buildings. In these models, no fees will be exchanged between the partnered buildings. OPL facilities placed in public areas are indexed by $l$ and buildings ($\forall i$) in the proximity of OPL system $l$ form a set indexed $L_i$. The maximum distance between OPL $l$ and adjacent buildings is considered 50 m for problem simplicity. Fig. 6 demonstrates the arrangement of SRM4.

In SRM4 the OPL provider seeks an annual service fee from each building in the partnership, while for SRM5 a fee is also charged to the carrier. The decisions involved include the amount of service fees and contract duration. The value created from OPL installation for partnered buildings ($\mathbb{E}v_i$) is calculated by Equation (7) and for carriers the value is equal to $\sum_{i \in L_i} \mathbb{E}v'_i$, where $\mathbb{E}v'_i$ is calculated by (21). For the provider, the cost of providing OPL facility $l$ ($\mathbb{E}c_l$) is calculated based on (38-40). We calculate the maximum number of daily deliveries using Equation (28). Then $b_l$ and $\mathbb{E}c_l$ are estimated using Equations (39) and (40), respectively.

$$ N_l = \sum_{i \in L_l} N_i \qquad (38) $$

$$ b_l = \left[ \frac{(1 - \theta(\sigma - 1))N_l}{B} \right] \qquad (39) $$

$$ \mathbb{E}c_l = \left( \frac{\omega}{T} + \varphi \right) b_l \qquad (40) $$

**Equilibrium point for SRM4:** The following optimisation model optimises decisions in SRM4. The model's objective function minimises the contract duration ($T_4$), while the equilibrium constraints ensure an NPM for both the OPL provider and the partnered buildings. The NPM considered for the partnered buildings would compensate for the access difficulties associated with the shared OPL, compared to receiving it exclusively for each building.

<figure><img src="image_8.png" /><figcaption>Fig. 6. Arrangement of SRM4.</figcaption></figure>
$$ \text{Min } T_4 \qquad (41) $$

Subject to:

$$ \text{NPM}\left(\sum_{i \in L_i} \tau_i\right) \leq \sum_{i \in L_i} \tau_i - \mathbb{E}c_i \rightarrow \sum_{i \in L_i} \tau_i \geq \frac{\mathbb{E}c_i}{1 - \text{NPM}} \qquad (42) $$

$$ \text{NPM}(\mathbb{E}v_i) \leq \mathbb{E}v_i - \tau_i \rightarrow \tau_i \leq \mathbb{E}v_i(1 - \text{NPM}) \qquad (43) $$

**Lemma 5.** The optimal values of the decisions in the model are as follows: The annual service fee of OPL facilities and each partnered building is $\mathbb{E}v_i(1 - NPM)$. T₄ is equal to $\frac{\omega b_i}{\sum_{i \in L_i} (\mathbb{E}v_i(1-NPM)^2 - \varphi b_i)}$. The detailed proof is presented in Appendix A1.

**Equilibrium point for SRM5:** This model pertains to the sale of facilities and services by the OPL provider to both buildings and carriers. In this SRM, the OPL provider sets $\tau'_i$, $\tau_i \forall i \in L_i$, and T₆ (minimum contract duration). The following optimisation model assists the OPL provider in optimally setting the service fees and contract duration.

$$ \text{Min } T_5 \qquad (44) $$

Subject to:

$$ \text{NPM}\left(\sum_{i \in L_i} \tau_i + \tau'_i\right) \leq \sum_{i \in L_i} \tau_i + \tau'_i - \mathbb{E}c_i \qquad (45) $$

$$ \sum_{i \in L_i} \tau_i + \tau'_i \geq \frac{\mathbb{E}c_i}{1 - \text{NPM}} \qquad (45) $$

$$ \text{NPM}\left(\sum_{i \in L_i} \mathbb{E}v'_i\right) \leq \sum_{i \in L_i} \mathbb{E}v'_i - \tau'_i \qquad (46) $$

$$ \tau'_i \leq \sum_{i \in L_i} \mathbb{E}v'_i(1 - \text{NPM}) \qquad (46) $$

$$ \text{NPM}(\mathbb{E}v_i) \leq \mathbb{E}v_i - \tau_i $$

$$ \tau_i \leq \mathbb{E}v_i(1 - \text{NPM}) \qquad (47) $$

**Lemma 6.** $\tau_i$ and $\tau'_i$ are equal to $\mathbb{E}v_i(1-NPM)$ and $\sum_{i \in L_i} \mathbb{E}v'_i(1-NPM)$, respectively. T₅ is equal to $\frac{\omega b_i}{\sum_{i \in L_i} (\mathbb{E}v_i(1-NPM)^2 - \varphi b_i)}$. The detailed proof is presented in Appendix A1.

### 3.7. A summary of models’ equilibrium points

Table 3 summarises the equilibrium points of all SRMs.

As shown, in SRMs where carriers contribute to service fees (SRM1, SRM3, and SRM5), buildings incur lower service fees compared to corresponding SRMs without carrier contributions (SRM0, SRM2, and SRM4, respectively). This gap arises from the reduced contract duration (shorter return) when carriers are involved in the business model. For instance, Equation (48) indicates that T₁ is consistently less than or equal to T₀. Consequently, with carrier participation in the contract, buildings would pay $\tau_i(T_0 - T_1)$ less than the total costs imposed on them in the basic SRM.

$$ T_1 - T_0 = \frac{\omega b_i}{\mathbb{E}v_i(1 - \text{NPM}) + \mathbb{E}v'_i(1 - \text{NPM})^2 - \varphi b_i} - \frac{\omega b_i}{\mathbb{E}v_i(1 - \text{NPM}) - \varphi b_i} \leq 0 \rightarrow T_1 \leq T_0 \qquad (48) $$

While this finding may seem straightforward, a more thorough comparison is needed to determine the optimal strategy for stakeholders, whether it involves partnerships, carrier involvement, or government support. Further exploration, through the establishment of models based on case studies, is necessary. In the following section, a case study from Melbourne, Australia, is utilised for comparison, yielding insights that can be extrapolated to other settings.

### 4. Experimental setting

To evaluate the proposed SRMs, we develop a case study based on the City of Melbourne, Australia. According to the 2021 Australian Census data, there are 10,430 buildings (buildings, or community

<table><caption>**Table 3**
Contracts’ equilibrium points.</caption><thead><tr><th>Contract ID</th><th>Contract equilibrium</th></tr></thead><tbody><tr><td>The basic SRM</td><td>τ<sub>i</sub> = E<sub>v<sub>i</sub></sub> &lt; explanationend &gt;<br>T<sub>0</sub> = (ωb<sub>i</sub>)/(E<sub>v<sub>i</sub></sub>(1-NPM) - ϕb<sub>i</sub>) &lt; explanationstart &gt;</td></tr><tr><td>SRM1</td><td>τ<sub>i</sub> = E<sub>v<sub>i</sub></sub><br>τ'<sub>i</sub> = E<sub>v'<sub>i</sub></sub>(1-NPM)</td></tr><tr><td>SRM2</td><td>T<sub>1</sub> = (ωb<sub>i</sub>)/(E<sub>v<sub>i</sub></sub>(1-NPM) + E<sub>v'<sub>i</sub></sub>(1-NPM)<sup>2</sup> - ϕb<sub>i</sub>)<br>τ<sub>i</sub> = E<sub>v<sub>i</sub></sub>(1-NPM) + (Σ<sub>j∈L<sub>i</sub></sub> E<sub>v'<sub>j</sub></sub>(1-NPM)<sup>2</sup>)<br>θ<sub>j</sub> = E<sub>v'<sub>j</sub></sub>(1-NPM)</td></tr><tr><td>SRM3</td><td>T<sub>2</sub> = (ωb<sub>i=host</sub>)/(E<sub>v<sub>i</sub></sub>(1-NPM)<sup>2</sup> + (Σ<sub>j∈L<sub>i</sub></sub> E<sub>v'<sub>j</sub></sub>(1-NPM)<sup>3</sup>) - ϕb<sub>i=host</sub>)<br>τ<sub>i</sub> = E<sub>v<sub>i</sub></sub>(1-NPM) + (Σ<sub>j∈L<sub>i</sub></sub> E<sub>v'<sub>j</sub></sub>(1-NPM)<sup>2</sup>)<br>τ'<sub>i</sub> = (E<sub>v'<sub>i</sub></sub> + (Σ<sub>j∈L<sub>i</sub></sub> E<sub>v'<sub>j</sub></sub>)(1-NPM))<br>θ<sub>j</sub> = E<sub>v'<sub>j</sub></sub>(1-NPM)</td></tr><tr><td>SRM4</td><td>T<sub>3</sub> = (ωb<sub>i=host</sub>)/(E<sub>v<sub>i</sub></sub>(1-NPM)<sup>2</sup> + (Σ<sub>j∈L<sub>i</sub></sub> E<sub>v'<sub>j</sub></sub>(1-NPM)<sup>3</sup>) + (E<sub>v'<sub>i</sub></sub> + (Σ<sub>j∈L<sub>i</sub></sub> E<sub>v'<sub>j</sub></sub>)(1-NPM)<sup>2</sup>) - ϕb<sub>i=host</sub>)</td></tr><tr><td>SRM5</td><td>τ<sub>i</sub> = E<sub>v<sub>i</sub></sub>(1-NPM)<br>T<sub>4</sub> = (ωb<sub>i</sub>)/(Σ<sub>i∈L<sub>i</sub></sub> E<sub>v<sub>i</sub></sub>(1-NPM)<sup>2</sup> - ϕb<sub>i</sub>)<br>τ<sub>i</sub> = E<sub>v<sub>i</sub></sub>(1-NPM)<br>τ'<sub>i</sub> = (Σ<sub>i∈L<sub>i</sub></sub> E<sub>v'<sub>i</sub></sub>(1-NPM))<br>T<sub>5</sub> = (Σ<sub>i∈L<sub>i</sub></sub> (E<sub>v<sub>i</sub></sub> + E<sub>v'<sub>i</sub></sub>)(1-NPM)<sup>2</sup> - ϕb<sub>i</sub>)</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>Fig. 7. Buildings in the city of Melbourne with more than 10 units.</figcaption></figure>

complex's) in the City of Melbourne, with the largest dwelling accom-
modating 1099 residency units. There are approved plans for an addi-
tional 1258 properties to be constructed in the near future. For the
purpose of our study, we focus on both existing and planned buildings
with more than 10 units. This results in 1499 buildings that comprise
217,723 units that represent 94.5 % of the total number of units in the
City of Melbourne. Fig. 7 provides an overview of the location and scale
of the selected buildings for our case study.

To accurately calibrate the formulation of revenue models, several
parameters are utilised, which are summarised in Table 4, along with
their sources.

To calibrate the parameters, we consider a series of assumptions.
First, we assume all buildings have full occupancy, where Dᵢ represents
the number of units in building i. Based on a survey conducted among
apartment households in Australia (Mohri et al., 2024d, 2025b), par-
ticipants disclosed their income levels and estimated yearly deliveries.
These parameters are then calibrated. Appendix A2 illustrates the cor-
relation between income and the number of deliveries, along with the
corresponding best-fitted function. Data from the Australian Census

conducted in 2021 (Australian Bureau of Statistics, 2021) provides the
distribution of weekly income for households in Melbourne. Assuming a
weekly rate of 38 working hours, the expected hourly income for
households is calculated, along with the probability of associated in-
come bracket. Figure A2 depicts these probabilities, thus modelling fᵢ(h)
using a discrete distribution function with 16 levels representing
different income brackets. In Australia, the predominant carrier,
Australia Post, holds a market share of over 65 %, often leaving unde-
livered parcels in designated post offices or public facilities. Other car-
riers, paying an access fee to Australia Post, utilise these facilities or
operate their own ADPs. According to the study of Mohri et al. (2024c),
more than 95 % of failed deliveries are left for customers to collect later,
implying that redelivery is not considered in the case study. According
to AliExpress (2024), the total fixed costs range from AU$8000 to AU
$12000, in addition to the international shipping expenses and instal-
lation costs for OPLs in buildings. Based on consultation with existing
OPL companies in Australia, these costs are estimated to fall within the
range of AU$2000 to AU$6000. Therefore, an expected fixed cost of AU
$14000 is adopted, with annual locker maintenance costs set at 10 % of
<table><caption>**Table 4**
Parameters setting.</caption><thead><tr><th>Parameter</th><th>Definition</th><th>Value</th></tr></thead><tbody><tr><td>D<sub>l</sub></td><td>Number of households in building i</td><td>Full occupancy<br/>α = 0.398 : β = 1.00</td></tr><tr><td>α &amp; β<sub>s</sub><br/>used in n =<br/>ah<sup>β</sup></td><td>Coefficients for relating income to<br/>number of deliveries</td><td>Figure A1 in Appendix A2;<br/>R<sup>2</sup> = 0.714</td></tr><tr><td>f<sub>i</sub>(h)</td><td>PDF of hourly income in building i</td><td>Figure A2 in Appendix A2</td></tr><tr><td>ε<sub>i</sub></td><td>Failed delivery rate</td><td>50.1 % (Mohri et al.,<br/>2024c)</td></tr><tr><td>M<sub>1</sub> &amp; M<sub>2</sub></td><td>Percentages of carriers using ADPs<br/>for failed parcels (M<sub>1</sub>) or offering<br/>redelivery (M<sub>2</sub>)</td><td>M<sub>1</sub> = 100; M<sub>2</sub> = 0</td></tr><tr><td>θ</td><td>Percentage of heavy parcels</td><td>21 % (Mohri et al., 2024c)</td></tr><tr><td>s<sub>walk</sub> &amp; s<sub>drive</sub></td><td>Walking and driving speeds,<br/>respectively</td><td>s<sub>walk</sub> = 5.1 km/h<br/>s<sub>drive</sub> = 33 km/h</td></tr><tr><td>d<sub>l</sub></td><td>Expected distance between<br/>customers and ADPs</td><td>900 m</td></tr><tr><td>λ</td><td>A coefficient for adjusting hourly<br/>operating costs of personal vehicles</td><td>1.3</td></tr><tr><td>ρ<sub>1</sub> &amp; ρ<sub>2</sub></td><td>Coefficient for adjusting maximum<br/>daily delivery to buildings</td><td>ρ<sub>1</sub> = 1.27; ρ<sub>2</sub> = 1.31 (Mohri et al., 2024c)</td></tr><tr><td>B</td><td>Number of small locker<br/>compartments in a locker bank</td><td>30 (Mohri et al., 2024c)</td></tr><tr><td>σ</td><td>Coefficient showing much larger<br/>are large locker compartments than<br/>small ones</td><td>2.5 (Mohri et al., 2024c)</td></tr><tr><td>ω &amp; φ</td><td>Fixed costs and annual costs of<br/>lockers, respectively</td><td>ω = AU$14000;<br/>φ = AU$1400</td></tr><tr><td>E(g<sub>i</sub>(t))</td><td>Expected delivery time for parcels<br/>to buildings with lockers</td><td>36 s (Mohri et al., 2024c)</td></tr><tr><td>E(g<sub>i</sub>(t'))</td><td>Expected delivery time for parcels<br/>to buildings without lockers</td><td>67 s (Mohri et al., 2024c)</td></tr><tr><td>h'</td><td>Hourly operating costs of delivery<br/>vehicles</td><td>80 AU$/hour (Mohri et al.,<br/>2024c)</td></tr><tr><td>ε̄</td><td>Parcel loading time onto vans</td><td>9.65 s (Mohri et al., 2024c)</td></tr></tbody></table>

the fixed costs, estimated at AU$1400. Finally, Mohri et al. (2024c) estimated the delivery times to buildings with and without OPLs. They revealed that a Lognormal distribution best fits the data, with an expected delivery time of 36 s for buildings with OPLs and 67 s for those without such facilities.

## 5. Results and discussion

This section is organised into three distinct subsections. Subsection 5.1 compares the basic SRM with SRM1, while Subsections 5.2 and 5.3 compare revenue models with and without partnership strategies, with

the former focusing on models without carriers' involvement and the latter describing models with carriers.

### 5.1. The basic SRM versus SRM1

In this section, we compare the basic SRM with SRM1, which includes a service fee for carriers in addition to the building charges. Fig. 8 (a) displays the variation in fees across different buildings, exhibiting a linear relationship with higher number of units. The slope of this trend is calculated as AU$ 46.19, indicating a positive value for each household as the result of OPL installation. Fig. 8(b) shows the expected service fees for carriers based on different building sizes under SRM1. As shown, a service fee of AU$14.48 is estimated for each building unit (i.e., household). Hence, approximately 31 % of OPL costs can be covered by carriers.

Although the annual service fee paid by the buildings are identical in both models, there are differences in contract durations. Fig. 9 illustrates the contract duration in the basic SRM for various building sizes. It highlights that the basic SRM may not be suitable for buildings smaller than 100 units due to excessively long contract durations. Conversely, buildings larger than 200 units benefit from the basic SRM, as they can receive OPL services and facilities with a contract of 3 years or shorter. Results show that each OPL can accommodate daily deliveries of 370 units. Therefore, if the number of units in a building is between two multiplicands of 370, excess OPL capacity can be observed. Therefore, buildings with unit numbers that are not multiples of 370 will have excess capacity in their lockers. This could potentially increase their service fees, prompting them to find ways to reduce the excess fees paid for idle capacity.

In Fig. 10, we compare the contract durations in both revenue models for small and large buildings. As shown, SRM1 displays a shorter contract duration, meaning that a lower cost will be incurred to buildings. However, the pattern of contract duration reduction is not uniform across all buildings. The primary observation is that SRM1 presents better duration for small buildings (i.e., less than 200 units). Larger buildings, predominantly, will have the economies of scale to fully embrace the cost of OPLs. Accordingly, negotiating with large buildings is much easier for the OPL provider than negotiating with small buildings, which have less attractive contract fees and durations. From the perspective of carrier, the average service time per parcel is higher in smaller buildings, as the time required for parking and entering the building is relatively same for different building sizes. One can argue smaller buildings don't have dedicated carrier parking and parcel handling bays, hence, leading to longer service time. Additionally, small buildings are more common in urban areas, as seen in our case study.

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Comparison of service fees charged to buildings and carriers in the basic SRM and SRM1.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 9. Contract durations for buildings based on the basic SRM.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 10. Comparison of contract duration for buildings in basic SRM and SRM1.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 11. Total cost savings for buildings resulting from substituting SRM1 with the basic SRM.</figcaption></figure>

$$ \Delta C_i = \begin{cases} 1.635 \times 10^5 D_i^{-0.576} & R^2 = 0.928 \quad 85 < D_i \le 370 \\ 1.201 \times 10^5 D_i^{-0.353} & R^2 = 0.989 \quad 370 < D_i \le 740 \\ 1.384 \times 10^5 D_i^{-0.293} & R^2 = 0.995 \quad 740 < D_i \le 1110 \end{cases} \quad (49) $$

Therefore, on an aggregate scale, carriers can significantly reduce their service costs. Therefore, it is recommended that OPL companies negotiate with carriers to receive financial support specifically for small buildings.

We further demonstrate the total cost saving ($\Delta C_i$) for buildings with 80–370 units, 370–740 units, and 740–1110 units in Fig. 11. The costing formulation is the shown in Equation (49).

As shown, for buildings with 85–185 units, the cost of OPL per unit is significantly lower in SRM1. While SRM1 remains attractive for buildings with more than 185 units, as building size increases, cost savings per unit diminishes. This observation again highlights the importance of involving carriers in OPL revenue models for small buildings. Furthermore, it can be seen that both basic SRM and SRM1 are not financially feasible for buildings with less than 85 units as the contract duration could exceed 10 years. Therefore, while SRM1 can create an attractive opportunity for providing OPL facilities and services in buildings with 85–120 units, which was not possible with the basic SRM, it still cannot attract buildings with fewer than 85 units.

## 5.2. Comparing the basic SRM versus SRM2 and SRM4

To compare the basic SRM with SRM2 and SRM4, we identify potential neighbourhood zones for testing partnership scenarios. To identify buildings in proximity, a 50-m radius is considered. Subsequently,
<figure><img src="image_14.png" /><figcaption>Fig. 12. Buildings and clusters for partnership scenarios in the city of Melbourne.</figcaption></figure>

<table><caption>**Table 5**
Details of the potential partnership scenarios in the city of Melbourne.</caption><thead><tr><th>Cluster ID</th><th>Total dwellings</th><th># OPLs</th><th># Partners</th><th># dwelling in host building</th><th># dwelling in joint buildings</th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>1</td><td>2207</td><td>6</td><td>4</td><td>700</td><td>282</td><td>584</td><td>641</td><td></td><td></td></tr><tr><td>2</td><td>1831</td><td>5</td><td>3</td><td>659</td><td>586</td><td>586</td><td></td><td></td><td></td></tr><tr><td>3</td><td>2207</td><td>6</td><td>4</td><td>700</td><td>282</td><td>584</td><td>641</td><td></td><td></td></tr><tr><td>4</td><td>1925</td><td>6</td><td>3</td><td>700</td><td>584</td><td>641</td><td></td><td></td><td></td></tr><tr><td>5</td><td>652</td><td>3</td><td>2</td><td>371</td><td>281</td><td></td><td></td><td></td><td></td></tr><tr><td>6</td><td>1455</td><td>4</td><td>4</td><td>505</td><td>263</td><td>312</td><td>375</td><td></td><td></td></tr><tr><td>7</td><td>1079</td><td>3</td><td>4</td><td>401</td><td>156</td><td>156</td><td>366</td><td></td><td></td></tr><tr><td>8</td><td>2207</td><td>6</td><td>4</td><td>700</td><td>282</td><td>584</td><td>641</td><td></td><td></td></tr><tr><td>9</td><td>734</td><td>2</td><td>7</td><td>260</td><td>32</td><td>32</td><td>68</td><td>111</td><td>111</td><td>120</td></tr><tr><td>10</td><td>365</td><td>1</td><td>3</td><td>206</td><td>10</td><td>149</td><td></td><td></td><td></td><td></td></tr><tr><td>11</td><td>348</td><td>1</td><td>3</td><td>193</td><td>45</td><td>110</td><td></td><td></td><td></td><td></td></tr><tr><td>12</td><td>2213</td><td>6</td><td>5</td><td>734</td><td>15</td><td>189</td><td>541</td><td>734</td><td></td><td></td></tr><tr><td>13</td><td>544</td><td>3</td><td>5</td><td>182</td><td>16</td><td>18</td><td>164</td><td>164</td><td></td><td></td></tr><tr><td>14</td><td>352</td><td>1</td><td>4</td><td>157</td><td>21</td><td>47</td><td>127</td><td></td><td></td><td></td></tr><tr><td>15</td><td>554</td><td>3</td><td>5</td><td>152</td><td>27</td><td>89</td><td>134</td><td>152</td><td></td><td></td></tr><tr><td>16</td><td>505</td><td>1</td><td>8</td><td>150</td><td>10</td><td>10</td><td>11</td><td>15</td><td>15</td><td>147</td><td>147</td></tr><tr><td>17</td><td>1841</td><td>5</td><td>7</td><td>369</td><td>85</td><td>254</td><td>254</td><td>255</td><td>255</td><td>369</td></tr><tr><td>18</td><td>920</td><td>5</td><td>4</td><td>805</td><td>23</td><td>41</td><td>51</td><td></td><td></td><td></td></tr><tr><td>19</td><td>167</td><td>1</td><td>4</td><td>60</td><td>15</td><td>46</td><td>46</td><td></td><td></td><td></td></tr><tr><td>20</td><td>361</td><td>1</td><td>5</td><td>132</td><td>26</td><td>26</td><td>45</td><td>132</td><td></td><td></td></tr><tr><td>21</td><td>715</td><td>2</td><td>5</td><td>436</td><td>16</td><td>34</td><td>52</td><td>177</td><td></td><td></td></tr><tr><td>22</td><td>1343</td><td>4</td><td>3</td><td>610</td><td>123</td><td>610</td><td></td><td></td><td></td><td></td></tr></tbody></table>

using a spatial join function in ArcGIS, buildings intersecting each other are identified, resulting in 22 clusters. Fig. 12 illustrates buildings and clusters, with more details provided in Table 5.

First, we compare the basic SRM with SRM2, where a building is chosen as the host, offering OPL facilities to nearby buildings. For each partnership scenario, we calculate the optimal service fee for the host and partnered buildings, the contract duration, and the total costs for the buildings over contract duration. Table A1 in Appendix A4 displays the raw outputs. It is worth noting that the annual service fee for the host building in SRM2 is computed by subtracting the fees paid by the partnered building to the host from the total service fee paid to the OPL provider. As shown in Table A1, both SRM2 and SRM4 benefit small buildings by reducing both service fee and contract duration. For instance, for a host building with 60 units, the contract duration decreases from 16.2 years in the basic SRM to 6.5 years in SRM2 and 4.7 years in SRM4. However, to make an accurate comparison, the total costs imposed on building over the contract duration in the basic SRM,

SRM2, and SRM4 are compared. Using the basic SRM as the reference revenue model, the cost savings achieved by switching to SRM2 and SRM4 are illustrated in Fig. 13.

As shown in Fig. 13, the total cost savings for host buildings vary notably with building size. For SRM2, the average cost savings are highest for small buildings (fewer than 300 units), averaging around 60–70 %, reflecting the strong impact of carrier contributions in smaller partnerships. For medium-sized buildings (300–600 units), the savings moderate to about 30–40 %, while for large buildings (over 600 units) the average benefit declines further, stabilising around 10–15 %. In contrast, SRM4 performs less consistently: while moderate savings are achieved for smaller buildings, cost savings diminish sharply with building size, and for large buildings (above roughly 600 units) the results even turn negative, indicating that SRM4 can become more expensive than the basic SRM in such cases.

The results suggest that partnership benefits for the host buildings are size-dependent: SRM2 is most effective for small to medium host
<figure><img src="image_15.png" /><figcaption>Fig. 13. Total cost savings for host buildings by switching from basic SRM to SRM2 or SRM4.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 14. Total cost savings for partnered buildings by switching from basic SRM to SRM2 or SRM4.</figcaption></figure>

buildings, whereas SRM4 may not be viable for larger buildings due to unbalanced cost sharing. Therefore, OPL providers should tailor partnership strategies to building size and evaluate both cost and partnership feasibility before implementation.

Next, we compare the service fee, contract duration, and total costs incurred for partnered buildings in the basic SRM, SRM2, and SRM4. Table A2 in Appendix A4 shows the raw outputs. The table indicates that SRM2 and SRM4 make OPL provision for small buildings with less than 40 units financially viable. While the basic SRM and SRM1 were practically infeasible for these buildings, resulting in very long contract durations, SRM2 and SRM4 reduce the duration to a range of 1.2–6.5 years.

To better illustrate and compare the revenue models for partnered buildings, Fig. 14 shows the total costs saving incurred for partnered buildings over the contract duration by switching from the basic SRM to SRM2 or SRM4. The total cost, calculated as the product of the service fee and contract duration, serves as a measure for this comparison.

As shown in Fig. 14, SRM2 and SRM4 both perform well for small partnered buildings (fewer than 200 units), achieving average cost savings of around 60–80 %. However, their performance diverges as

building size increases. For SRM2, savings decline sharply with size and become negative for larger buildings (above 400–500 units), indicating that this model may increase costs relative to the basic SRM in larger buildings. In contrast, SRM4 maintains positive savings even for medium and large buildings, though the magnitude of savings gradually decreases with size. The results suggest that SRM2 is more suitable for small partnered buildings, while SRM4 offers a more stable and scalable option across a wider range of building sizes. Therefore, for partnerships involving small buildings, government land provision is not essential, as SRM2 can effectively support these arrangements. However, for partnerships that include medium or large partnered buildings, SRM4 becomes more attractive, as the involvement of local governments in providing public land for shared OPLs significantly enhances cost-effectiveness and feasibility.

Most interesting, Figs. 13 and 14 reveal contrasting outcomes. The results show that SRM2 generally leads to lower costs for host buildings across most size ranges, while SRM4 becomes cost-effective only for partnered buildings with fewer than 250 units. Therefore, SRM2 appears more attractive for host buildings, whereas SRM4 provides greater benefits for smaller partnered buildings. If the OPL provider can identify
partnership configurations where a subset of small buildings jointly share an OPL facility, the host building in such partnerships would experience a higher perceived value.

Since partnered buildings typically outnumber host buildings, and SRM4 is relatively more attractive to them, encouraging their participation remains challenging. Although SRM4 enables these smaller buildings to access OPL services cost-effectively—unlike in the Basic SRM, where exclusive adoption is not viable—it is generally more advantageous for them to participate in partnerships involving OPLs on public land. Hence, local government facilitation in allocating public spaces for OPLs can make SRM4 a more practical and high-priority option for OPL providers, particularly in areas where buildings are reluctant to act as hosts or partners. Nevertheless, even without government support, forming partnerships remains more cost-effective for buildings than hosting exclusive OPL facilities.

### 5.3. SRM1 versus SRM3 and SRM5

As outlined in Subsection 3.6, the inclusion of carriers in revenue models brings along benefits for the OPL host regardless of partnership with neighbouring buildings. However, it is crucial to examine the costs incurred to buildings in revenue models with and without partnerships. In this section, we compare SRM1, SRM3, and SRM5. As summarised in Table 1, these SRMs assume the involvement of carriers as service buyer, with their difference being in the partnership configuration. Specifically, SRM1 does not consider partnership, while SRM3 involves neighbouring buildings and SRM5 includes the local government. These configurations lead to varying cost and contract duration values.

In Figs. 15 and 16, the total costs incurred to buildings in SRM1, SRM3, and SRM5 for host and partnered buildings are presented, respectively. Fig. 15 indicates that in most cases, SRM3 leads to lower fees for the host buildings, followed by SRM5 and SRM1. The only exception is observed for buildings larger than 800 units, in which SRM1 outperforms other models. Such an observation can be justified because once the number of units surpasses a certain number, partnerships may lead to higher coordination costs. Alternatively, a building may prefer to use the OPL facility exclusively for its own residents and not engage in any partnership scenarios. Therefore, it is important for OPL providers to design partnerships that exclude large buildings from joint arrangements. Interestingly, a host building can also generate profit by utilising SRM3. One example is the building with 369 units shown in Fig. 15. In other words, the access charges imposed for the use of OPL to external partners (i.e., partner buildings and carrier), and the benefits for residents surpass the OPL costs.

For partnered buildings, as shown in Fig. 16, SRM5 generally results in lower fees across most building sizes, followed by SRM3 and SRM1. However, in two cases (buildings with 281 and 610 units), SRM1 yields lower fees for partnered buildings. These buildings belong to clusters 5 and 22 in Table 5, which include only two and three buildings in the partnership, respectively. This indicates that partnership scenarios with very few participating buildings may lead to less balanced cost-sharing outcomes. While partnership scenarios generally make OPL contracts more attractive for buildings, the results indicate that they are not universally beneficial. In some cases, especially when only a few buildings participate, cost-sharing may not deliver the expected advantages. Therefore, OPL providers should carefully assess the suitability of each partnership configuration and compare it with non-partnership options before implementation.

## 6. Conclusion

This study presents enhancements to the basic SRM model tailored specifically for OPL providers and a single building. An extensive assessment of the value proposition and advanced extensions to traditional revenue management models is presented. We further evaluated the performance and operational implications of these SRM extensions for potential beneficiaries, including host buildings, carriers, and partnered buildings, using an extensive case study. In contrast to the conventional dyadic revenue model, which only considers a simplified payer-payee approach, the SRM extensions proposed in this work provide pathways for modern and sustainable partnerships among all beneficiaries. This research serves as a stepping stone towards a new knowledge base in the field of alternative delivery points, particularly related to improving the efficiency of last-mile delivery operations. Specifically, we aim to unpack future research on modelling and optimisation of complex, yet practical, multi-stakeholder city logistics.

Our work also touches on a new interface of transport and city logistics research with real state economics. Due to increased urban logistics activity, optimal utilisation of both residential and commercial properties is becoming a central decision-making parameter for carriers and other stakeholders. Operationally, efficient access to OPLs and other shared logistics facilities such as micro-hubs and loading docks could have major performance implications for carriers, retailers and their customers. Importantly, due to high capital expenses and limited availability, such facilities are often being used by competing and completing operators (Mohri et al., 2024e). Hence, developing appropriate access undertakings is a promising avenue for future research, enduring their maximum use and operational efficiency. From a

<figure><img src="image_17.png" /><figcaption>Fig. 15. Comparing total costs over contract duration for host buildings.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. 16. Comparing total costs over contract duration for partnered buildings.</figcaption></figure>

strategic perspective, major national carriers and e-commerce platforms have an interest in designing and developing modern urban logistics facilities to streamline the growing e-commerce delivery demand. Such investment decisions must be supported with robust technoeconomic assessment, further encouraging research in the interface of city logistics, property management and real estate economics.

## 6.1. Implementation outcomes

By testing revenue models and comparing the results, several findings emerged. Firstly, this study found that the basic SRM may not be suitable for buildings with fewer than 200 units due to excessively long contract durations. Hence, the likelihood of accepting OPL facilities and services for buildings with fewer than 200 units based on the basic SRM is low. Conversely, buildings with over 200 units can benefit significantly even from the basic SRM, with payment contracts lasting three years or less. However, buildings with unit numbers not divisible by 370 (estimated capacity) may experience excess locker capacity, prompting consideration of sharing this excess capacity with neighbouring buildings. If host buildings provide OPLs for neighbouring buildings, their total costs are reduced compared to the basic SRM. Thus, participating as a host in a partnership scenario is more advantageous, particularly for small buildings. However, from the perspective of partnered buildings, especially large ones, this partnership may incur slightly higher costs than solely receiving OPLs. Nevertheless, hosts could lower fees and still yield greater benefits. Consequently, a lower profit margin for partnered buildings is anticipated in this partnership scenario.

Additionally, if local governments provide public places for placing OPLs, another partnership scenario emerges where a group of buildings utilise OPL services without exchanging fees. Results suggest that this partnership would either lower or maintain costs for all buildings compared to the basic SRM, with marginal benefits for large buildings. Hence, this partnership should primarily involve a group of small buildings.

Once carriers agree to pay a service fee, buildings benefit whether they exclusively provide OPLs or participate in a partnership. Even without any partnership, costs incurred for buildings are substantially reduced, particularly for smaller buildings with 85-185 units, where receiving OPLs exclusively becomes cost-effective. The results also show that the benefits of carrier participation are not uniform across all building sizes. SRM2 yields the highest cost savings for small buildings (fewer than 300 units) but becomes less effective as building size increases, while SRM4 remains advantageous for larger partnerships when public land provision is available. By including a service fee for carriers

in revenue models, buildings, regardless of size, prefer to receive OPL services and facilities as hosts. If unable to act as hosts, the next cost-effective alternative is for buildings to join shared public OPLs rather than exclusively providing them for their own use. However, from the perspective of a partnered building, partnering with a host building is not cost-effective, leading them to opt for shared public OPLs. If shared public OPLs are unavailable, then it is preferable for buildings to receive OPL services and facilities through a partnership agreement rather than exclusively for their own use.

While scenarios with free public land naturally yield the most cost-effective outcomes, incorporating land leasing costs into the analysis slightly changes the results. As shown in Appendix A3, adding an average annual land cost of around AU$500 per locker bank increases total building costs by roughly 5%, yet all contracts remain feasible and profitable. These findings highlight that although government support significantly enhances affordability, the overall conclusions remain valid even when nominal land costs are considered. Furthermore, the sensitivity analyses confirm that the qualitative conclusions hold even when profit margins vary across stakeholders, reinforcing the robustness of the models under different financial conditions. Additionally, since this partnership is suitable for buildings of various sizes, multiple potential neighbourhoods can be identified, as demonstrated in a case study in the city of Melbourne, significantly reducing delivery points for carriers and consequently cutting their costs beyond what is measured in the explored revenue models. Thus, local government permission to place OPLs in public spaces would increase the likelihood of receiving carrier support. Moreover, these findings highlight the feasibility of launching a government scheme to provide OPLs for compact neighbourhoods, potentially coupled with a policy to restrict home delivery in areas covered by shared public OPLs.

## 6.2. Managerial implications

This study provides several practical insights for OPL providers, carriers, and local governments involved in advancing shared locker systems and city logistics initiatives.

For OPL providers, the results underscore the importance of tailoring partnership models to building characteristics and local conditions. The analysis shows that SRM2 is most beneficial for smaller buildings, whereas SRM4 becomes more attractive for larger partnerships when public land is available. Providers should, therefore, apply data-driven evaluation tools to identify optimal partnership compositions and develop differentiated pricing structures that reflect building size, density, and neighbourhood configuration. Additionally, sharing a small
portion of surplus profits or reducing annual service fees can accelerate adoption among smaller buildings and improve customer retention under competitive conditions.

For carriers, the findings suggest that even modest service fee contributions can make OPL deployment substantially more viable for buildings, strengthening overall delivery efficiency. Carriers can leverage these partnerships to reduce vehicle travel distances and delivery failures, particularly in dense urban areas. By co-investing in shared OPL infrastructure, carriers not only reduce operational costs but also enhance service reliability and environmental performance, aligning with corporate sustainability goals.

For local governments, the research highlights their pivotal role in facilitating the scaling of OPL systems. When carriers are reluctant to pay service fees, governments can employ policy levers such as temporary financial incentives, allocation of public land for shared OPLs, or inclusion of OPLs in broader urban freight sustainability programs. The study's sensitivity analysis also shows that even moderate land leasing fees (e.g., AU$500 per locker annually) increase total costs by only about 5%, confirming that public support remains an efficient means of promoting equitable access to OPL infrastructure. Governments can further use planning regulations to encourage developers to integrate OPL spaces within new buildings, reducing long-term dependency on street-level infrastructure.

Finally, for the real estate and urban development sectors, this research reveals the emerging connection between property management and last-mile logistics. By integrating OPLs into residential and commercial buildings, developers can enhance property value, attract e-commerce-driven tenants, and contribute to broader sustainability objectives. Strategic alignment between logistics operators, property managers, and municipalities will be critical in achieving efficient, space-conscious urban delivery ecosystems.

## 6.3. Limitations and future research

This study comes with limitations that could be addressed in future research. First, the fixed-term revenue model used in this study assumes consistent service quality, which may not capture variations in performance across different contract structures. Furthermore, the fixed service fee structure is designed to ensure financial stability but does not account for fluctuations in demand or service performance. Future research could explore dynamic or demand-responsive pricing models, where service fees fluctuate based on factors such as delivery volume, service performance, or market conditions, offering greater flexibility and adaptability. Additionally, the assumption of homogeneous acceptance behaviour across buildings overlooks potential behavioural differences, which could be explored in future studies to better understand diverse stakeholder needs. The model also assumes equal NPMs for OPL companies, carriers, and buildings, which simplifies comparisons but may not reflect real-world variations in profitability. By adjusting these assumptions and incorporating more dynamic pricing models, new research avenues could emerge, offering more tailored contract structures and contributing to the wider adoption of OPLs in urban freight systems. Furthermore, future studies could consider incorporating the terms and conditions set by local governments for providing land into business models, examining how these factors influence the financial viability and scalability of OPL initiatives.

### CRediT authorship contribution statement

Seyed Sina Mohri: Writing – original draft, Validation, Methodology, Investigation, Conceptualization. Hadi Ghaderi: Writing – review & editing, Methodology, Conceptualization. Reza Zanjirani Farahani: Writing – review & editing, Conceptualization. Neema Nassir: Writing – review & editing, Conceptualization. Russell G. Thompson: Writing – review & editing, Supervision, Investigation, Conceptualization.

## Appendix A1

**Proof of lemma 1:** The OPL provider ensures that the NPM is met by determining the service fee $\tau_i$ through Constraint (14). This constraint ensures that the fee charged must cover both the operational costs and meet the required NPM. By simplifying the constraint, it is ensured that $\tau_i$ must always

be greater than or equal to $\frac{(\omega_0 + \varphi)b_i}{1-NPM}$. At the same time, Constraint (15) imposes an upper bound on the service fee to ensure it does not exceed the perceived value of the OPL service by the building, $\mathbb{E}v_i$, i.e., $\mathbb{E}v_i \ge \tau_i$.

Since the OPL provider is motivated by NPM to seek larger service fees, Constraint (14), while staying within Constraint (13), the fee is set at $\mathbb{E}v_i$, the highest possible fee that still satisfies Constraint (13). Therefore, we substitute $\tau_i = \mathbb{E}v_i$ into Constraint (14), which yields the formula for the minimum required contract duration. The contract duration must be long enough to ensure the service fee allows the provider to meet its NPM while respecting the perceived value constraint.

By substituting $\tau_i = \mathbb{E}v_i$ into Constraint (14) and solving for $T_0$, we obtain Constraint (A1), which represents the minimum contract duration required to achieve the NPM while ensuring the service fee is consistent with the perceived value. Therefore, since the model's objective function minimises $T_0$, the minimum $T_0$ that satisfies constraint (A1) is given by $\frac{\omega b_i}{\mathbb{E}v_i(1-NPM)-\varphi b_i}$.

$$ \mathbb{E}v_i \ge \frac{(\omega_0 + \varphi)b_i}{(1-NPM)} \quad \rightarrow \quad T_0 \ge \frac{\omega b_i}{\mathbb{E}v_i(1-NPM) - \varphi b_i} \quad (A1) $$

**Proof of lemma 2:** Objective function (22) helps the OPL provider to determine the minimum possible contract duration. To make the contract attractive to both carriers and the building, the OPL provider must accept annual service fees paid by both parties. For the building, Constraint (15) ensures that the annual service fee charged by the OPL provider does not exceed the building's perceived annual value of the OPLs. Therefore, the maximum reasonable $\tau_i$ that can be requested from building $i$ is $\mathbb{E}v_i$. For the carriers, Constraint (23) is formulated. This ensures that the annual expected value from using the service exceeds the fees charged while meeting the NPM. Simplifying this constraint, the maximum service fee ($\tau_i$) charged by OPL provider to carrier is $\mathbb{E}v_i(1-NPM)$.

Constraint (24) is then added to ensure the contract is profitable for the OPL provider considering the NPM. Based on this constraint, the OPL provider sets two distinct service fees: $\tau_i$ for the building and $\tau'_i$ for the carrier. Constraints (15) and (24) together establish the maximum values for $\tau_i$ and $\tau'_i$ as $\mathbb{E}v_i$ and $\mathbb{E}v_i(1-NPM)$, respectively. Substituting these values into Constraint (23), as shown in Constraint (A2), simplifies the model. This results in the contract duration ($T_1$) being greater than or equal to $\frac{\omega b_i}{\mathbb{E}v_i(1-NPM)+\mathbb{E}v_i(1-NPM)^2-\varphi b_i}$. Since the objective function minimises $T_1$, the optimal value for $T_1$ is its lower bound in Constraint (A2).
$$ \mathbb{E}v_i + \mathbb{E}v'_i(1 - \text{NPM}) \geq \frac{\mathbb{E}c_i}{1 - \text{NPM}} \rightarrow \mathbb{E}v_i + \mathbb{E}v'_i(1 - \text{NPM}) \geq \frac{\left(\frac{\omega}{T_1} + \varphi\right)b_i}{(1 - \text{NPM})} \rightarrow \tag{A2} $$

$$ T_1 \geq \frac{\omega b_i}{\mathbb{E}v_i(1 - \text{NPM}) + \mathbb{E}v'_i(1 - \text{NPV})^2 - \varphi b_i} $$

Proof of lemma 3: Similar to previous SRMs, Objective function (29) seeks to minimise the contract duration $T_2$, while ensuring the OPL provider meets the necessary NPM. To guarantee profitability, outlined by Constraint (30). Accordingly, Constraint (31) ensures that the service fee for host building $i$, $\tau_i$, must be less than or equal to the combined expected values of the building and its partnered buildings, adjusted by the NPM factor. More specifically, the service fee $\tau_i$ is capped at $(\mathbb{E}v_i + \sum_{j \in J_i} \theta_j)(1 - \text{NPM})$, where $\mathbb{E}v_i$ is the expected value of host building $i$ and $\theta_j$ represents the expected value for each partnered building $j$.

For each partnered building $j$, Constraint (32) ensures that the maximum service fee $\theta_j$ charged to each building is $\mathbb{E}v_j(1 - \text{NPM})$. This ensures that the fees for partnered buildings are also set at a level that meets the NPM requirement. By substituting the maximum values for $\theta_j$ into Constraint (32), the OPL provider can determine the maximum possible service fee for the host building $i$. The result of this substitution, as shown in Constraint (A3), indicates that the maximum service fee for host building $i$ is the sum of $v_i(1 - \text{NPM})$ and the total of the fees charged to the partnered buildings, $\sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^2$.

$$ \begin{aligned} \tau_i &\leq \left( \mathbb{E}v_i + \sum_{j \in J_i} \theta_j \right) (1 - \text{NPM}) \rightarrow \tau_i \leq \left( \mathbb{E}v_i + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM}) \right) (1 - \text{NPM}) \rightarrow \\ \tau_i &\leq \mathbb{E}v_i(1 - \text{NPM}) + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^2 \end{aligned} \tag{A3} $$

Next, by inserting this maximum value of $\tau_i$ into Constraint (30), the contract duration $T_2$ can be derived. Accordingly, contract duration $T_2$ is constrained to be less than or equal to: $\frac{\omega b_{i,host}}{\mathbb{E}v_i(1 - \text{NPM})^2 + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^3 - \varphi b_{i,host}}$. This upper bound ensures that the contract duration is no longer than necessary, given the maximum allowable service fees for the host and partnered buildings. Finally, since the objective function (29) seeks to minimise $T_2$, the optimal contract duration corresponds to the lower bound of this upper constraint, as shown in Constraint (A4).

$$ \begin{aligned} \mathbb{E}v_i(1 - \text{NPM}) + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^2 &\geq \frac{\mathbb{E}c_{i,host}}{1 - \text{NPM}} \rightarrow \\ \mathbb{E}c_{i,host} &\leq \mathbb{E}v_i(1 - \text{NPM})^2 + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^3 \rightarrow \\ \left(\frac{\omega}{T_2} + \varphi\right)b_{i,host} &\leq \mathbb{E}v_i(1 - \text{NPM})^2 + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^3 \rightarrow \end{aligned} \tag{A4} $$

$$ T_2 \geq \frac{\omega b_{i,host}}{\mathbb{E}v_i(1 - \text{NPM})^2 + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^3 - \varphi b_{i,host}} $$

Proof of lemma 4: Similar to SRM2, although buildings are inherently non-profit entities, the OPL provider ensures that a NPM is met for both the host and partnered buildings in this partnership, due to the security and access concerns that may arise for the buildings. The annual value of OPL service for the households of host building $i$ is equal to $\mathbb{E}v_{i,host}$, which was formulated by Constraint (25). For each partnered building, the value of OPL service is $\mathbb{E}v_j$, calculated by Constraint (7). Host building $i$ charges partnered building ($j$) an annual fee of $\theta_j$. The value of OPL service for carriers to OPL with partnered buildings is equal to $\mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j$, where $\mathbb{E}v'_i$ and $\mathbb{E}v'_j$ are calculated by Constraint (21). Finally, the cost of providing the OPL system and services ($\mathbb{E}c_{i,host}$) was calculated by Equations (26)–(28).

Now we estimate the equilibrium point. SRM3 aims to provide value greater than the fees to buyers, while ensuring profit for the OPL provider. Hence, the contract's decisions include the annual service fees charged to the host building $i$ and carriers ($\tau_i$ and $\tau'_i$), fees charged to partnered buildings ($\theta_j$) and the duration of the contract ($T_3$).

According to Constraint (34), the NPM of the OPL provider is satisfied with the contract, while the NPM of carriers, host and partnered buildings are ensured by Constraints (35) to (37). According to (37), the maximum annual fee charged to partnered buildings is equal to $\mathbb{E}v_j(1 - \text{NPM})$. By substituting the maximum annual fee in (36), the maximum annual service fee ($\tau_i$) charged to building $i$ by OPL provider is calculated in Constraint (A5). This maximum fee is equal to $\mathbb{E}v_i(1 - \text{NPM}) + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^2$.

$$ \begin{aligned} \tau_i &\leq \left( \mathbb{E}v_i + \sum_{j \in J_i} \theta_j \right) (1 - \text{NPM}) \rightarrow \tau_i \leq \left( \mathbb{E}v_i + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM}) \right) (1 - \text{NPM}) \rightarrow \\ &\leq \mathbb{E}v_i(1 - \text{NPM}) + \sum_{j \in J_i} \mathbb{E}v_j(1 - \text{NPM})^2 \end{aligned} \tag{A5} $$

According to Constraint (35), the maximum annual fee that the OPL provider can ask from carriers ($\tau'_i$) is $(\mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j)(1 - \text{NPM})$. By substituting the maximum annual fees for $\tau_i$ and $\tau'_i$ in (34), a lower bound for the duration of the contract ($T_3$) is determined in Constraint (A6). Therefore, as the model's objective minimises $T_3$, the lower bound is set as the optimal value of $T_3$.
$$ \tau_i + \tau'_i \geq \frac{\mathbb{E}c_{i,i=host}}{1-NPM} \rightarrow $$

$$ \mathbb{E}v_i(1-NPM) + \sum_{j \in J_i} \mathbb{E}v_j(1-NPM)^2 + \left( \mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j \right) (1-NPM) \geq \frac{\mathbb{E}c_{i,i=host}}{1-NPM} \rightarrow $$

$$ \mathbb{E}c_{i,i=host} \leq \mathbb{E}v_i(1-NPM)^2 + \sum_{j \in J_i} \mathbb{E}v_j(1-NPM)^3 + \left( \mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j \right) (1-NPM)^2 \rightarrow $$

(A6)

$$ \left( \frac{\omega}{T_3} + \varphi \right) b_{i,i=host} \leq \mathbb{E}v_i(1-NPM)^2 + \sum_{j \in J_i} \mathbb{E}v_j(1-NPM)^3 + \left( \mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j \right) (1-NPM)^2 \rightarrow $$

$$ T_3 \geq \frac{\omega b_{i,i=host}}{\mathbb{E}v_i(1-NPM)^2 + \sum_{j \in J_i} \mathbb{E}v_j(1-NPM)^3 + \left( \mathbb{E}v'_i + \sum_{j \in J_i} \mathbb{E}v'_j \right) (1-NPM)^2 - \varphi b_{i,i=host}} $$

**Proof of lemma 5:** Constraints (42) and (43) satisfy the profits of OPL provider and buildings in the partnership, respectively. According to Constraint (43), the maximum annual service fee charged to each building is $\mathbb{E}v_i(1-NPM)$. By replacing $\tau_i$ with $\mathbb{E}v_i(1-NPM)$ in (42), a lower bound for duration of the contract ($T_4$) is derived in Constraint (A7). Given the objective function (41) minimises $T_4$, the lower bound, $\sum_{i \in J_i} \frac{\omega b_i}{\mathbb{E}v_i(1-NPM)^2 - \varphi b_i}$, is the optimal value of $T_4$.

$$ \sum_{i \in L_i} \mathbb{E}v_i(1-NPM) \geq \frac{\mathbb{E}c_l}{1-NPM} \rightarrow \mathbb{E}c_l \leq \sum_{i \in L_i} \mathbb{E}v_i(1-NPM)^2 \rightarrow $$

$$ \left( \frac{\omega}{T_4} + \varphi \right) b_l \leq \sum_{i \in L_i} \mathbb{E}v_i(1-NPM)^2 \rightarrow T_4 \geq \frac{\omega b_l}{\sum_{i \in L_i} \mathbb{E}v_i(1-NPM)^2 - \varphi b_l} $$

(A7)

**Proof of lemma 6:** Using Constraints (45) and (46), the profit of OPL provider and carrier are determined. Constraint (47) is used to satisfy the profit of each building in the partnership. According to (47), the maximum annual service fee charged to each building is $\mathbb{E}v_i(1-NPM)$. Also, Constraint (46) determines the maximum annual service fee for carriers as $\sum_{i \in L_i} \mathbb{E}v'_i(1-NPM)$. Using the maximum levels of the service fees in (45), the contract duration ($T_5$) must be equal or greater than $\sum_{i \in L_i} \frac{\omega b_i}{\mathbb{E}v_i(1-NPM)^2 - \varphi b_i}$, as shown in (A8). Therefore, considering the objective function in (44), the optimal value of $T_5$ is

$$ \sum_{i \in L_i} \tau_i + \tau'_i \geq \frac{\mathbb{E}c_l}{1-NPM} $$

$$ \sum_{i \in L_i} \mathbb{E}v_i(1-NPM) + \sum_{i \in L_i} \mathbb{E}v'_i(1-NPM) \geq \frac{\mathbb{E}c_l}{1-NPM} $$

$$ \mathbb{E}c_l \leq \sum_{i \in L_i} (\mathbb{E}v_i + \mathbb{E}v'_i)(1-NPM)^2 $$

(A8)

$$ \left( \frac{\omega}{T_5} + \varphi \right) b_l \leq \sum_{i \in L_i} (\mathbb{E}v_i + \mathbb{E}v'_i)(1-NPM)^2 $$

$$ T_5 \geq \frac{\omega b_l}{\sum_{i \in L_i} (\mathbb{E}v_i + \mathbb{E}v'_i)(1-NPM)^2 - \varphi b_l} $$
Appendix A2

<figure><img src="image_19.png" /><figcaption>Fig. A1. Correlation between annual income and number of deliveries</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. A2. Income categories for households and the corresponding probabilities of belonging to each category.</figcaption></figure>

Appendix A3

For the sake of modelling simplicity in the SRMs, two key assumptions were made in Subsection 3.1.

The first assumption concerns the equality of NPMs among the stakeholders (buildings, carriers, and the OPL provider) involved. Although this assumption may be reasonable in practice, discrepancies in their actual NPMs are likely. To assess the sensitivity of model outcomes to such discrepancies, we define the NPMs for the OPL provider, carriers, and buildings as *NPM*, *NPM*₁, and *NPM*₂, respectively, where *NPM* = *α*₁*NPM* and *NPM*₂ = *α*₂*NPM*. The parameters *α*₁ and *α*₂ take values within the range [0.5, 2]. To examine the effect of varying NPM ratios, we consider extreme and median values of *α*₁ and *α*₂, resulting in nine distinct scenarios where each parameter assumes values of 0.5, 1, or 2. The SRM5, which incorporates all stakeholders (the OPL provider, carriers, and buildings), is employed to examine the effects of varying NPMs on total building costs. The baseline scenario corresponds to the case where *α*₁ = 1 and *α*₂ = 1 (the scenario used in Subsection 5.3). For each scenario, the total building costs are recalculated, and the percentage deviations from the baseline scenario are determined to assess the sensitivity of outcomes to differences in NPM assumptions. The results are visualised in Figure A3.
<figure><img src="image_21.png" /><figcaption>Fig. A3. Sensitivity of total building costs to variations in NPM assumptions</figcaption></figure>

The sensitivity analysis presented in Figure A3 shows two distinct trends. Increasing $α_1$ raises total building costs, as higher carrier profit expectations mean they contribute less to paying service fees to the OPL provider. For instance, when carriers expect a 60% NPM ($α_1 = 2$), total building costs increase by about 20% compared with the baseline. In contrast, increasing $α_2$ reduces total costs because when buildings accept higher profit margins, they bear a smaller portion of the total service cost; for example, at $α_2 = 2$, total costs fall by around 20%. Importantly, the contract duration in all cases remains below five years, indicating that these cost adjustments are feasible within short-term agreements. From a practical standpoint, scenarios where carriers accept lower NPMs and buildings target higher NPMs appear more attractive, as they reduce total building costs and encourage broader adoption of the OPL partnership model.

The second assumption relates to the cost associated with land provision by local governments for installing OPLs in public areas. While empirical evidence suggests that governmental agencies often support sustainability-oriented projects, local councils may nonetheless charge the OPL provider an annual leasing fee per facility. In all SRM formulations, $φ$ denotes the annual locker cost incurred by the OPL provider, initially set at AU$1400 in the Melbourne case study. In the city of Melbourne, leasing a parking space costs approximately AU$3200 per year and can accommodate around four locker banks, implying a land leasing cost of about AU$800 per locker bank. To examine the potential impact of land provision costs, a sensitivity analysis varies $φ$ from AU$2200 to AU$3000 in increments of AU$200. This corresponds to an annual land cost per locker ranging from AU$800 to AU$1,600, reflecting a realistic scenario. The SRM5 model, which incorporates all stakeholders (the OPL provider, carriers, and buildings), is employed to examine the effects of varying NPMs and additional land provision costs on total building costs.

Figure A4 presents the sensitivity analysis results for total contract duration and total costs under different partnership scenarios. Incorporating a land leasing cost of AU$800 per locker bank increases total building costs by approximately 2%. However, all contracts remain feasible, with durations below 3.5 years, indicating that while land costs slightly raise expenses, they do not compromise the viability or profitability of the partnerships.

<figure><img src="image_22.png" /><figcaption>Fig. A4. Sensitivity of total costs and contract durations to land leasing costs</figcaption></figure>
## Appendix A4

<table><caption>**Table A1**
Comparison of the basic SRM, SRM2, and SRM4 for host buildings based on service fees, contract duration, and total costs</caption><thead><tr><th>Cluster ID</th><th># Dwelling in host building</th><th>Total dwelling</th><th>Service fee in the basic SRM</th><th>Service fee in SRM2</th><th>Service fee in SRM4</th><th>Contract duration in the basic SRM</th><th>Contract duration in SRM2</th><th>Contract duration in SRM4</th><th>Total building costs in the basic SRM</th><th>Total building costs in SRM2</th><th>Total building costs in SRM4</th></tr></thead><tbody><tr><td>19</td><td>60</td><td>334</td><td>2771</td><td>4361</td><td>1940</td><td>16.2</td><td>6.5</td><td>4.7</td><td>44950</td><td>5842</td><td>9025</td></tr><tr><td>20</td><td>132</td><td>361</td><td>6097</td><td>9450</td><td>4268</td><td>3.9</td><td>2.2</td><td>1.7</td><td>23849</td><td>4535</td><td>7348</td></tr><tr><td>16</td><td>150</td><td>358</td><td>6928</td><td>12883</td><td>4849</td><td>3.3</td><td>1.5</td><td>1.2</td><td>22780</td><td>2159</td><td>5689</td></tr><tr><td>15</td><td>152</td><td>1108</td><td>7020</td><td>14012</td><td>4914</td><td>3.2</td><td>5.8</td><td>4.0</td><td>22682</td><td>5887</td><td>19794</td></tr><tr><td>14</td><td>157</td><td>352</td><td>7251</td><td>9489</td><td>5076</td><td>3.1</td><td>2.2</td><td>1.8</td><td>22451</td><td>7022</td><td>9002</td></tr><tr><td>13</td><td>182</td><td>1088</td><td>8406</td><td>14076</td><td>5884</td><td>2.6</td><td>5.8</td><td>4.1</td><td>21535</td><td>13661</td><td>24316</td></tr><tr><td>11</td><td>193</td><td>348</td><td>8914</td><td>9747</td><td>6240</td><td>2.4</td><td>2.1</td><td>1.8</td><td>21225</td><td>10107</td><td>11216</td></tr><tr><td>10</td><td>206</td><td>365</td><td>9514</td><td>10258</td><td>6660</td><td>2.2</td><td>2.0</td><td>1.7</td><td>20911</td><td>10269</td><td>11320</td></tr><tr><td>9</td><td>260</td><td>734</td><td>12008</td><td>19133</td><td>8406</td><td>1.7</td><td>2.2</td><td>1.7</td><td>19998</td><td>8315</td><td>14196</td></tr><tr><td>17</td><td>369</td><td>1841</td><td>17042</td><td>45243</td><td>11930</td><td>1.1</td><td>2.3</td><td>1.7</td><td>19060</td><td>-5486</td><td>20070</td></tr><tr><td>5</td><td>371</td><td>1089</td><td>17135</td><td>18354</td><td>11994</td><td>2.5</td><td>3.9</td><td>3.2</td><td>42862</td><td>36083</td><td>38708</td></tr><tr><td>7</td><td>401</td><td>1079</td><td>18520</td><td>28308</td><td>12964</td><td>2.3</td><td>2.2</td><td>1.7</td><td>42075</td><td>14183</td><td>22418</td></tr><tr><td>21</td><td>436</td><td>715</td><td>20137</td><td>20410</td><td>14096</td><td>2.1</td><td>2.0</td><td>1.7</td><td>41321</td><td>22996</td><td>24548</td></tr><tr><td>6</td><td>505</td><td>1455</td><td>23324</td><td>37826</td><td>16327</td><td>1.7</td><td>2.2</td><td>1.7</td><td>40194</td><td>15749</td><td>27861</td></tr><tr><td>22</td><td>610</td><td>2563</td><td>28173</td><td>36310</td><td>19721</td><td>1.4</td><td>4.9</td><td>3.8</td><td>39036</td><td>62256</td><td>75322</td></tr><tr><td>2</td><td>659</td><td>1831</td><td>30436</td><td>47829</td><td>21305</td><td>1.3</td><td>2.2</td><td>1.7</td><td>38638</td><td>21699</td><td>36073</td></tr><tr><td>1</td><td>700</td><td>2207</td><td>32330</td><td>56736</td><td>22631</td><td>1.2</td><td>2.2</td><td>1.7</td><td>38353</td><td>17747</td><td>38118</td></tr><tr><td>3</td><td>700</td><td>2207</td><td>32330</td><td>56736</td><td>22631</td><td>1.2</td><td>2.2</td><td>1.7</td><td>38353</td><td>17747</td><td>38118</td></tr><tr><td>4</td><td>700</td><td>2207</td><td>32330</td><td>50354</td><td>22631</td><td>1.2</td><td>2.6</td><td>2.0</td><td>38353</td><td>27595</td><td>44808</td></tr><tr><td>8</td><td>700</td><td>2207</td><td>32330</td><td>56736</td><td>22631</td><td>1.2</td><td>2.2</td><td>1.7</td><td>38353</td><td>17747</td><td>38118</td></tr><tr><td>12</td><td>734</td><td>2213</td><td>33900</td><td>57201</td><td>23730</td><td>1.1</td><td>2.2</td><td>1.7</td><td>38143</td><td>20576</td><td>39843</td></tr><tr><td>18</td><td>805</td><td>1840</td><td>37179</td><td>28628</td><td>26026</td><td>1.6</td><td>4.3</td><td>4.0</td><td>59684</td><td>106456</td><td>105363</td></tr></tbody></table>

<table><caption>**Table A2**
Comparison of the basic SRM, SRM2, and SRM4 for partnered buildings based on service fees, contract duration, and total costs</caption><thead><tr><th>Cluster ID</th><th># Dwelling in partnered building</th><th>Total dwelling</th><th>Service fee in the basic SRM</th><th>Service fee in SRM2</th><th>Service fee in SRM4</th><th>Contract duration in the basic SRM</th><th>Contract duration in SRM2</th><th>Contract duration in SRM4</th><th>Total building costs in the basic SRM</th><th>Total building costs in SRM2</th><th>Total building costs in SRM4</th></tr></thead><tbody><tr><td>10</td><td>10</td><td>365</td><td>462</td><td>323</td><td>323</td><td>INF</td><td>2.0</td><td>1.7</td><td>INF</td><td>649</td><td>549</td></tr><tr><td>16</td><td>10</td><td>358</td><td>462</td><td>323</td><td>323</td><td>INF</td><td>1.5</td><td>1.2</td><td>INF</td><td>496</td><td>379</td></tr><tr><td>16</td><td>10</td><td>358</td><td>462</td><td>323</td><td>323</td><td>INF</td><td>1.5</td><td>1.2</td><td>INF</td><td>496</td><td>379</td></tr><tr><td>16</td><td>11</td><td>358</td><td>508</td><td>356</td><td>356</td><td>INF</td><td>1.5</td><td>1.2</td><td>INF</td><td>546</td><td>417</td></tr><tr><td>12</td><td>15</td><td>2213</td><td>693</td><td>485</td><td>485</td><td>INF</td><td>2.2</td><td>1.7</td><td>INF</td><td>1063</td><td>814</td></tr><tr><td>16</td><td>15</td><td>358</td><td>693</td><td>485</td><td>485</td><td>INF</td><td>1.5</td><td>1.2</td><td>INF</td><td>744</td><td>569</td></tr><tr><td>16</td><td>15</td><td>358</td><td>693</td><td>485</td><td>485</td><td>INF</td><td>1.5</td><td>1.2</td><td>INF</td><td>744</td><td>569</td></tr><tr><td>19</td><td>15</td><td>334</td><td>693</td><td>485</td><td>485</td><td>INF</td><td>6.5</td><td>4.7</td><td>INF</td><td>3141</td><td>2256</td></tr><tr><td>13</td><td>16</td><td>1088</td><td>739</td><td>517</td><td>517</td><td>INF</td><td>5.8</td><td>4.1</td><td>INF</td><td>2978</td><td>2138</td></tr><tr><td>21</td><td>16</td><td>715</td><td>739</td><td>517</td><td>517</td><td>INF</td><td>2.0</td><td>1.7</td><td>INF</td><td>1044</td><td>901</td></tr><tr><td>13</td><td>18</td><td>1088</td><td>831</td><td>582</td><td>582</td><td>INF</td><td>5.8</td><td>4.1</td><td>INF</td><td>3350</td><td>2405</td></tr><tr><td>14</td><td>21</td><td>352</td><td>970</td><td>679</td><td>679</td><td>INF</td><td>2.2</td><td>1.8</td><td>INF</td><td>1497</td><td>1204</td></tr><tr><td>18</td><td>23</td><td>1840</td><td>1062</td><td>744</td><td>744</td><td>INF</td><td>4.3</td><td>4.0</td><td>INF</td><td>3178</td><td>3010</td></tr><tr><td>20</td><td>26</td><td>361</td><td>1201</td><td>841</td><td>841</td><td>INF</td><td>2.2</td><td>1.7</td><td>INF</td><td>1863</td><td>1447</td></tr><tr><td>20</td><td>26</td><td>361</td><td>1201</td><td>841</td><td>841</td><td>INF</td><td>2.2</td><td>1.7</td><td>INF</td><td>1863</td><td>1447</td></tr><tr><td>15</td><td>27</td><td>1108</td><td>1247</td><td>873</td><td>873</td><td>INF</td><td>5.8</td><td>4.0</td><td>INF</td><td>5062</td><td>3516</td></tr><tr><td>9</td><td>32</td><td>734</td><td>1478</td><td>1035</td><td>1035</td><td>INF</td><td>2.2</td><td>1.7</td><td>INF</td><td>2259</td><td>1747</td></tr><tr><td>9</td><td>32</td><td>734</td><td>1478</td><td>1035</td><td>1035</td><td>INF</td><td>2.2</td><td>1.7</td><td>INF</td><td>2259</td><td>1747</td></tr><tr><td>21</td><td>34</td><td>715</td><td>1570</td><td>1099</td><td>1099</td><td>INF</td><td>2.0</td><td>1.7</td><td>INF</td><td>2219</td><td>1914</td></tr><tr><td>18</td><td>41</td><td>1840</td><td>1894</td><td>1326</td><td>1326</td><td>95.6</td><td>4.3</td><td>4.0</td><td>181023</td><td>5665</td><td>5366</td></tr><tr><td>11</td><td>45</td><td>348</td><td>2078</td><td>1455</td><td>1455</td><td>47.1</td><td>2.1</td><td>1.8</td><td>97864</td><td>3105</td><td>2615</td></tr><tr><td>20</td><td>45</td><td>361</td><td>2078</td><td>1455</td><td>1455</td><td>47.1</td><td>2.2</td><td>1.7</td><td>97864</td><td>3224</td><td>2505</td></tr><tr><td>19</td><td>46</td><td>334</td><td>2125</td><td>1487</td><td>1487</td><td>41.8</td><td>6.5</td><td>4.7</td><td>88776</td><td>9631</td><td>6919</td></tr><tr><td>19</td><td>46</td><td>334</td><td>2125</td><td>1487</td><td>1487</td><td>41.8</td><td>6.5</td><td>4.7</td><td>88776</td><td>9631</td><td>6919</td></tr><tr><td>14</td><td>47</td><td>352</td><td>2171</td><td>1520</td><td>1520</td><td>37.6</td><td>2.2</td><td>1.8</td><td>81528</td><td>3351</td><td>2695</td></tr><tr><td>18</td><td>51</td><td>1840</td><td>2355</td><td>1649</td><td>1649</td><td>26.7</td><td>4.3</td><td>4.0</td><td>62977</td><td>7046</td><td>6675</td></tr><tr><td>21</td><td>52</td><td>715</td><td>2402</td><td>1681</td><td>1681</td><td>24.9</td><td>2.0</td><td>1.7</td><td>59897</td><td>3394</td><td>2928</td></tr><tr><td>9</td><td>68</td><td>734</td><td>3141</td><td>2198</td><td>2198</td><td>12.0</td><td>2.2</td><td>1.7</td><td>37747</td><td>4800</td><td>3713</td></tr><tr><td>17</td><td>85</td><td>1841</td><td>3926</td><td>2748</td><td>2748</td><td>7.8</td><td>2.3</td><td>1.7</td><td>30432</td><td>6423</td><td>4623</td></tr><tr><td>15</td><td>89</td><td>1108</td><td>4111</td><td>2877</td><td>2877</td><td>7.2</td><td>5.8</td><td>4.0</td><td>29407</td><td>16685</td><td>11590</td></tr><tr><td>11</td><td>110</td><td>348</td><td>5080</td><td>3556</td><td>3556</td><td>5.1</td><td>2.1</td><td>1.8</td><td>25873</td><td>7589</td><td>6393</td></tr><tr><td>9</td><td>111</td><td>734</td><td>5127</td><td>3589</td><td>3589</td><td>5.0</td><td>2.2</td><td>1.7</td><td>25755</td><td>7835</td><td>6061</td></tr><tr><td>9</td><td>111</td><td>734</td><td>5127</td><td>3589</td><td>3589</td><td>5.0</td><td>2.2</td><td>1.7</td><td>25755</td><td>7835</td><td>6061</td></tr><tr><td>9</td><td>120</td><td>734</td><td>5542</td><td>3880</td><td>3880</td><td>4.5</td><td>2.2</td><td>1.7</td><td>24820</td><td>8470</td><td>6552</td></tr><tr><td>22</td><td>123</td><td>2563</td><td>5681</td><td>3977</td><td>3977</td><td>4.3</td><td>4.9</td><td>3.8</td><td>24552</td><td>19630</td><td>15188</td></tr></tbody></table>

(continued on next page)
<table><caption>Table A2 (continued)</caption><thead><tr><th>Cluster ID</th><th># Dwelling in partnered building</th><th>Total dwelling</th><th>Service fee in the basic SRM</th><th>Service fee in SRM2</th><th>Service fee in SRM4</th><th>Contract duration in the basic SRM</th><th>Contract duration in SRM2</th><th>Contract duration in SRM4</th><th>Total building costs in the basic SRM</th><th>Total building costs in SRM2</th><th>Total building costs in SRM4</th></tr></thead><tbody><tr><td>14</td><td>127</td><td>352</td><td>5866</td><td>4106</td><td>4106</td><td>4.1</td><td>2.2</td><td>1.8</td><td>24222</td><td>9053</td><td>7282</td></tr><tr><td>20</td><td>132</td><td>361</td><td>6097</td><td>4268</td><td>4268</td><td>3.9</td><td>2.2</td><td>1.7</td><td>23849</td><td>9457</td><td>7348</td></tr><tr><td>15</td><td>134</td><td>1108</td><td>6189</td><td>4332</td><td>4332</td><td>3.8</td><td>5.8</td><td>4.0</td><td>23711</td><td>25121</td><td>17450</td></tr><tr><td>16</td><td>147</td><td>358</td><td>6789</td><td>4752</td><td>4752</td><td>3.4</td><td>1.5</td><td>1.2</td><td>22934</td><td>7294</td><td>5576</td></tr><tr><td>16</td><td>147</td><td>358</td><td>6789</td><td>4752</td><td>4752</td><td>3.4</td><td>1.5</td><td>1.2</td><td>22934</td><td>7294</td><td>5576</td></tr><tr><td>10</td><td>149</td><td>365</td><td>6882</td><td>4817</td><td>4817</td><td>3.3</td><td>2.0</td><td>1.7</td><td>22830</td><td>9665</td><td>8187</td></tr><tr><td>15</td><td>152</td><td>1108</td><td>7020</td><td>4914</td><td>4914</td><td>3.2</td><td>5.8</td><td>4.0</td><td>22682</td><td>28496</td><td>19794</td></tr><tr><td>7</td><td>156</td><td>1079</td><td>7205</td><td>5043</td><td>5043</td><td>3.1</td><td>2.2</td><td>1.7</td><td>22495</td><td>11197</td><td>8721</td></tr><tr><td>7</td><td>156</td><td>1079</td><td>7205</td><td>5043</td><td>5043</td><td>3.1</td><td>2.2</td><td>1.7</td><td>22495</td><td>11197</td><td>8721</td></tr><tr><td>13</td><td>164</td><td>1088</td><td>7574</td><td>5302</td><td>5302</td><td>2.9</td><td>5.8</td><td>4.1</td><td>22158</td><td>30523</td><td>21911</td></tr><tr><td>13</td><td>164</td><td>1088</td><td>7574</td><td>5302</td><td>5302</td><td>2.9</td><td>5.8</td><td>4.1</td><td>22158</td><td>30523</td><td>21911</td></tr><tr><td>21</td><td>177</td><td>715</td><td>8175</td><td>5722</td><td>5722</td><td>2.7</td><td>2.0</td><td>1.7</td><td>21692</td><td>11554</td><td>9966</td></tr><tr><td>12</td><td>189</td><td>2213</td><td>8729</td><td>6110</td><td>6110</td><td>2.4</td><td>2.2</td><td>1.7</td><td>21332</td><td>13396</td><td>10259</td></tr><tr><td>17</td><td>254</td><td>1841</td><td>11731</td><td>8212</td><td>8212</td><td>1.7</td><td>2.3</td><td>1.7</td><td>20077</td><td>19194</td><td>13815</td></tr><tr><td>17</td><td>254</td><td>1841</td><td>11731</td><td>8212</td><td>8212</td><td>1.7</td><td>2.3</td><td>1.7</td><td>20077</td><td>19194</td><td>13815</td></tr><tr><td>17</td><td>255</td><td>1841</td><td>11777</td><td>8244</td><td>8244</td><td>1.7</td><td>2.3</td><td>1.7</td><td>20063</td><td>19270</td><td>13870</td></tr><tr><td>17</td><td>255</td><td>1841</td><td>11777</td><td>8244</td><td>8244</td><td>1.7</td><td>2.3</td><td>1.7</td><td>20063</td><td>19270</td><td>13870</td></tr><tr><td>6</td><td>263</td><td>1455</td><td>12147</td><td>8503</td><td>8503</td><td>1.6</td><td>2.2</td><td>1.7</td><td>19960</td><td>18827</td><td>14510</td></tr><tr><td>5</td><td>281</td><td>1089</td><td>12978</td><td>9085</td><td>9085</td><td>1.5</td><td>3.9</td><td>3.2</td><td>19752</td><td>35366</td><td>29318</td></tr><tr><td>1</td><td>282</td><td>2207</td><td>13024</td><td>9117</td><td>9117</td><td>1.5</td><td>2.2</td><td>1.7</td><td>19741</td><td>20188</td><td>15356</td></tr><tr><td>3</td><td>282</td><td>2207</td><td>13024</td><td>9117</td><td>9117</td><td>1.5</td><td>2.2</td><td>1.7</td><td>19741</td><td>20188</td><td>15356</td></tr><tr><td>8</td><td>282</td><td>2207</td><td>13024</td><td>9117</td><td>9117</td><td>1.5</td><td>2.2</td><td>1.7</td><td>19741</td><td>20188</td><td>15356</td></tr><tr><td>6</td><td>312</td><td>1455</td><td>14410</td><td>10087</td><td>10087</td><td>1.4</td><td>2.2</td><td>1.7</td><td>19458</td><td>22335</td><td>17213</td></tr><tr><td>7</td><td>366</td><td>1079</td><td>16904</td><td>11833</td><td>11833</td><td>1.1</td><td>2.2</td><td>1.7</td><td>19078</td><td>26270</td><td>20461</td></tr><tr><td>17</td><td>369</td><td>1841</td><td>17042</td><td>11930</td><td>11930</td><td>1.1</td><td>2.3</td><td>1.7</td><td>19060</td><td>27884</td><td>20070</td></tr><tr><td>6</td><td>375</td><td>1455</td><td>17320</td><td>12124</td><td>12124</td><td>2.5</td><td>2.2</td><td>1.7</td><td>42748</td><td>26844</td><td>20689</td></tr><tr><td>12</td><td>541</td><td>2213</td><td>24986</td><td>17490</td><td>17490</td><td>1.6</td><td>2.2</td><td>1.7</td><td>39739</td><td>38346</td><td>29367</td></tr><tr><td>1</td><td>584</td><td>2207</td><td>26972</td><td>18881</td><td>18881</td><td>1.5</td><td>2.2</td><td>1.7</td><td>39279</td><td>41809</td><td>31802</td></tr><tr><td>3</td><td>584</td><td>2207</td><td>26972</td><td>18881</td><td>18881</td><td>1.5</td><td>2.2</td><td>1.7</td><td>39279</td><td>41809</td><td>31802</td></tr><tr><td>4</td><td>584</td><td>2207</td><td>26972</td><td>18881</td><td>18881</td><td>1.5</td><td>2.6</td><td>2.0</td><td>39279</td><td>48468</td><td>37383</td></tr><tr><td>8</td><td>584</td><td>2207</td><td>26972</td><td>18881</td><td>18881</td><td>1.5</td><td>2.2</td><td>1.7</td><td>39279</td><td>41809</td><td>31802</td></tr><tr><td>2</td><td>586</td><td>1831</td><td>27065</td><td>18945</td><td>18945</td><td>1.5</td><td>2.2</td><td>1.7</td><td>39259</td><td>41365</td><td>32077</td></tr><tr><td>2</td><td>586</td><td>1831</td><td>27065</td><td>18945</td><td>18945</td><td>1.5</td><td>2.2</td><td>1.7</td><td>39259</td><td>41365</td><td>32077</td></tr><tr><td>22</td><td>610</td><td>2563</td><td>28173</td><td>19721</td><td>19721</td><td>1.4</td><td>4.9</td><td>3.8</td><td>39036</td><td>97350</td><td>75322</td></tr><tr><td>1</td><td>641</td><td>2207</td><td>29605</td><td>20723</td><td>20723</td><td>1.3</td><td>2.2</td><td>1.7</td><td>38776</td><td>45889</td><td>34906</td></tr><tr><td>3</td><td>641</td><td>2207</td><td>29605</td><td>20723</td><td>20723</td><td>1.3</td><td>2.2</td><td>1.7</td><td>38776</td><td>45889</td><td>34906</td></tr><tr><td>4</td><td>641</td><td>2207</td><td>29605</td><td>20722</td><td>20723</td><td>1.3</td><td>2.6</td><td>2.0</td><td>38776</td><td>53198</td><td>41031</td></tr><tr><td>8</td><td>641</td><td>2207</td><td>29605</td><td>20723</td><td>20723</td><td>1.3</td><td>2.2</td><td>1.7</td><td>38776</td><td>45889</td><td>34906</td></tr><tr><td>12</td><td>734</td><td>2213</td><td>33900</td><td>23730</td><td>23730</td><td>1.1</td><td>2.2</td><td>1.7</td><td>38143</td><td>52026</td><td>39843</td></tr></tbody></table>

## Data availability

No data was used for the research described in the article.

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