# Integrated production planning of orders with priorities and due dates in the automotive industry

Ayman Mahmoud, Mohammed Hichame Benbitour, Evren Sahin, Zied Jemai, Marc Baratte

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Ayman Mahmoud, Mohammed Hichame Benbitour, Evren Sahin, Zied Jemai, Marc Baratte. Integrated production planning of orders with priorities and due dates in the automotive industry. Computers & Industrial Engineering, 2025, 209, pp.111347. 10.1016/j.cie.2025.111347. hal-05200645

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# Integrated production planning of orders with priorities and due dates in the automotive industry

Ayman Mahmoud<sup>a,d</sup>,*, Mohammed Hichame Benbitour<sup>b</sup>, Evren Sahin<sup>a</sup>, Zied Jemai<sup>a,c</sup>,
Marc Baratte<sup>d</sup>

## ARTICLE INFO

### Keywords:

- Production planning

- Integrated production planning

- End-to-end supply chain

- Automotive industry

## ABSTRACT

This paper addresses the integrated production planning problem by developing a mixed integer mathematical optimisation model (MIP). A numerical study using data from an OEM (Original Equipment Manufacturer) assembly plant is conducted. The study underlines the model's ability to coordinate planned inbound and outbound logistics activities with the OEM assembly plant's production plan. Our model enables us to handle disruptions in a supply chain (e.g., variations in lead times, shortages, and an increase in supply costs) in a coordinated way with an end-to-end perspective, including supply, distribution and production activities, to minimise the overall cost of operations, based on extensive data. Our aim is to provide practical guidance for the performance of operations (in terms of logistics, emergency shipments — thus emissions, leading to sustainable operations, inventory reduction and capacity utilisation) as well as improving supply chain agility (how to best cope with disruptions arising in inbound/outbound operations, and to ensure stability in production). Results indicate that the production plan provided by our model improves the adherence to release dates of 35% of the manufacturing orders compared to the current industrial tool used by the car manufacturer and reduces the holding cost of components by 80% on the studied horizon.

## 1. Introduction

This paper considers the issue of integrated planning in an automotive supply chain. The planning process refers to selecting manufacturing orders for the assembly lines of production sites and integrating them into the master production plan, which is established during the Sales and Operations Planning (S&OP) process. These orders are typically generated by a separate entity responsible for managing customer orders, which is part of the OEM's commercial business unit (Volling, Matzke, Grunewald, & Spengler, 2013; Volling & Spengler, 2011). The process is two-fold; first, orders are placed into production periods, where, according to the product being produced, the production period can represent a month, a week, a day or a shift in a day. Orders selected must respect constraints such as component availability and platform-related (product family) production capacity. Then, manufacturing orders are scheduled for each period to form a sequence that respects the operational constraints, such as human resources and machine capacities. This production sequence is typically defined over one to three months, where the first six to fourteen days of the horizon

are frozen (i.e., it cannot be modified unless for emergency measures). Production dates within the frozen period cannot be changed, but the sequence can be modified based on short-term variations up until a week before production. Sometimes, the OEM assembly plant modifies the sequence on the same day due to disruptions such as a quality issue with a component or a machine breakdown (Jana, 2018). Our paper considers the planning horizon of the four weeks following the frozen horizon.

The planning process of assembly operations in the OEM plant involved up to 2500 with components required (up to 4000 components per vehicle produced). Such a process requires the use of a digital planning optimisation tool. However, in the study context, the current tool faces some limitations. These limitations affect the end-to-end visibility on resource constraints to find the optimal global production plan with the least impact on the supply chain at minimum operational cost (Graves, Tomlin, & Willems, 2022). Additionally, recurrent supply chain disruptions, including supply shortages, highlight the critical need for alternative solutions. Such solutions ensure sustainable

<footnote><sup>a</sup> Université Paris-Saclay, CentraleSupélec, Laboratoire Génie Industriel, Gif-sur-Yvette, 91190, France</footnote>

<footnote><sup>b</sup> Métis Laboratory, EM Normandie Business School, Clichy, 92110, France</footnote>

<footnote><sup>c</sup> OASIS-ENIT, University of Tunis, Tunis, El Manar, BP 37, Le Belvédère, Tunisia</footnote>

<footnote><sup>d</sup> Renault SAS, Guyancourt, 78289, France</footnote>

<footnote>* Corresponding author at: Université Paris-Saclay, CentraleSupélec, Laboratoire Génie Industriel, Gif-sur-Yvette, 91190, France.
E-mail address: ayman.mahmoud@centralesupelec.fr (A. Mahmoud).</footnote>
production plans and avoid the severe financial consequences of a
complete production stop, where every 60 to 90 s of idle time equates
to the lost profit of one car (Boysen, Emde, Hoeck, & Kauderer, 2015).

Financial challenges involved in the planning process are of the utmost importance. The supply chain cost per vehicle produced can reach up to 1000 Euros, and between 200 and 400 Euros is incurred for transport from suppliers to the OEM assembly plant alone (Baller, Fontaine, Minner, & Lai, 2022). We estimate this cost component to increase in the coming years to meet the ever-increasing sustainable transport requirements (e.g. clean energy transportation). Supply chain costs can be much higher during disruptions, such as rupturing a component stock due to quality conditions (shortage in the component inventory). Car manufacturers' supply chains constantly innovate to reduce these costs. Integrating operations within the supply chain by elaborating a production plan that adapts to the supply of components and distribution of product plans has effectively reduced global operational costs in assembly-based industries (Hrabec, Hvattum, & Hoff, 2022). Integration can contribute to a more sustainable supply chain; for example, Hülagü, Dullaert, Eruguz, Heijungs, and Inghels (2025) integrated the supply chain planning optimisation with life cycle assessment (LCA).

This paper proposes an integrated approach for building a pro-
duction plan that considers commercial demand alongside upstream
(inbound) and downstream (outbound) resource constraints. Motivated
by recurrent disruptions like the most recent pandemic and the elec-
tronic components crisis, we focus on enhancing the production plan's
reactivity to internal or external changes, thereby minimising impacts
on the supply chain and operational costs. An integrated planning ap-
proach is more efficient as it directly incorporates multiple constraints,
reducing the need for numerous plan iterations (Emrouznejad, Abbasi,
& Sicakyüz, 2023; Quetschlich, Moetz, & Otto, 2021), and is essential
for managing the complexity of simultaneous supply, production, and
distribution in the automotive industry. Our study focuses on how
supply chain disruptions, such as delays, resource shortages, and rising
supply costs, can be managed across inbound logistics, production,
and outbound distribution. Our approach minimises overall operational
costs while improving efficiency. Furthermore, it also allows for more
sustainable operations by minimising disruptive and resource-intensive
activities such as emergency shipments, which directly reduces emis-
sions. Indeed, our model contributes to more sustainable production
by optimising logistics costs, for instance, by reducing the number of
trucks required for distribution and lowering overall inventory levels.

Our work contributes to the existing literature by demonstrating, through analysis of real industrial data, how production and associated inbound/outbound operations can be efficiently coordinated by a systemic approach in a complex supply chain like an automotive OEM. It further demonstrates the impact of supply chain disruptions on production plans and presents effective reactive strategies. A key academic advancement lies in its novel mathematical formulations, fostering an enhanced synergy with existing industrial data infrastructures. This synergy enables functionalities that were missing in the research work we analysed, such as modifying planned shipment quantities from suppliers in response to evolving conditions. Furthermore, our model distinguishes itself through comprehensive objective functions capturing end-to-end operational costs. Incorporating detailed, automotive industry-specific parameters related to supply planning and outbound distribution costs also enriches the model's ability to represent current complexity of industrial end-to-end operations.

From the industrial perspective, our work is being tested and im-
plemented in real use cases, highlighting the limitations of current
tools deployed for production planning. This close collaboration with
industry stakeholders was instrumental in ensuring our solutions are
practically feasible. The model we present stems from a recognised
need for organisational transformation in the way current stakeholders
— notably production planners and production control managers —
define and execute production within the automotive industry.

The paper's organisation is as follows: first, we review existing literature on production planning (Section 2). Section 3 presents the problem statement, while Section 4 develops the mathematical model. A case study built from the context of Renault company is presented in Section 5, and Section 6 concludes the paper and presents some relevant future work.

## 2. Literature review

This section reviews existing integrated planning approaches and
highlights the contributions of our model. We focus on studies relevant
to our study, notably those deadling with integration of inbound and
outbound operations.

Production planning in the automotive industry has been challeng-
ing since the start of mass production (Dörmer, Günther, & Gujjula,
2015). Factories do not possess unlimited resources to cope with any
conceivable mix of cars; instead, manufacturing facilities are designed
to accommodate certain levels of models and features, and production
plans must adhere to these limitations (Hindi & Ploszajski, 1994). The
production planning problem involves selecting a subset of car orders
from the extensive order bank presented by the sales department to
manufacture in a given planning horizon, all while ensuring overall
capacities are maintained (no resource capacity is violated) (Hindi
& Ploszajski, 1994; Volling et al., 2013; Volling & Spengler, 2011).
Disruptions impacting operations, either in inbound logistics for com-
ponents' supply or outbound distribution for the delivery to the end
customers, increasingly complicate this task. Geopolitical events are a
significant root cause for these disruptions, impacting global logistics,
causing delivery delays, and supply shortages. Consequently, the cost
of adapting supply and distribution plans to align with production
schedules increases. This leads industrials and researchers to explore
new opportunities for integration. Two primary goals drive this explo-
ration: firstly, to enhance supply chain resilience and achieve a global
optimum across supply, production, and distribution planning rather
than a local production optimum that leads to high operational costs or
proves infeasible due to logistical constraints or disruptions. Secondly,
operational integration aims for cost reduction (Hrabec et al., 2022).

The concept of an integrated supply chain dates to the 1950s, when Clark (1958) focused on inventory problems and economic order quantities in multi-echelon systems. Integration focuses on synchronising different supply chain processes, such as production and distribution or the integration can be within the manufacturing stage; for example, Santana and Fuchigami (2025) introduced an optimisation model integrating the scheduling in a multistage assembly plant considering post processes, which are processing machines operating on assembled products, this continuity in exploring new integration approaches from the 1950s to now only strengthen the value of the integration. The literature also studies the integration of routing decisions with production scheduling. Moons, Ramaekers, Caris, and Arda (2017) discuss the operational-level integration of production scheduling and vehicle routing, emphasising the benefits of combined decision-making in reducing total costs. Similarly, Hrabec et al. (2022) quantifies the potential savings from integrated planning compared to sequential planning, demonstrating substantial cost reductions when production, inventory, and routing decisions are considered jointly, Ben-Daya and Al-Nassar (2008) optimise a system that deals with inventory and production coordination in a three-layer supply chain involving suppliers, manufacturers and retailers, their work showed considerable savings, Ramezanian, Mahdavi, and Shahparvari (2025) introduced another integrated approach where mobile production facilities (trucks) assemble orders while being delivered to the final customer.

More specifically, the integration of inbound logistics with produc-
tion planning has been explored in the literature (Comelli, Gourgand,
& Lemoine, 2008; Hein & Almeder, 2016; Hrabec et al., 2022), but
the relationship between production planning and vehicle routing has
received less attention. In many cases, these are solved sequentially,
leading to sub-optimal solutions. Optimising both production planning and vehicle routing, a key aspect of inbound logistics offers the potential for operational cost savings and improved service levels. Indeed, various researchers have highlighted the broader importance of coordination in optimising overall inbound logistics. Baller et al. (2022) discuss how inbound logistics management, involving complex operational processes and systems, affects company performance.

Additionally, better visibility into demand can reduce transportation distances and minimise backorders. Fabri and Ramalhinho (2024) underscore the impact of inbound logistics on operational efficiency. Within this context, the specific challenge of the Production Routing Problem, which integrates decisions on component supply with vehicle routing, has been further explored by Hein and Almeder (2016), who found that the value of coordination increases as the problem size grows. Where build-to-order processes are standard, Lim, Alpan, and Penz (2017) emphasise the role of Sales and Operations Planning (S&OP) in aligning production capacities with unpredictable market demand, mainly when sourcing components from distant locations.

On the other hand, integration of outbound logistics with production planning extends the classic production planning problem with distribution planning; the latter part can be treated as vehicle routing planning from the OEM's assembly plant to the final customers. Boudia, Louly, and Prins (2006) addresses the production distribution problem, determining the optimal production quantities, distribution schedules, and delivery routes to minimise total costs, including setup, holding, and distribution expenses. Zhang, Li, Zhang, Yang, and Wu (2024) emphasise the need for flexible and adaptive scheduling techniques in automotive production, particularly given the industry's susceptibility to disruptions in outbound distributions, which can significantly impact production and lead to the saturation of the OEM assembly plant's garages.

Most of the research work we presented developed a mixed integer linear programming model to optimise the integrated production planning problem. This problem is also known in the literature as the aggregate production planning problem. In some cases, aggregation levels can correspond to the integration of inbound and outbound operations. Research work also includes metaheuristics and algorithms due to the complexity of the problem. In terms of solution procedure, Zhao et al. (2024) use a swarm optimisation algorithm (The Jellyfish Optimisation Algorithm) to solve the production scheduling problem with logistical constraints reflecting components availability and use, Makui, Heydari, Aazami, and Dehghani (2016) used the Benders decomposition algorithm (BDA) to solve the APP for products that lose value quickly after a season (such as holidays gifts), and Chiu, Lo, Pai, Chiu, and Chiu (2024) introduced an optimisation model of production-shipping operations where they employed postponement, outsourcing, and expedited rate strategies to reduce operational costs.

In our work, we have identified relevant research that has been instructive to our work and also shows examples of integration in production planning; for integration approaches in the automotive industry, we refer the readers to Moons et al. (2017), Müllerklein, Fontaine, and Ostermeier (2022), Quetschlich et al. (2021) and Zhang et al. (2024). For references on automotive production planning, readers are referred to Bolat (2003), Dörmer et al. (2015) and Hindi and Ploszajski (1994).

Despite progress in integrated production planning research, several gaps persist in the literature. For instance, while Quetschlich et al. (2021) highlight the need for mathematical models addressing routing through multi-echelon supply networks, their focus often stops short of considering outbound distribution alongside inbound supply and production planning. Dolgui, Ivanov, and Simchi-levi (2025) highlighted the need for more research addressing the response to disruptive events, reducing the time to recover as well as increasing the time to survive. Our paper addresses this gap by offering several contributions: (1) We develop a comprehensive model that achieves an integration of inbound logistics, production planning, and outbound distribution

operations—an approach particularly scarce in the automotive context (Komiijani & Sajadieh, 2024). Unlike conceptual models that tend to simplify operational reality, our model is distinguished by novel formulations that explicitly incorporate a rich set of industry-specific constraints. These include commercial priorities, complex re-ordering and contractual supply policies, and a variable supplier capacity depending on the ordering point on the horizon. (2) Existing literature on managing component supply within integrated models often presents limited reactive measures, such as basic emergency orders (Sali & Giard, 2015). In our model, we include decision variables for emergency shipments and production order priorities to ensure feasibility, and allow for the dynamic modification of previously scheduled shipment quantities from suppliers based on their capacity extracted from the industrial data and the OEM plant needs. (3) Finally, a notable gap lies in the rigorous validation of integrated planning models using real-world industrial data, especially through direct benchmarking against company digital tools and quantifying benefits through performance metrics (AlMulhim, 2021). To our knowledge, no prior comparative study has published a direct comparison of an advanced integrated model's output against that of a currently operating industrial tool within the automotive sector, nor has there been sufficient emphasis on quantifying disruption-related cost savings.

### 3. Problem description

This section aims to present the OEM supply chain under study as well as our modelling assumptions. In the OEM case under study, and in the case of other car manufacturers, production plans are built based on the Master Production Schedule (MPS), which is then communicated to production planning, supply planning, and distribution planning teams. Although the production planning team currently uses a digitalised decision-making tool that primarily optimises manufacturing objectives by considering communicated industrial constraints on resources, visibility into the broader impact of the production plan across the supply chain remains fragmented. This results in sub-optimal performance in the interaction between production, supply and distribution planners, as shown in Fig. 1 affecting production efficiency, inventory levels, operations costs, and customer satisfaction. Indeed, the currently used planning tool focuses mainly on manufacturing objectives, such as meeting promised release dates, without integrating other crucial complementary objectives, such as maximising the utilisation of outbound distribution capacities. This limited perspective hinders the adoption of a holistic, end-to-end supply chain perspective: a production plan optimised solely for adherence to OEM assembly plant release dates may generate high component supply costs, leading to poor overall performance. Unexpected disruptions, such as component damage or quality issues, delivery delays caused by accidents or weather conditions, and truck unavailability, further complicate this situation. Such disruptions generate instability in the production plan and throughout all supply chain echelons.

To overcome these challenges, we propose an optimisation approach that enables better coordination across production, pre-production (upstream operations), and post-production stages (downstream operations), including inbound/outbound logistics, warehousing, and distribution. Indeed, beyond solely optimising production (i.e., focusing on metrics like meeting release dates or maximising capacity utilisation), our model integrates broader objectives, including the delays and costs associated with component supply, and overall inventory levels.

#### 3.1. *The automotive supply chain network*

The supply chain network under study encompasses several key stages (echelons) and represents the end-to-end perspective we considered in our model: multiple suppliers, inbound logistics operations, the OEM assembly plant operations, which houses a component inventory
<figure><img src="image_3.png" /><figcaption>Fig. 1. Supply chain network information and physical flows.</figcaption></figure>

<table><caption>**Table 1**
Example of manufacturing orders requested by customers.</caption><thead><tr><td>Customer order</td><td>Demand</td><td>Product</td><td>Quantity</td><td>Priority</td><td>Destination</td></tr></thead><tbody><tr><td>1</td><td>1</td><td>3</td><td>1</td><td>2</td><td>x</td></tr><tr><td>1</td><td>2</td><td>7</td><td>5</td><td>3</td><td>y</td></tr><tr><td>2</td><td>1</td><td>2</td><td>1</td><td>1</td><td>x</td></tr><tr><td>2</td><td>2</td><td>3</td><td>1</td><td>1</td><td>x</td></tr><tr><td>2</td><td>3</td><td>9</td><td>1</td><td>2</td><td>x</td></tr></tbody></table>

and a finished vehicle garage, and an outbound distribution network serving multiple customer destinations. Components are sourced from suppliers and reach the OEM assembly plant via inbound logistics. Upon arrival, these components are stored in the plant's dedicated inventory before being supplied to the assembly lines for vehicle production. Once assembled into the vehicle, finished vehicles are transferred to the plant's garage, serving as a temporary holding area before their dispatch to their respective destinations. The supply chain involves several flows (see Fig. 1): (i) inbound flows from suppliers to the component inventory, accommodating both regular scheduled deliveries and options for expedited shipments in the case when an emergency shipment is requested from the supplier; (ii) internal flows within the OEM assembly plant, specifically the movement of components from inventory to the assembly lines and the transfer of completed vehicles from the plant to the plant's garage; and (iii) outbound flows of assembled products from the garage through the distribution network to multiple destinations to satisfy market demand.

## 3.2. Modelling assumptions

To formulate an integrated planning across the automotive supply chain, our model lies on several assumptions:

(i) Customers send orders to the OEM assembly plant. The set of customer orders is denoted $\mathcal{O}$. Each order $o \in \mathcal{O}$ comprises a set of demands $\mathcal{D}$. Each demand $d$ is related to a product $i$. Each demand specifies the quantity required for product (vehicle) $i$, the priority $w$, $w \in [0,3]$ where (0) is the most prioritised, and delays in production with respect to their promised release date from the OEM assembly plant $DD_{o,d}$ are penalised based on the products priority, and the destination $q$. We give an example of a set of customer orders in Table 1. We denote by $\mathcal{P}$ the set of all the products requested by customers' demands.

(ii) The manufacturing of each product requires a set of components. The set of all components used by the plant is denoted $\mathcal{K}$. Each

component $k \in \mathcal{K}$ is supplied by at least one supplier. The set of suppliers is denoted $\mathcal{S}$. Each supplier $s$ of component $k$ offers a standard lead time, $\ell t_{k,s}$ and an emergency lead time, $lte_{k,s}$. The OEM assembly plant incurs the costs $Sc_k^s$ and $Sec_k^s$ for the standard and emergency supply modes, respectively. The emergency supply has a shorter lead time ($lte_{k,s} < \ell t_{k,s}$) and is more costly ($Sec_k^s > Sc_k^s$). Also, each supplier $s$ has a limited capacity $Scap_{k,s}^s$. The OEM assembly plant keeps an inventory of each component.

(iii) The OEM assembly plant has a production capacity per day $Cap_t$ (products/day). Each product belongs to a set of model groups $\mathcal{G}$. For example, a product belongs to the model group $g \in \mathcal{G}$ of leather seats and to the model group of opening rooftops. There is also a limit on the number of products that can be produced per day per model group (this limit is described as a percentage of $Cap_t$). The production is also constrained by the availability of components (inventory) and by the resource constraints (related to inventory, consumption, products diversity) which ensure that there is a global equilibrium in the OEM assembly plant.

(iv) The production planning is done based on a rolling horizon logic, where the horizon is the set of periods $\mathcal{T}$ that start right after the frozen horizon, which is usually between 6 and 14 days. The production planning problem involves selecting products to manufacture in each period (day) $t \in \mathcal{T}$. The production plan is calculated daily. The production of a vehicle is always completed within the same period (the duration of assembly is 1 period). The OEM assembly plant decides whether to keep the manufactured products in the garage or to deliver them (dispatch) to the customer. The OEM assembly plant garage has a limited capacity denoted $Mfp$.

(v) For each product $i \in \mathcal{P}$, there is a promised release date which describes the start of production date that the manufacturing facility is engaged to. The promised release date is an engagement between the production planners and the sales function. Each product has an expected delivery date, which is the forecast product delivery date to the customer. It is an engagement between the sales function and the customers. The OEM assembly plant incurs a penalty if the promised release date or the forecast product delivery date is not respected.

(vi) All shipments considered in our model are direct. Therefore, any route from a supplier to the OEM assembly plant or from the plant to a final customer that involves multiple intermediate segments (e.g., an outbound journey from the OEM assembly plant via several ports to the end destination) is represented as a single, aggregated leg. The total lead time for this direct route is calculated as the sum of all constituent intermediate durations. Accordingly, while our model
coordinates transportation resources to ensure the timely delivery of components and finished products across the supply chain (encompassing both inbound and outbound logistics), it does not perform detailed route optimisation as addressed by the well-known Vehicle Routing Problem (VRP) (Laporte, 1992).

(vii) The operational costs considered in our model are based on our collaboration with the OEM plant. These costs include direct monetary expenses, such as emergency shipments and inventory holding costs (of components and finished products), as well as non-monetary factors that have a significant impact, such as order lateness, setup and unassigned capacity. These non-monetary impacts are converted into financial equivalents using weighting coefficients to integrate them into a single objective function.

## 4. Mathematical formulation

The mixed-integer linear programming model we propose aims at optimising production plans while coordinating inbound and outbound planning and minimising operational costs. In this section, we first introduce the fundamental formulation of the production planning problem.

The production planning problem or the order selection problem is the selection from the large number of car orders presented by the marketing and sales department (order bank) a subset to manufacture in the studied planning horizon, ensuring that overall capacities are not violated (Hindi & Ploszajski, 1994) over a studied horizon $\mathcal{T}$. Let $P$ be the number of products we select at periods $t \in \mathcal{T}$ where $t1$ denotes the first period in the studied horizon. The set of products $P$ is indexed with $i$. $m_{i,t}$ denotes a binary decision variable for manufacturing the product $i$ at period $t$.

$$m_{i,t} = \begin{cases} 1 & \text{if product } i \text{ is to be produced at period } t \\ 0 & \text{otherwise} \end{cases} \qquad (1)$$

We denote by $rc_i^k$ the maximum acceptable consumption volume of attribute $k$ at period $t$, attribute $k$ can be, for example, a component. The quantity of $k$ is defined with $G_{i,k}$ which describes products $i$ that require attribute $k$ (Gozinto factor, Comelli et al. (2008)), with a variable $c$ that defines the quantity needed of the attribute $k$ where $c \in \mathbb{N}$, also called the Bill of Materials BOM, such as,

$$G_{i,k} = \begin{cases} c & \text{if order } i \text{ requires attribute } c \times k \end{cases} \qquad (2)$$

Then, to maximise the number of orders selected in the studied horizon, the problem can be written as:

$$\min \sum_{i=1}^{p} \sum_{t=t1}^{\tau} -m_{i,t} \qquad (3)$$

subject to

$$\sum_{i=1}^{p} G_{i,k} \times m_{i,t} \le rc_i^k, \quad \forall k, t \qquad (4)$$

The constraint ensures that the capacity limits at the respective periods are not violated, such as the consumption capacity of attribute $k$ per period $t$. Extending the model to include other operations, such as the distribution of the products or the supply of components, requires adding other decision variables to the production planning problem.

To consider outbound distribution, the production distribution problem, is a problem where the goal is to find an optimal solution of for both the production plan and distribution of the orders (Boudia et al., 2006). The set of destinations is $Q$, the number of destinations (markets) the manufacturing orders are going to be delivered to, and $Dps_i^q$ denotes the scheduled volume of products going to market $q$ at period $t$ and $Q_i$ defines the destination $q$ of product $i$.

Two decision variables are introduced, $gr_{i,t}$, $dp_{i,t}$ that describe if order $i$ is stored in the OEM assembly plant garage after production

or dispatched at period $t$, respectively. The model then evolves and is additionally subject to:

$$m_{i,t1} = gr_{i,t1} + dp_{i,t1}, \quad \forall i \qquad (5)$$

$$m_{i,t} + gr_{i,t-1} = gr_{i,t} + dp_{i,t}, \quad \forall t > t1, i \qquad (6)$$

$$\sum_{i, \text{ where } Q_i=q}^{P} dp_{i,t} \le Dps_i^q, \quad \forall q, t \qquad (7)$$

The constraints define a continuity relationship between manufacturing, storing and dispatching an order $i$ at period $t$ and ensuring we do not exceed the available distribution scheduled capacity $Dps_i^q$ for each destination $q$ at period $t$. The model can include other constraints, such as respecting the OEM assembly plant's garage's maximum capacity, and other objectives, such as minimising unassigned capacities in distribution. We add these constraints and objectives to our model.

We introduce $I_{k,t0}$, representing the initial inventory level of component $k$. The decision variable $pc_{k,t}$ determines the quantities of component $k$ ordered from the supplier in period $t$, while $lt_k$ represents the lead time required for the component to be delivered to the manufacturing facility. $pc_{k,t}$, $lt_k$ can be extended by adding a supplier subscript $s$ to differentiate between various suppliers ($pc_{k,t}^s$). Additionally, we can introduce another decision variable ($pe_{k,t}$, or $pe_{k,t}^s$) for purchasing components in an expedited setting for emergencies, and this will incur an additional cost, as we can see in Eq. (11). The inventory level of component $k$ at period $t$ is defined by $I_{k,t}$. This extended model incorporates the Gozinto factor to map the consumption of components, ensuring a more accurate representation of the supply-production interface.

### Sets related to production planning:

$\mathcal{T}$: Set of planning periods indexed by $t$. (Cardinality: $T$), First period: $t1$, index $\tau$ represents the weeks, first week: $\tau1$.

$\mathcal{O}$: Set of customer orders indexed by $o$. (Cardinality: $O$) Order $o$ is a set of demands where each demand is a quantity of product $i$ with priority $w$.

$\mathcal{D}$: Set of demands indexed by $d$. (Cardinality: $D$), $D \subset \mathcal{O}$

$\mathcal{P}$: Set of products indexed by $i$. (Cardinality: $P$)

$\mathcal{G}$: Set of model groups indexed by $g$. (Cardinality: $G$) items of $P$ are linked to at least one item of $G$

$\mathcal{W}$: Set of priorities indexed by $w$. (Cardinality: $W$)

$\mathcal{L}$: Set of assembly lines indexed by $l$. (Cardinality: $L$)

### Sets related to supply and components:

$\mathcal{K}$: Set of components indexed by $k$. (Cardinality: $K$)

$\mathcal{S}$: Set of suppliers indexed by $s$. (Cardinality: $S$)

### Sets related to outbound distribution:

$\mathcal{Q}$: Set of destinations indexed by $q$. (Cardinality: $Q$)

$$I_{k,t1} = I_{k,t0} - \sum_{i=1}^{p} (G_{i,k} \times m_{i,t1}) + pc_{k,(t1-lt_k)} \quad \forall k, \text{ where } lt_k = 0 \qquad (8)$$

$$I_{k,t} = I_{k,t-1} - \sum_{i=1}^{p} (G_{i,k} \times m_{i,t}) + pc_{k,(t-1-lt_k)} \quad \forall k, t - lt_k > t1 \qquad (9)$$

where the constraints ensure the inventory balance and non-negativity conditions, the model can include other constraints, such as respecting maximum inventory levels, and objectives, such as minimising the supply of components. The two introductory formulations represent the foundations for the model we present in this paper: the **integrated production planning** developed in the following paragraphs. This model employs mixed-integer linear programming to combine order planning, component supply, and distribution operations.

The planning horizon is defined, and the parameters introduced in this model can be categorised into input data, such as demand, lead-time and constraint-related parameters, such as maximum production capacity. A daily or weekly subscript can link our parameters to the
studied horizon $\mathcal{T}$. For example, resource capacities may constrain the production of a model group either daily (using subscript $t$) or at an aggregated level over a week of production (using subscript $\tau$).

The decision variables in this model can be categorised into manufacturing-related variables, such as deciding which manufacturing order to produce at which period, and logistics-related variables, such as how many completed (produced) orders to hold in stock (to keep in the OEM assembly plant garages) and when to dispatch them. Moreover, supply-related variables include which part to purchase as an emergency, a classic shipment, or modifying an expected delivery period while respecting delivery lead-time. Emergency shipments have shorter lead times and are more expensive. Then, we could choose between modifying an expected shipment or ordering a new classic shipment while respecting the constraints, which involve changing the quantities expected to be delivered from suppliers.

The decision variables ($gr_{i,t}$, $I_{k,t}$, $pe_{k,t}^s$, $pd_{i,t}^q$, $dp_{i,t}$, $m_{i,t}$) are included in the objective function (F) expressed in (14) that is designed to minimise the total cost, which is the sum of four cost components. Eq. (10) (HC) represents inventory costs such as the holding cost of components and finished products; Eq. (11) (ESC) The cost of purchasing components over the planning horizon (emergency shipments) and emergency dispatch cost of product $i$ at period $t$ during the studied horizon, Eq. (12) (MC) represents the total cost of manufacturing a product, including tardiness to reduce the cost of tardiness and earliness in the studied horizon, where $\mathcal{L}(t)$ is expressed in Eq. (15) and stability($t'$, $t$) is expressed in Eq. (18), and Eq. (13) (UC) represents negative (unassigned) capacities costs.

$$HC = \phi \times [\sum_{i \in \mathcal{T}} \sum_{t \in \mathcal{T}} \sum_{g \in \mathcal{G}} (M g_{i,g} \times HG_g \times gr_{i,t}) + \sum_{k \in \mathcal{K}} \sum_{i \in \mathcal{T}} (H_k \times I_{k,t})] \quad (10)$$

### Production Order parameters:

$mi_{i,t}$ : Initial production plan over the same horizon $\mathcal{T}$.

$m'_i$ : A binary indicator for demands that are cancelled.

$DD_{o,d}$ : Promised release date $t$ of demand $d$ of order $o$.

$DD'_{o,d}$ : Expected delivery date $t$ of demand $d$ of order $o$ to the destination.

$Pr_{o,d}$ : Priority $w$ of demand $d$ of order $o$.

$O_i$ : Order $o$ linked to the product $i$.

$D_i$ : Demand $d$ linked to the product $i$.

$Q_i$ : Destination $q$ of the product $i$.

$G'_k$ : Components needed to build product $i$, Bill of Material (BOM).

$M g_{i,g}$ : A binary indicator if product $i$ is in model group $g$.

$In v^k$ : Initial Inventory of components at $t = t1$.

$Scap_{k,s}$ : Supply capacity of a component $k$ from supplier $s$ over a week $\tau$.

$Sc_k^s$ : Supply cost of component $k$ from supplier $s$.

$Sec_k^s$ : Emergency supply cost of component $k$ from supplier $s$.

$H_k$ : Holding cost of component $k$ per period $t$.

$Cap_t$ : Production capacity of the OEM assembly plant in period $t$.

$Cap'_t$ : Production capacity of the OEM assembly plant in period $t$ for group $g$.

$KL_{g,t}$ : Production flag, 1 means we could produce products from the model group $g$ at period $t$.

$rc_t^k$ : Maximum consumption capacity of component $k$ at period $t$.

$rc w_{\tau}^g$ : Weekly maximum production capacity for group $g$ in week $\tau$.

### Logistics Parameters:

$D_s^{k,s}$ : Volume of $k$ confirmed shipments from supplier $s$ delivered in $t$.

$D_s^{t,s}$ : Volume of $k$ expected shipments from supplier $s$ delivered in $t$.

$M_k$ : Maximum capacity of inventory for each part $k$.

$m_k$ : Minimum inventory to keep at the end of each period $t$.

$lt_{k,s}$ : Delivery lead time of component $k$ from supplier $s$ in classic shipment.

$lte_{k,s}$ : Delivery lead time of component $k$ from supplier $s$ in emergency shipment.

$HG_g$ : Holding cost of product $i$ in the OEM assembly plant's garage for one period $t$ for a model group $g$.

$Mf_p$ : Maximum inventory of Finished Products.

$Dps_q^q$ : Dispatch schedule for destination $q$ in period $t$.

$ltd_q$ : Delivery lead-time of order going to destination $q$.

$Dec_q$ : Dispatch emergency cost to destination $q$ of one vehicle.

$R$ : A large number.

### Due date and production cost parameters:

$\alpha_{o,d}(t, DD_{o,d})$ : Earliness cost of demand $d$ of order $o$.

$\beta_{o,d}(t, DD_{o,d})$ : Tardiness cost of demand $d$ of order $o$.

$\gamma_{o,d}(t)$ : Additional production costs of demand $d$ of order $o$.

$\mathcal{L}(t)^i$ : Cost of producing the demand $d$ of order $o$ in the period $t$.

$$ESC = \psi \times [\sum_{i \in \mathcal{T}} \sum_{s \in S} \sum_{k \in \mathcal{K}} pe_{k,t}^s \times Sec_k^s + \sum_{i \in \mathcal{P}} pd_{i,t}^q \times Dec_q] \quad (11)$$

$$MC = \epsilon \times [\sum_{i \in \mathcal{P}} (\mathcal{L}(t)^i \times m_{i,t} + \Theta_{o,d} \times dp_{i,t}) + \sum_{i \in \mathcal{P}} stf(t' \times mi_{i,t'}, t \times m_{i,t})] \\ \forall t \in \mathcal{T}, t' \in \mathcal{T} \quad (12)$$

$$UC = v \times (Cap_t - \sum_{i \in \mathcal{P}} m_{i,t}) + \mu \times \sum_{i \in \mathcal{P}} Dps_i^{Q_i} - dp_{i,t}, \quad \forall t \in \mathcal{T} \quad (13)$$

### Production Planning:

$l_{s_i}$ : Manufacturing orders not positioned in the studied horizon $\mathcal{T}$.

$m_{i,t}$ : Binary variable if product $i$ is produced at period $t$.

$gr_{i,t}$ : Binary variable if product $i$ is stored in the OEM assembly plant's garages at period $t$.

### Supply Planning:

$cp_{k,t}$ : Quantity of component $k$ consumed over a period $t$.

$I_{k,t}$ : Inventory level of each component $k$ at the end of period $t$.

$pc_{k,t}$ : Quantity of component $k$ to purchase from supplier $s$ at period $t$.

$pm_{k,t}$ : Quantity of component $k$ to add to a current delivery from supplier $s$ at period $t$.

$pe_{k,t}^s$ : Quantity of component $k$ to purchase from supplier $s$ at period $t$ in emergency mode.

### Distribution Planning:

$dp_{i,t}$ : Binary variable if product $i$ is dispatched at period $t$.

$pd_{i,t}^q$ : Binary variable if product $i$ is dispatched at period $t$ but the capacity planned $Dps_i^q$ is exceeded.

$$\text{Minimize } F = HC + \sum_{i \in \mathcal{T}} \sum_{t' \in \mathcal{T}} MC + \sum_{t \in \mathcal{T}} UC + ESC \quad (14)$$
## Total cost of production:

$$ \mathcal{L}(t)^i = \begin{cases} \alpha_{o,d}(t, DD_{o,d}) - \alpha_{o,d}(t+1, DD_{o,d}) + \gamma_{o,d}(t), & \text{if } DD_{o,d} > t, \\ - \dots - \\ Pr_{o,d}^{-1} \times [\beta_{o,d}(t+1, DD_{o,d}) - \beta_{o,d}(t, DD_{o,d})] + \gamma_{o,d}(t), & \text{if } DD_{o,d} < t, \\ - \dots - \\ \gamma_{o,d}(t), & \text{if } DD_{o,d} = t \end{cases} \quad (15) $$

The link between the product *i* and the order *o* and the demand *d* is defined by $O_i$ and $D_i$. We pre-set the coefficients: $\delta$ as the penalty factor for delay (1), $\omega$ as the weight factor for deviation from the ideal date (0.2), and $\theta$ as the weight factor for favouring smaller desired dates (0.01). The tardiness cost function $\beta_{o,d}(t, DD_{o,d})$ is monotonically increasing with the number of late days, represented by $t - DD_{o,d}$. This tardiness function is quadratic, with the coefficients $\delta, \omega$, and $\theta$. Similarly, the earliness cost function $\alpha_{o,d}(t, DD_{o,d})$ is analogous to the tardiness cost function but with smaller coefficients, signifying a higher penalty for lateness compared to earliness. Moreover, the order priority coefficient is multiplied by the lateness cost function, indicating that higher-priority orders incur higher penalties for lateness. $o, d$ are defined using $O_i$ and $D_i$, the choice of a quadratic penalty cost function to avoid single products having extreme delays. $Pr_{o,d}^{-1}$ defines the commercial priority of the manufacturing order, where four values are used between 1 and 4, and 1 is the most prioritised.

In Eq. (15) the setup cost function $\gamma_{o,d}(t)$ is introduced for specific product types, such as “bi-tone” or “opening rooftop”, requiring additional manoeuvres. The notation in Eq. (15) is previously presented in the work of Bolat (2003), and the priority is introduced into the cost:

$$ \beta_{o,d}(t, DD_{o,d}) = [\delta \times (\omega \times (t - DD_{o,d}) + \theta \times (DD_{o,d} - t))]^2 \quad \text{if } DD_{o,d} < t, \quad (16) $$

## Delivery Lateness:

The parameter $DD_{o,d}$ describes the promised release date, $DD'_{o,d}$ describes the promised delivery date to the destination, which is a prognostic date calculated using the average delays of manufacturing and transportation. In Eq. (17), we introduce the delivery lateness cost function; the function is used to calculate the cost of lateness that will be later minimised in the objective function (14). The function is used later to calculate a satisfaction indicator that measures the percentage of orders delivered within the grace period of the expected delivery, which is up to one week of a delay from the promised delivery date, as shown in the results in Table 3, $\Theta_{o,d}$ is only calculated if the dispatch period $t$ is beyond the promised delivery date $DD'_{o,d}$ otherwise the cost is null. In the industry, however, it is not recommended to have early deliveries because customers with big orders usually do not have enough space to store the products; it is recommended not to exceed two weeks before the promised delivery date, according to our interviews with the experts.

$$ \Theta_{o,d}(t, DD'_{o,d}) = [\Gamma \times (t + ltd^{O_i} - DD'_{o,d})] \quad \text{if } DD'_{o,d} < t, \quad (17) $$

## Production Plan stability:

The objective is to generate a new production plan that aligns with the initial (previous) production plan. In general, the production planners generated the initial production plan last time; if the production planner calculated the production plan daily, the initial production plan would be the day before. The stability concept is critical as OEM assembly plants adjust human resources and machinery based on specific model mixes for each production period. Maintaining stability ensures that these adjustments are not impacted. Stability is measured by comparing the initial production plan with the updated solution, accounting for cancelled demands. The stability indicator calculates the total difference between the initial date of assembly product *i* in $m_{i,t}$ and its new date in $m_{i,t}$, as shown in Eq. (18) calculated for each product

$$ stf(t', t) = a \times [(b \times |t' - t| + c \times |t' - t|)]^2 \quad (18) $$

where $a, b, c$ are coefficients of predefined values currently used by the automobile manufacturer, $t$ is the period where the demand $d$ of order $o$ is produced, $t'$ is the period where the demand has been previously positioned, and $t1$ is the first period in the studied horizon. The indicator does not consider a new demand added or a previous demand cancelled. We multiply the indicator by the coefficient $a$, which represents the percentage of demands changed or cancelled using a simple formulation $(\sum_{i \in P} mi'_i)/P$; it allows the production planner to understand better the impact of order changes on production film stability.

The OEM assembly plant is subject to specific constraints, such as the OEM assembly plant's maximum production capacity, the inventory of components and the garage where produced orders are stored at maximum capacity. The model is also subject to continuity (balance) constraints to balance between the components consumed and the orders produced, the orders stored in the garage, and the orders dispatched to the customers. The objective function is subject to the following constraints:

Continuity constraints ensure the correct balance between inventory levels, consumption and supply of components, production of orders, storage in the garages, and dispatch (distribution). These are the main constraints ensuring the correct balance between multiple operations in the supply chain. Eqs. (19) (produced orders initial balance) and (20) (components supply initial inventory balance) realise the balance at '$t1$' and Eqs. (21) (produced orders balance) and (22) (components supply inventory balance) ensure balance from '$t2$' until end of the horizon. The remainder of the constraints are production related constraints (Eqs. (23) → (29)), supply related constraints (Eqs. (30) → (36)), and outbound distribution related constraints (Eq. (34)):

$$ m_{i,t1} = dp_{i,t1} + pd_{i,t1}^q + gr_{i,t1}, \quad \forall i \in P \quad (19) $$

$$ \begin{aligned} I_{k,t1} = & Ds_{k,t1}^{k,s} + Inv^k - cp_{k,t1} + pm_{k,t1}^s \\ & + (pc_{k,t1-lt_{k,s}}^s + pe_{k,t1-lte_{k,s}}^s, \quad \text{if } lt_{k,s} = lte_{k,s} = 0) \\ & \forall k \in \mathcal{K}, s \in S \end{aligned} \quad (20) $$

$$ dp_{i,t} + gr_{i,t} + pd_{i,t}^q = gr_{i,t-1} + m_{i,t}, \quad \forall i \in P, t \in \mathcal{T} \ \& \ t > t1 \quad (21) $$

$$ \begin{aligned} I_{k,t} = & I_{k,t-1} - cp_{k,t} + (pc_{k,t-lt_{k,s}}^s + pe_{k,t-lte_{k,s}}^s, \quad \text{if } t - lt_{k,s}, t - lte_{k,s} \ge 0) \\ & +Ds_{t}^{k,s} + pm_{k,t}^{s}, \quad \forall k \in \mathcal{K}, s \in S, t \in \mathcal{T} \ \& \ t > t1 \end{aligned} \quad (22) $$

$$ \begin{aligned} \sum_{i \in P} m_{i,t} \le Cap_t, \quad \forall t \in \mathcal{T}, & \\ (pc_{k,t-lt_{k,s}}^s + pm_{k,t-lte_{k,s}}^s) \le Scap_{k,s}^\tau, \quad \forall k \in \mathcal{K}, s \in S, t \in \mathcal{T}, \tau \in \mathcal{T} \ \& \ t - lt_{k,s} \in \tau \end{aligned} \quad (24) $$

$$ \sum_{i \in P} (m_{i,t} \times Mg_{i,g}) \le Cap_{g,t}^s \times KL_{g,t}, \quad \forall t \in \mathcal{T}, g \in G \quad (25) $$

$$ \sum_{i \in P} G_{i,k} \times m_{i,t} \le rc_t^k, \quad \forall k \in \mathcal{K}, t \in \mathcal{T} \quad (26) $$

$$ \sum_{i \in P} (m_{i,t} \times Mg_{i,g}) \le rcw_{\tau}^g, \quad \forall \tau \in \mathcal{T}, g \in G \quad (27) $$

$$ \sum_{i \in P} (ls_i + \sum_{t \in \mathcal{T}} m_{i,t}) = P \quad (28) $$

$$ \sum_{i \in P} gr_{i,t} \le Mfp, \quad \forall t \in \mathcal{T} \quad (29) $$

$$ I_{k,t} \le M_k, \quad \forall k \in \mathcal{K}, t \in \mathcal{T} \quad (30) $$

$$ I_{k,t} \ge m_{k,s}, \quad \forall k \in \mathcal{K}, t \in \mathcal{T} \quad (31) $$

$$ cp_{k,t} = \sum_{i \in P} m_{i,t} \times G_{i,t}^q, \quad \forall t \in \mathcal{T}, k \in \mathcal{K} \quad (32) $$
<figure><img src="image_4.png" /><figcaption>Fig. 2. Summary of model's decision variables and constraints.</figcaption></figure>

$$pm_{k,t}^s \le R \times Ds_t^{t,k,s} \quad \forall t \in T, k \in \mathcal{K}, s \in S \quad (33)$$

$$\sum_{i, \text{ where } Q_i=q}^{P} dp_{i,t} \le Dps_t^q, \quad \forall q \in Q, t \in T \quad (34)$$

$$m_{i,t}, gr_{i,t}, dp_{i,t}, pd_{i,t}^q \in \{0,1\}, \quad \forall i \in P, t \in T, q \in Q \quad (35)$$

$$pm_{k,t}^s, ls_i, pe_{k,t}^s, pm_{k,t}^s, pc_{k,t}^s, cp_{k,t}, I_{k,t} \in \mathbb{N} \quad \forall t \in T, k \in \mathcal{K}, s \in S, i \in P \quad (36)$$

Constraint (23) ensures production does not exceed the capacity per period, and constraint (25) ensures that the capacity of production of each model group (Cap'g,t) is not exceeded. Production should also not exceed the resource constraint, whereas the daily (constraint (26)) and weekly (constraint (27)) resource constraints are translated in $rc_t^k$ and $rcw_t^g$. The resource constraints reflect global manufacturing limits that not only ensure production harmonisation over a longer planning horizon but are also and are essential for representing other operational constraints, such as those related to human resources, machine capacities, and specific facilities like the paint workshop capacity. Constraint (28) balances products between production and a lost sale; the sum of both should equal the total demand. For the supply-related constraints, constraints (30), (31) ensure inventories of components do not exceed maximum and minimum limits respectively, constraint (32) update components consumed at each period, and constraint (36) ensures that the purchase can only be modified if an expected delivery is scheduled for the same period t where R is a sufficiently large number.

Constraint (34) ensures that dispatch capacities are not violated in the outbound distribution. We only purchase dispatch if the planned distribution capacity exceeds the orders we need to dispatch at period t. This is done by respecting the dispatch capacity constraint and adding cost to $pd_{i,t}^q$ while including it in the *Produced orders initial balance* constraint. In that sense, $pd_{i,t}^q$ will only be greater than zero if $dp_{i,t}$ is constrained by $Dps_t^q$. The cost of emergency dispatch is small compared to holding the product until a dispatch capacity is available and the lateness are available.

Fig. 2 visualises the decision variables area of application over the supply chain network studied and the constraints. The mathematical model's objective function aims to find an optimal solution while respecting global industrial constraints. However, applying the model to a complex system makes interpreting the solution challenging. To

address this, we incorporated aggregated indicators to help users of the model better understand the impact of the solution on orders and introduced industry-specific rules to meet the use case's requirements. In Section 5, we present indicators related to the service level. We introduce supply and distribution rules, which provide a more accurate representation of the costs associated with these operations.

## 5. A case study in renault assembly plant

This section focuses on applying the model developed in a Renault assembly plant. We aim to compare the production plan results obtained by our model against those obtained by the existing industrial tool used at Renault and subsequently evaluate the performance of our model in a scenario involving significant outbound distribution disruptions.

As explained before, the plant's current planning process involves teams operating in a fragmented approach that limits end-to-end coordination. Fig. 1 shows that teams often function in a client-supplier relationship with unidirectional information flow. For instance, the production planning team primarily serves the commercial team, which manages the order bank and communicates with the customer the projected delivery date based on the expected delays in assembling and delivering the product. Subsequently, the OEM assembly plant is the client for the supply and distribution services, which are expected to adapt to its needs. This current structure leads to misaligned performance objectives and additional costs. The production planning team prioritises respecting manufacturing order release dates and adhering to internal constraints, ensuring no component inventory deficits or impacts on other orders. On the other hand, the distribution planning team focuses on optimising their available capacity, minimising finished goods inventory in garages, and meeting customer delivery dates. These misaligned objectives lead to a production plan optimal for the OEM assembly plant (e.g., a high degree of adherence to release dates), which is often sub-optimal from an end-to-end supply chain perspective, potentially significantly increasing overall costs or failing to utilise available distribution capacities.

The case study presented in this section represents a broader collaborative project with the company, covering multiple use cases across three factories located in different areas, aiming to quantify the benefits of integrated operations facilitated by our model. Indeed, to demonstrate our model's capability in addressing such outbound distribution
coordination with production planning challenges, we applied it in several contexts. In an OEM assembly plant in Europe, where finished products are transported by commercial boats between busy ports (e.g., between the port of Barcelona in Spain and the port of Livorno in Italy), distribution planners often work with average weekly maritime capacities rather than precise capacities. Our model proved its value, enabling the supply chain to use available capacities when increased (e.g., from 700 to 900 places available) and ensure maximal capacity utilisation (i.e. adapt the production volumes to the available distribution capacity).

Another scenario was tested in an OEM assembly plant in Latin America. Vehicles are transported via large maritime vessels from Brazil to Mexico (from the Santos Port of Brazil to the Tuxpan Port of Mexico), where distribution planners book places in advance with 3-PL transporters. Our model can easily accommodate this context; for example, the parameter $Dps_i^q$ represented weekly dispatch capacity for the case in the European assembly plant ($t \to \tau$) and daily dispatch capacity for the case in the Latin American assembly plant. Furthermore, our model was tested on integrating inbound operations with the production planning and validated at another OEM assembly plant in Europe. We tested the model on multiple disruptive scenarios, including component shortages and unexpected changes in production volumes—situations where current planning tools and information flows provide limited visibility for identifying feasible, integrated solutions that minimise the impact of disruptions and operational costs.

These applications across different factories and challenges (as viewed in the sensitivity analyses in Appendix A) support the portability of our model, demonstrating its ability to provide robust and efficient solutions in varied real-world manufacturing environments. The remainder of this section is threefold: first, in 5.1, we explain how the data from the OEM assembly plant was collected and some industry-specific policies we integrated into our model; second, we evaluate the service levels. In 5.2, we explain the experiment setting and show the results of our model in an operational scenario without a disruptive event where we compare the production plan given by our model with the production plan given by the current production planning tool used by the OEM assembly plant, then we show the results when a disruptive event takes place in the supply chain.

## 5.1. Case study specific data collection, industrial rules and solution indicators

This section introduces how we collected data and formulated rules and policies necessary for the numerical study.

### Data collection

The data is collected from different industrial tools. The tables are uploaded into the company's data cloud; depending on the tool, the data is exported on a defined frequency (i.e. daily, weekly). Fig. 6 displays the four main blocs of data sources from which we collected data from a high-level perspective. We categorised data into four main blocs: (1) Manufacturing orders data, such as the release dates and the commercial priority; (2) the industrial capacities data, such as the manufacturing capacity and the human resources; (3) the inbound supply and supplier's data, such as the expected shipments and the suppliers' capacity, (4) the outbound distribution data, such as the lead times of deliver, costs and capacities. The data presented in Fig. 6 is managed within a centralised data lake deployed on the Google Cloud Platform (GCP) and was collected using a set of SQL queries developed during our work. It was then filtered and validated using Python to generate problem instances. These instances provide input for the optimisation model, including parameter data such as initial inventories and constraint data such as manufacturing capacity over the planning horizon.

### Industrial rules

Indeed, in our work, we introduce two rules specific to the automotive industry: one related to outbound distribution operations costs and one related to supply decisions. Both rules are introduced to our model, where the dispatch cost is evaluated using the dispatched volumes for each destination $q$ within the given dispatch capacity limits. The emergency dispatch cost, however, remains fixed ($Dec_q$). The supply capacity rule is applied to the parameter ($Scap_{k,s}^r$) that is included in Eq. (24).

### Distribution cost over capacity:

The contracts with 3-PL companies are usually over a long term (from 1 to 3 years) where the customer (the car manufacturer) defines a volume of vehicles to be transported from one OEM assembly plant to a specific destination; the volumes are based on the long term master production scheduling (from 1 to 2 years), contractually, certain flexibility can be implemented depending on the agreement between both parties (e.g. for a route OEM assembly plant/destination (OEM, q) the volume of cars that can be transported is 1000 +/-10%) the flexibility percentage can range from 0 to 15%, usually in maritime transport flexibility is lower than road transport. Exceeding this flexibility, the distribution team negotiates additional capacity with their suppliers at an additional cost, and in some cases, they subcontract with another 3-PL supplier if the first supplier cannot provide the capacity required; in the latter case, the additional cost is more consequential.

In this context, we introduce the following distribution cost structure: for each week $\tau$ of the studied horizon with length $T$, the volumes (number of products) we should distribute $v$, we define a general transportation cost function $DC_{\tau,q}(v)$ a nondecreasing and piecewise linear in the total volume transported $v \ge 0$. Let $V_q$ denote the volumes set for each destination $q$ representing a different cost level; for simplification, we denote the intervals with numbers $\{V_q1, \dots, V_qn\}$, knowing that the first volume level is within the contractual flexibility. The cost function $DC_{\tau,q}(v)$ is formulated as follows:

$$DC_{\tau,q}(v) = \begin{cases} 0 & \text{if } v < V_q 1, \\ b1 & \text{if } v \in [V_q 1; V_q 2), \\ \dots & \text{if } v \in [V_q n - 1; V_q n], \\ bn & \text{if } v \in [V_q n - 1; V_q n], \\ \infty & \text{if } v > V_q n \end{cases} \quad (37)$$

### Supply rules in the horizon:

We compare the ordered quantities against the supplier's available capacity to manage supplier capacity constraints in our production planning model. For instance, if a supplier can provide 2000 parts in an industrial week $Sx$, this quantity is initially assumed to be available. However, if an order is already confirmed, the supplier may allocate this capacity to another customer, limiting the supply planner from increasing the order quantity on short notice.

Based on interviews with supply planners, we developed a rule to handle this scenario more accurately than relying solely on supplier capacity, which is often erroneous for short-term planning. The constraints and parameters we established, while rough estimates, provide a more realistic approach. These parameters are indicative and open to discussion.

The rules developed are as follows (compared to the date of the order confirmation): Horizon 1 (0 to 3 weeks): No flexibility versus the programmed quantity (frozen). Horizon 2 (4 to 6 weeks): Maximum flexibility of 4% versus the programmed quantity within capacity limits. Horizon 3 (7 to 9 weeks): Maximum flexibility of 6% versus the programmed quantity within capacity limits. Horizon 4 (3 months and beyond): The full capacity can be considered. These rules enable more realistic planning by accounting for the supplier's potential capacity reallocation and providing a structured framework for flexibility based on the planning horizon.
A fundamental difference exists between the distribution and component suppliers. The first has allocated space that we can consume and is usually paid upfront by contracts that endure from 1 to 3 years; for the latter, the manufacturing facility is more dynamic and has a production line that produces for many customers (car manufacturers), so maybe the distribution supply should be more flexible and modify the politics of contracting. Still, vehicle distribution is limited in capacity in markets such as Europe, which drives car manufacturers to prefer maintaining stable, long-term contracts instead of short-term ones and ensuring customer satisfaction.

## Solution quality indicators

Our model aims to minimise the holding cost of finished products, purchased materials, and lateness-associated costs. However, not all production plans (scenarios) are equal. To evaluate and compare different production plans, we introduce the following indicators (the service level and the service level per order). These indicators allow users to understand better the solution provided by the optimisation model and its impact on the orders, such as the impact of the new production plan concerning the promised release dates of each order.

We calculate the percentage of dispatches compared to the total demand for the service level indicators. This indicator translates the percentage of demand satisfied. The following equations illustrate the calculation of this indicator:

$$SL1 = \frac{\sum_{i \in P} \sum_{t \in T} \sum_{q \in Q} (d p_{i,t} + p d_{i,t}^q)}{P} \quad (38)$$

Eq. (38) shows the global service level, the ratio of demand fulfilled over the total number of products to build; a demand is fulfilled when the order is dispatched.

$$SL2(o) = \frac{\sum_{i \in P, \text{ where } O_i = o} \sum_{t \in T} \sum_{q \in Q} (d p_{i,t} + p d_{i,t}^q)}{\sum_{i \in P, \text{ where } O_i = o} (i)} \quad (39)$$

Eq. (39) shows the service level of each order. The service level indicator allows the production planner to evaluate if the service level impact affects a specific group of orders, and the model allows the user to evaluate the service level over each demand simply by replacing $O_i$ by $D_i$.

The indicators provide production planners with insights into the solution. For instance, they can identify how significantly a particular disruption affects specific orders, allowing them to respond effectively. In our application, these indicators are secondary and not included in the objective function (1) to avoid overcomplicating the objective function and (2) due to the complexity of quantifying these indicators. The lack of visibility on the volume of each order makes it challenging to generalise the objective function. Customer satisfaction is also calculated, and the delivery date should be within a specific time window that does not exceed two weeks before the promised delivery date and one week after that date; we calculate the customer satisfaction in Eq. (40), where a customer receiving an order that is on time and in full (OTIF) is satisfied, to calculate this we extend Eq. (39) to calculate the percentage of all products i that are linked to the demand d are delivered within the current time window interval $[DD'_{o,d} - 15d; DD'_{o,d} + 7d]$, we define this indicator to be our customer satisfaction metric, which indicates the aggregated percentage of orders delivered in time and in full.

$$SL3 = \frac{\sum_{d \in D} \left( \frac{\sum_{i \in P, \text{ where } D_i = d} \sum_{t \in T, \text{ where } i \in \{DD'_{o,d} - 15d; DD'_{o,d} + 7d\}} (d p_{i,t} + p d_{i,t}^q)}{\sum_{i \in P, \text{ where } D_i = d} (i)} \right)}{D} \quad (40)$$

## 5.2. Experiment setting and results

We presented the industrial context, and the data collected spans over the period from the industrial week (S8) to the industrial week (S10) of 2024; the data was collected during the industrial week (S5) the reason is twofold: (1) to be able to study the horizon before entering into the frozen period (between 6 and 14 days) which is the period in the industry where we cannot change the production plan except for disruptions within the OEM assembly plant such as a disruption in the human resources due to social movements or a technical incident, (2) this allows us to have flexibility over the supply quantities ordered (see Section 5.1).

Our experiment compares our model's end-to-end production plan with the industrial tool's production plan (Sc1). Secondly, we show how the production plan can adapt to a distribution constraint while minimising the impact on the supply chain echelons (Sc2) and compare the outcome with the industrial tool's production plan. In both tests, we compare plans over the following criteria: (a) supply of components cost, (b) production plan stability, (c) the holding cost of components and the holding cost of assembled vehicles, and (d) the lateness impact on vehicles that were rescheduled and the impact on the solution quality indicators presented in Eqs. (38) → (40).

The program is coded in Python and runs on a laptop with an AMD Ryzen 3 PRO 5450U with Radeon Graphics (2.60 GHz) in 50 s based on an average of 10 runs. We use Gurobi® to solve integer and linear programs. In total, 8251 manufacturing orders were planned over a horizon of three weeks; the problem is to find an integrated supply, production, and transportation plan that fulfils all manufacturing orders to minimise inventory holding and transportation costs while minimising additional operational costs related to emergency shipments and distributions and respecting customer satisfaction by respecting the promised delivery and release dates.

In the 8251 manufacturing orders planned for assembly in an OEM assembly plant that has a daily production capacity of $Cap_i$ of 650 manufacturing orders, 902 manufacturing orders are delivered to a specific market (destination) and have planned release dates in the industrial week S10, henceforward called Target Population, in our first study, we run our model using our end to end data framework (Fig. 6) where we compare the production plan given by the model with the production plan generated by the current industrial tool (see Figs. 3 and 5) where the target population is shown in black and other manufacturing orders are shown in grey.

The industrial tool's production plan exists in the data we collected. However, the tool does not show the plan's costs, so to compare the industrial tool's production plan with our model, we introduced the exact dates of production planned in the industrial tool as a constraint to the model. We implemented a hard constraint where $m_{i,t} = m_{i,t'}$, $\forall i \in P, t \in T$. This constraint allowed us to evaluate the performance of the industrial tool's production plan on the same objective costs that our current model minimises. The results of this experiment are presented in the sections below. In the first part, we test our model on an instance at a Renault OEM assembly plant. To highlight the differences between the plans, we focus on manufacturing orders in the target population going to a specific destination.

### 5.2.1. Comparing our model with the industrial tool production plan

We first analyse the production plans from the target population's perspective. We can see a significant shift in the dates planned for the target population, where 510 manufacturing orders for the target population will be released on the industrial week (S10). The remaining 392 orders from the target population will be released during industrial week (S8). Our analysis shows that no additional costs were linked to buying more spaces for the distribution capacities. However, we notice a significant reduction in the holding of components with a decrease of 80.1%; this change in dates increased the instability. In total, 5088 manufacturing orders changed the planned release dates compared to
<figure><img src="image_5.png" /><figcaption>Fig. 3. (a) the production plan using the current industrial tool at Renault, (b) the production plan using our model.</figcaption></figure>

the industrial tool's production plan, displaying a larger spectrum of lateness between 0 and 5 days, with 35.44% of the manufacturing orders better adhering to the promised release dates. We also noticed in the production plan that the volume of orders in the last period (08/03/2024) is slightly lower in our model because the industrial tool has an additional objective to smooth the volumes over the horizon, which we decided to eliminate. After all, it contradicted the objective of minimising the unassigned production capacities we introduced in our model.

This change in the production plan better adapts to the objective of reducing the inventory levels, which directly impacts the holding cost. Regarding the supply of components, only an increase in orders from suppliers of 2% is generated. No emergency supply of components was required for both production plans, the average lateness was increased by 0.7 days, which impacted the adherence to the release dates, and the customer satisfaction dropped from 97.84% to 95.64% which is not a significant drop but shows how small compromises in other objectives (in our case in the adherence to the release dates and the customer satisfaction) can serve the overall supply chain operational costs, so by reducing the holding of components.

### 5.2.2. Impact of a disruptive event impacting the planned outbound distribution capacities

In October 2023, the outbound distribution team informed the production planning team of limited space on a maritime transport scheduled for the 10th industrial week of 2024 ($S_{10}$, first week of March). They requested that only 200 vehicles destined for a specific market be released this week, as any additional orders would incur high holding costs in either the OEM assembly plant's or the port's garages. The production planning team had initially scheduled the release of 902 vehicles in $S_{10}$, but with the transport disruption, only 200 could be shipped. Proceeding with the original plan would leave 702 vehicles waiting in the port garage if they leave the garage of the OEM assembly plant, generating holding costs.

Both teams should ensure that this change will not impact the supply planning; The manufacturing facility and its suppliers are linked directly. In turn, component suppliers are indirectly connected by unique customer orders and the associated Bill of Materials (BOM). Consequently, the OEM assembly plant's weekly production schedule changes impact the material requirements planning and other suppliers'

associated quoted call orders. This interconnectedness means initiating countermeasures can lead to cascading disturbances in the supply chain (see Fig. 1).

If operational costs are generated (e.g., emergency shipments of some components), they should be much less than storing the assembled products in the port. In standard settings, the objective is to minimise inventory. However, according to industry experts, excess volumes due to unconsumed components are tolerated during supply chain disruptions, as it is a better scenario than not having sufficient quantities of the necessary components. The advantage of our study is that we have the real industry costs of holding, the supply, and the emergency supply of components. The only cost we could not calculate is customer satisfaction. Still, we know that the promised delivery date can be exceeded by a defined number of days, so we implemented that into our formulation (see 5.1). Fig. 4 displays two configurations: on the left, we present how the production plan adapts to the distribution plan and holding costs while presenting the orders to the studied destination with the flag with zigzag lines and other markets with straight lines. On the right side, the condition is to keep 200 vehicles in this industrial week ($S_{b}$), and we show how the production plan reacts accordingly. The figure reflects this change in the number of vehicles with straight and zigzag lines.

Our model found an optimal solution by selecting 200 orders from the 902 orders in the industrial week $S_{10}$ instead of the 902 initially selected. The only metric we could compare was the average lateness compared to the promised release dates, where the average lateness in our model for the 8251 manufacturing orders is 1.817 days, which is a decrease in the adherence to the release dates compared to the current industrial tool by 44.96%.

Our model only selected 200 vehicles from the target population, positioning the rest (702 orders) in earlier weeks, as shown in Fig. 5. This is done by changing the data in $Dps_t^q = 200$, and $pd_{i,t}^q = 0$ at $t \in \tau = S_{10}$ and $q$ = destination of Target Population. The other 702 was in the industrial week $S_{9}$, which is logical since the objective is to maintain stability and respect the initial promised release dates. This change satisfies the objectives of the distribution team but comes at a cost. We also noticed the choice of producing the orders of the target population on the last production day of the industrial week $S_{10}$, to reduce the holding cost of the assembled orders.
<figure><img src="image_6.png" /><figcaption>Fig. 4. Use case description.</figcaption></figure>

The most significant impact of introducing this disruption is the increase in the cost of supply of components of 87.41% and a decrease in the cost of modifying programmed shipments of components of 30.24%; this explains how a change in the production plan can impact supply decisions. In further analysis, the model found the optimal solution by suggesting new commands from suppliers since the expected shipment dates did not align with the change in the production plan; this new command impacted the expected deliveries later, resulting in a few modifications in the expected deliveries. Table 2 displays the supply and consumption data of a component chosen randomly to represent the impact of the production film on the inbound operations. Customer satisfaction is also impacted by a decrease of 19.8%, which is logical since 702 orders for other markets (destinations) are pushed to the industrial week S10, which increases the average lateness of 44.96%. Finally, the stability of the production plan is impacted, as 5477 manufacturing orders changed the planned release dates compared to the industrial tool's production plan.

We could compare the case with only 200 vehicles from the target population in industrial week S10 to the case where the current production planning tool used by the team placed 902 vehicles if we introduce some assumptions on the operations. The distribution team's request was not fulfilled. Two potential costs arise: (a) in the best-case setting, we assume there are 702 available spaces in the garage, and the additional cost would be holding these vehicles in the OEM assembly plant's garage since they cannot be transported to the port; (b) in the worst-case setting, there is no capacity to hold these vehicles in the garage, and they must be dispatched to the port to wait for shipment. The additional cost of not coordinating with the distribution team while using the current industrial production planning tool lies between these extremes that we calculated: [30, 221; 37, 231] €, and the details of our cost estimation are in Appendix B.

In addition to the objectives linked to the inbound supply, we further analyse the following indicators that can be categorised into aggregated indicators and indicators on the component level. For the first category, we look into the inventory levels at each period in the studied horizon and the total cost of holding, supply, and emergency operations. We also analyse inventory levels that are close to the security stock level. On the component level, we look into the consumption, the modifications to expected deliveries, and the supplier information. Table 2 shows an excerpt of the data for a component. The values have been modified to preserve industrial confidentiality.

Table 2 displays multiple information about the components consumed in the assembly of the orders. In this example, we present the engine MOT-6954R (a pseudonym of an engine component), where we have visibility on the supplier's long-term and short-term capacity, where the long-term supply capacity is for orders that are for dates in the horizon 6 months from the date the order was confirmed. The short-term is for other orders below 6 months. This is done while respecting the industry-specific rules presented in 5.1, the lead time of the engine is one day since the supplier of the engine is an OEM,

<caption>Table 2</caption>

An excerpt of the supply data on a component level (dates 23/02, 24/02, and 27/02 are removed from the table since no consumption (Cons.), Supply or Supply Modification took place).

<table><tbody><tr><td>Reference code</td><td colspan="10">MOT-6954R</td></tr><tr><td>Description</td><td colspan="10">Engine</td></tr><tr><td>Initial inventory</td><td colspan="10">357</td></tr><tr><td>Supplier code</td><td colspan="10">SE-297</td></tr><tr><td>Supplier name</td><td colspan="10">Engine Supplier</td></tr><tr><td>Lead time</td><td colspan="10">1</td></tr><tr><td>Supplier Cap. ST</td><td colspan="10">50</td></tr><tr><td>Supplier Cap. LT</td><td colspan="10">150</td></tr><tr><td>Cost</td><td colspan="10">900</td></tr><tr><td>LT emergency</td><td colspan="10">1</td></tr><tr><td>Cost emergency</td><td colspan="10">500 + 900</td></tr><tr><td colspan="12">Expected confirmed deliveries</td></tr><tr><td>Dates</td><td colspan="10">20/02</td></tr><tr><td>Quantity</td><td colspan="10">143</td></tr><tr><td colspan="12">Expected provisional deliveries</td></tr><tr><td>Dates</td><td colspan="10">-</td></tr><tr><td>Quantity</td><td colspan="10">-</td></tr><tr><td>Dates</td><td colspan="10">-</td></tr><tr><td>Cons.</td><td>Sc1</td><td>0</td><td>427</td><td>73</td><td>0</td><td>0</td><td>0</td><td>0</td><td>42</td><td>237</td><td>411</td><td>70</td></tr><tr><td></td><td>Sc2</td><td>0</td><td>427</td><td>73</td><td>0</td><td>6</td><td>7</td><td>234</td><td>17</td><td>176</td><td>250</td><td>70</td></tr><tr><td>Supply</td><td>Sc1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td></td><td>Sc2</td><td>0</td><td>0</td><td>0</td><td>6</td><td>0</td><td>234</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>Supply M.</td><td>Sc1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>42</td><td>237</td><td>411</td><td>70</td></tr><tr><td></td><td>Sc2</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>7</td><td>0</td><td>17</td><td>176</td><td>250</td><td>70</td></tr></tbody></table>

the lead time is small, the cost of one unit is calculated in euros, and the emergency cost is added to the normal cost if the component is ordered in the emergency mode. The emergency lead time is much shorter than the normal lead time for other components since the components in everyday scenarios are delivered with maritime transport. The component is delivered in an emergency by air transport. For each component, we have visibility of expected deliveries, where some are confirmed, where we cannot modify the quantity, and other deliveries are provisional, where we can modify the quantity until it is confirmed from the supplier side.

For the outbound stream, we can calculate the aggregated indicators: the total cost of outbound distribution and distance travelled, the consumption of available trucks and the percentage of unused capacity, the total number of vehicles to dispatch to their respective markets, and customer satisfaction. On the vehicle level, we have the following information: the distribution cost, the truck identifier, the expected
<figure><img src="image_7.png" /><figcaption>Fig. 5. (a) the production plan using the current industrial tool at Renault, (b) the production plan using our model.</figcaption></figure>

<table><caption>**Table 3**
An excerpt of the outbound distribution data for each manufacturing order.</caption><tr><td>Order ID</td><td>1-1-3-1</td></tr><tr><td>Planned Prod.</td><td>21/02/2024</td></tr><tr><td>Holding in garage</td><td>0</td></tr><tr><td>Dispatch date</td><td>21/02/2024</td></tr><tr><td>Earliest arrival date</td><td>27/02/2024</td></tr><tr><td>Latest arrival date</td><td>03/03/2024</td></tr><tr><td>Expected arrival date</td><td>08/03/2024</td></tr><tr><td>On time delivery</td><td>1</td></tr><tr><td>Travel Distance (km)</td><td>730</td></tr><tr><td>Transport mode</td><td>Truck</td></tr><tr><td>Transport supplier (3-PL)</td><td>Transport Company</td></tr><tr><td>Transport Identifier</td><td>SU-50017</td></tr><tr><td>Destination centre</td><td>CE-0017</td></tr><tr><td>Arrival city</td><td>Cachoeirinha</td></tr><tr><td>Country</td><td>Brazil</td></tr><tr><td>Commercial priority</td><td>3</td></tr></table>

arrival date, and the lateness compared to the promised arrival date. Table 3 shows an excerpt of the data with the values modified for confidentiality.

Table 3 displays information linked to the outbound distribution operations; the dispatch plan is based on availability constraints of transport modes headed to a particular destination that the (3-PL) supplier provides. Our model currently considers that outbound distribution occurs in a single step. Customer satisfaction is measured by comparing the expected arrival date to the customer and the calculated arrival date.

The current production planning approach remains fragmented due to its limited integration with other production stages, such as in-bound logistics, warehousing, and distribution. It restricts the current stakeholders' ability to make better decisions, especially in disruptive scenarios, and the overall process efficiency. Our model enables a more resilient and adaptive planning process, reducing instability and improving decision-making. As a result, disruptions that previously required days to resolve can now be managed within the same day (an improvement in the time to recovery). The model also simplifies processes, alleviates stress for planners, and, most importantly, prevents avoidable costs, ensuring a more efficient and stable supply chain. While evaluating all the costs that could be avoided is complex, we

show in (Appendix B) an example of one of the costs we reduced in our use case.

Our model focuses on key supply chain performance metrics. With visibility on supplier delays, inventory levels, and distribution constraints in the production planning process, we automatically enhance adherence to customer on-time delivery and reduce the time from order placement to final delivery, minimising distribution inventory days. These improvements ensure an improvement in the on-time delivery and a more accurate delay (time to produce and deliver the manufacturing order) calculation; the end customer satisfaction is measured by ensuring deliveries occur within a set time window, no more than two weeks early and no more than one week late.

The production planners then assess the new scenario by comparing the additional operational costs with the holding costs of vehicles at the port. If the increase in operational costs is significantly lower than the holding costs, it is advantageous to implement the change. If a scenario is implemented, they have to ensure its feasibility with the stakeholders, such as the component suppliers and the 3-PL providers, so a minor modification to the scenario can be expected. For the first time, this scenario provides the supply chain team with a quantitative and prescriptive tool that facilitates informed decision-making, optimising the performance of various components within the supply chain at Renault.

## 6. Conclusions

In this paper, we developed a model for optimising a production plan in an OEM plant. The model is designed to adapt dynamically to disruptions across the supply chain. Its primary objective is to minimise operational costs while maintaining stability in disruptions. Developed with an industrial partner, the model leverages digital tools to enhance decision-making during crises and improve overall supply chain resilience. Through our case study, we examined critical operational challenges, such as whether the available distribution capacity could accommodate all deliveries to the port and the additional costs incurred when it could not. We also analysed the ability of the supply chain to fulfil all production requirements, as well as the consequences — both financial and in terms of customer satisfaction — of potential delays.
Beyond this case, our study can be applied to other industries, addressing the inefficiencies of siloed supply chain operations and promoting a more integrated, resilient approach to production planning.

The work presented stands out due to its realistic approach, providing insights that align closely with industry scenarios. By comparing our production plans with outcomes from other data instances, we ensured that our solutions reflected feasible and practical situations. Industry experts further validated this scenario, reviewing our findings and confirming that the proposed model offers valuable, prescriptive guidance. The integration should be seen from a process lens; a key contribution of integrated planning would be a faster response to disruptions in the supply chain, going from multiple days to react to a disruptive event to finding a solution on the same day, and process bottlenecks should be identified in the research.

Despite its strengths, our model has some limitations. First, while we leverage a rich dataset, we use an aggregated approach while modelling inbound and outbound logistics. We assume all shipments are direct. Consequently, any multi-echelon route from the manufacturing facility to the final customer, such as a vehicle's outbound journey involving multiple steps from the OEM assembly plant to the end destination, is aggregated into a single, direct route. The total lead time for this aggregated route is the sum of all intermediate leg lead times. Second, aggregation also affects resource capacity modelling, combining multiple factors, including machine capacity and human resource availability, potentially oversimplifying real-world constraints. Third, the model suggests component orders based on the expected delivery dates in the supply plan, which are subject to change. Since we assume deterministic lead times, the model does not explicitly account for supply uncertainty.

For future research, one potential direction could be to extend the studied horizon to a longer one, ideally a six-month planning horizon to match the output of industrial tools in the market. To achieve this, one may explore alternative mathematical modelling approaches to maintain acceptable execution times, such as aggregating the production plan by weeks instead of days or narrowing the focus to critical components. Secondly, while our model demonstrates the value of integrated planning, particularly in responding to disruptions, its applicability beyond automotive and assembly-based industries requires adaptation. For instance, industries such as food (Aazami & Saidi-Mehrabad, 2021; Guarnaschelli, Salomone, & Méndez, 2020), textiles (Darvishi, Ghasemy Yaghin, & Sadeghi, 2020), and oil & gas (Bonino et al., 2025) would require industry-specific constraints and parameter adjustments.

## CRediT authorship contribution statement

**Ayman Mahmoud:** Writing – review & editing, Software, Formal analysis, Visualization, Methodology, Conceptualization, Writing – original draft, Project administration, Data curation. **Mohammed Hichame Benbitour:** Validation, Methodology, Writing – review & editing, Project administration, Conceptualization, Supervision, Investigation. **Evren Sahin:** Writing – review & editing, Project administration, Funding acquisition, Supervision, Investigation, Validation, Methodology, Conceptualization. **Zied Jemai:** Supervision, Validation, Conceptualization, Writing – review & editing, Project administration. **Marc Baratte:** Validation, Funding acquisition, Project administration, Supervision.

## Acknowledgment

This research was conducted in partnership with the Renault Group and the Laboratoire de Génie Industriel (LGI). The project was funded by the French ANRT (Association Nationale de la Recherche et de la Technologie) through the CIFRE grant N° 2021/1344.

## Appendix A. Sensitivity analysis

The sensitivity analysis conducted throughout our model's development aimed to evaluate its robustness under various conditions, ensuring its applicability in different industrial settings. By testing different parameters and disruption scenarios, we examined how the model adapts to changes in (1) problem size, (2) disruptions, and (3) cost weights. The experiments were performed on synthetic and industrial data from multiple Renault factories.

For the first study, we evaluated the execution time and computational limits. Since the problem we are tackling is NP-Hard, we needed to ensure that the problem sizes we introduced could be resolved within acceptable time frames. As our application is not real-time, we have a relaxed threshold margin, accepting solutions within a cut-off time of 20 min. Given the context of our application, which does not require immediate or optimal solutions, we did not develop a metaheuristics approach.

We introduced varying problem sizes to reflect real-world data from Renault's factories, ranging from small-scale scenarios to large-scale OEM assembly plant operations, to identify the conditions under which the model becomes infeasible due to memory limits. Results in this analysis showed that the model finds solutions with a GAP < 1% for OEM assembly plant instances handling between 250 and 500 manufacturing orders per period, with 1250 components considered, a planning horizon of 6 months (which is the maximum industrial planning horizon we consider in our application), and 2500 manufacturing orders in the order bank, execution times remained within reasonable bounds (less than 20 min). However, the optimisation model exceeded memory limits in the larger tested scenarios. While these results provided a baseline for the computational performance of our model, improvements in model execution code and optimisation techniques significantly reduced computation time.

For our second study, we introduced multiple disruption scenarios to assess the performance of our model. We introduced four types of disruptive events that commonly impact supply chain operations. These included inventory disruptions, variations in delivery schedules, emergency shipment constraints, and a combination of disruption events. In our analysis, inventory disruptions were modelled by introducing shortages in key components, affecting different percentages of manufacturing orders (20%, 40%, ..., → 100%). These shortages could be generated by human error, accidental loss, or quality issues, significantly impacting production continuity. Delivery schedule disruptions tested supplier reliability by shifting committed delivery times and simulating delays caused by supplier capacity limitations, OEM assembly plant incidents, or traffic conditions, such as bad weather conditions. Lastly, emergency shipment constraints evaluated the model's ability to adapt when expedited procurement options were either delayed or unavailable.

The analysis examined the model's ability to adjust production schedules, reallocate resources, and minimise disruption impacts. Key performance metrics included execution time, reliance on emergency shipments, schedule stability, and order shortfalls. We compared these results to the base production scenario. We assessed the model's capacity to maintain the production plans' stability while minimising the disruptive event's impact on the supply chain.

A final test of the sensitivity analysis examined the impact of cost weight variations on production planning decisions. The model incorporates cost components (see Eqs. (10)), (11), (12), and (13). Moreover, their relative importance was adjusted to determine the optimal balance for decision-making. This analysis helped identify the cost coefficients best aligned with the use case objectives. In this sensitivity analysis, fine-tuning cost parameters, we observed shifts in priorities, resource allocation and spending in emergency costs. Our model demonstrated its ability to handle varying problem sizes and
<figure><img src="image_8.png" /><figcaption>Fig. 6. Data diagram.</figcaption></figure>

different disruptions. The study validated the model's applicability and robustness.

## Appendix B. Calculating the cost of holding vehicles post assembly

Calculating the gains is challenging since not all information is available. In this section, we explain how the holding costs were calculated. As mentioned in our results, the manufacturing orders, if not dispatched, have to be stored. Ideally, they would be stored in the OEM assembly plant's garages. The garages, however, have limited capacities and come with a cost.

The cost generated is because of the immobilisation value of the product, which has yet to be billed. The immobilisation value refers to the value tied up in inventory that has yet to be sold or billed. This immobilisation impacts Renault's free cash flow (FCF). This cost is known. Certain assumptions are made; we consider that for our *Target Population*, only one shipment is scheduled every week, so if we miss the first shipment, then the cars have to stay in the garage for at least one week, so we assume that for this one week, no other events will oblige the OEM assembly plant to dispatch the 702 vehicles. The holding cost in our model is *HG*, which is calculated in Renault due to the immobilisation value and the insurance and is representative of the global average, which yields a holding cost $HG = 6.15 \epsilon$ per day
spent in the garage, so for 702 vehicles it will cost 4,317 € of holding cost per day so 30,221 € for a week of holding to distribution.

This is the best scenario in our cost estimation since the cost of holding vehicles at the port is more significant. If there are no places left in the garages, the supply chain team will have to send the vehicles to wait for shipment in the port; after discussing with distribution planners, each port allows a defined number of *Free Days* where the car manufacturer can store the vehicles at the port, this is a common industrial practice to allow better flexibility in the logistics and time windows. In our calculation, we assume that the number of *Free Days* allowed is 2, the *Free Days* in the industry can vary however between 0 to 5 days, which means that the cost will be for storing the vehicles for 5 days, with a holding cost at the port of 2€ per vehicle per day including insurance, so that it will cost the distribution team in addition to the immobilisation cost 7020€, in total this yields an additional cost of 37,231€. With this calculation, we defined the *max & min* operational cost that the distribution team would pay if they did not react to the change in the distribution plan. Since the team can decide to keep some in the garages and some at the port, we estimate the actual cost between these two extremes [30, 221, 37, 231]€.

## Data availability

The data that has been used is confidential.

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