# Multi-Location Assortment Optimization with Drone and Human Courier Joint Delivery
## 2 Literature Review
proposed tractable mixed-integer second-order conic programming (MISOCP) and derived strengthening cuts to obtain an optimal store location and assortment in the MMNL model [35]. Our study is also closely connected with multi-location assortment planning. There is scant literature about it. [PERSON] and [PERSON] focused on the assortment-based cooperation method for firms in different locations [36]. [PERSON] and [PERSON] studied the strategy of assortment planning and pricing under a competitive environment [37]. [PERSON] and [PERSON] considered a supply chain going through not only an independent retailer but also its own direct channel [38]. [PERSON] studied the problem of assortment optimization, where multiple distribution centers are used for retailers [33]. Therefore, as far as we know, our work is the first to discuss multi-location assortment planning under cooperative delivery by drone and human courier. Moreover, some store operating strategies are also available as a result of this work. Below, we review the literature related to our MADH problem, as shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Topic** & **Constraint** & **Choice Model** & **Comments** \\ \hline \hline [PERSON] and [PERSON] (2008) [36] & Assortment-based cooperation among independent producers & Cooperation constraint & Assortment-based substitution & An analytical model to determine the characteristics of firms and products, explore what firms should cooperate with and set the parameters of it \\ [PERSON] et al. (2010b) [28] & Assortment optimization problem & Unconstrained & MMNL & Given the first PTAS for the assortment problem under MMNL model \\ [PERSON] et al. (2010a) [22] & Dynamic assortment optimization problem & Capacity constraint & MNL & An adaptive policy for joint parameter estimation and assortment optimization \\ [PERSON] and [PERSON] (2015) [38] & Pricing and assortment problem through dual channels & Cardinality constraint & NL & Given optimal pricing strategies and characterize scenarios in which the assortment preferences are in conflict \\ [PERSON] and [PERSON] (2016) [37] & Assortment and Price Competition & Cardinality constraint & MNL & compete or retailers compete jointly in assortment and prices \\  & & & & A conic quadratic mixed-integer programming formulation and valid inequalities to strengthen \\ [PERSON] (2016) [33] & Multi-Location assortment problem & Cardinality constraint & MMNL & Conic quadratic mixed-integer formulation with McCormick inequalities \\  & Geographical relationship between distribution centers and customers & Spatial constraint & MMNL & Approximation algorithms with guaranteed performance under reasonable assumptions \\  & & & & \\ [PERSON] et al. (2018) [39] & “Product framing” and pricing problem & Cardinality constraint & MMNL & With guaranteed performance under reasonable assumptions \\ [PERSON] and [PERSON] (2017) [27] & Assortment problem & & & \\ [PERSON] and [PERSON] (2017) [27] & where customers choose with nested consideration sets & Spatial constraint & MMNL & FPTAS based on dynamic programming formulation \\  & & & & \\  & & & & \\ [PERSON] et al. (2022) [40] & Assortment and Location problem of locker & Cardinality constraint & MMNL & MILP with McCormick estimators and two embedded algorithms for large scale problem \\  & & & & \\  & & & & \\ [PERSON] et al. (2021) [35] & Store location and location-dependent assortment problems & Cardinality constraint & MMNL & Conic programming (MISOCP) reformulation and structural properties \\  & & & & \\  & Multi-location assortment problem under drone and human courier delivery & Cardinality/Drone load capacity & MMNL & Conic quadratic mixed-integer formulation with McCormick inequalities, marginal revenue and delivery distance \\  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Literature review of closely related topics.