Inspired by the concept of generalized due dates introduced by Hall (IIE Transactions, 18(2), 220–222), in this article we first define four new generalized parameters in machine scheduling: the generalized release dates (GRD), generalized processing times (GPT), generalized rejection costs (GRC), and generalized delivery times (GDT). We then study order acceptance and scheduling problems with delivery consideration under the generalized parameters of GRD, GPT, GRC, and GDT, respectively. The objective of each scheduling problem in consideration is to minimize the maximum delivery completion time of the accepted jobs plus the total rejection penalty cost of the rejected jobs. We show that two of the six problems studied in this article are weakly NP‐hard while the other four ones can be solved in polynomial time. For each NP‐hard problem, we provide a pseudo‐polynomial time algorithm, a 2‐approximation algorithm and a fully polynomial‐time approximation scheme.
{"title":"Order acceptance and scheduling with delivery under generalized parameters","authors":"Lingfa Lu, Jinwen Ou, Xue Yu, Liqi Zhang","doi":"10.1002/nav.22135","DOIUrl":"https://doi.org/10.1002/nav.22135","url":null,"abstract":"Inspired by the concept of generalized due dates introduced by Hall (IIE Transactions, 18(2), 220–222), in this article we first define four new generalized parameters in machine scheduling: the generalized release dates (GRD), generalized processing times (GPT), generalized rejection costs (GRC), and generalized delivery times (GDT). We then study order acceptance and scheduling problems with delivery consideration under the generalized parameters of GRD, GPT, GRC, and GDT, respectively. The objective of each scheduling problem in consideration is to minimize the maximum delivery completion time of the accepted jobs plus the total rejection penalty cost of the rejected jobs. We show that two of the six problems studied in this article are weakly NP‐hard while the other four ones can be solved in polynomial time. For each NP‐hard problem, we provide a pseudo‐polynomial time algorithm, a 2‐approximation algorithm and a fully polynomial‐time approximation scheme.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79866669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantifying the benefits of customized vaccination strategies: A network‐based optimization approach","authors":"SumsChi-Kwong Li, Hrayer Aprahamian","doi":"10.1002/nav.22134","DOIUrl":"https://doi.org/10.1002/nav.22134","url":null,"abstract":"","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"196 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76056672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study deals with redundancy mechanisms of coherent systems with statistically dependent component and redundancy lifetimes. We derive the distortion function of coherent system with a redundancy mechanism at component level, and then we present the usual stochastic order and hazard rate order on redundant system lifetimes. The main results not only enrich the framework of research in this line but also supplement some corresponding results in recent references. Several examples are presented to illustrate the results as well.
{"title":"Redundancy mechanisms to systems with statistically dependent component and redundancy lifetimes","authors":"Yinping You, Xiaohu Li, Ying Wei","doi":"10.1002/nav.22133","DOIUrl":"https://doi.org/10.1002/nav.22133","url":null,"abstract":"This study deals with redundancy mechanisms of coherent systems with statistically dependent component and redundancy lifetimes. We derive the distortion function of coherent system with a redundancy mechanism at component level, and then we present the usual stochastic order and hazard rate order on redundant system lifetimes. The main results not only enrich the framework of research in this line but also supplement some corresponding results in recent references. Several examples are presented to illustrate the results as well.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89770767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Drug shortages are becoming more frequent and severe in the United States, especially for generic drugs. A lack of economic incentives has been cited as a root cause. Only few firms choose to produce a such drugs, and, if they do, these firms do not allocate large levels of capacity. Hence, total industry supply is limited, increasing the odds of shortages. We develop and analyze a stylized game‐theoretic model of a generic drug market to understand the impact of various governmental interventions on the total industry equilibrium supply. We explicitly consider firm market entry and exit decisions and the participating firms' incentives to allocate productive capacity to the focal drug market. We first characterize sustainable numbers of active drug manufacturers and their equilibrium capacity allocation decisions for a given regulatory environment. We then analyze the effects of different possible policy interventions on these equilibrium decisions and total industry capacity. Finally, we consider the impact of combinations of different interventions and, importantly, the sequence in which such combined interventions are introduced. A key result of our analysis is that the sequence of policy interventions may have an important effect on the resulting equilibrium industry capacity. When changing the regulatory environment, policymakers should be careful never to lead a sequence of changes with an adjustment that adversely affects pharmaceutical firms' incentives to allocate capacity to the focal drug market; we show that starting with capacity‐supporting interventions always is a dominant strategy when aiming to increase total industry capacity.
{"title":"Capacity shortages, regulation, and firm incentives in the generic drugs industry","authors":"H. S. Heese, Eda Kemahlioglu-Ziya","doi":"10.1002/nav.22132","DOIUrl":"https://doi.org/10.1002/nav.22132","url":null,"abstract":"Drug shortages are becoming more frequent and severe in the United States, especially for generic drugs. A lack of economic incentives has been cited as a root cause. Only few firms choose to produce a such drugs, and, if they do, these firms do not allocate large levels of capacity. Hence, total industry supply is limited, increasing the odds of shortages. We develop and analyze a stylized game‐theoretic model of a generic drug market to understand the impact of various governmental interventions on the total industry equilibrium supply. We explicitly consider firm market entry and exit decisions and the participating firms' incentives to allocate productive capacity to the focal drug market. We first characterize sustainable numbers of active drug manufacturers and their equilibrium capacity allocation decisions for a given regulatory environment. We then analyze the effects of different possible policy interventions on these equilibrium decisions and total industry capacity. Finally, we consider the impact of combinations of different interventions and, importantly, the sequence in which such combined interventions are introduced. A key result of our analysis is that the sequence of policy interventions may have an important effect on the resulting equilibrium industry capacity. When changing the regulatory environment, policymakers should be careful never to lead a sequence of changes with an adjustment that adversely affects pharmaceutical firms' incentives to allocate capacity to the focal drug market; we show that starting with capacity‐supporting interventions always is a dominant strategy when aiming to increase total industry capacity.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74242129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
W. Wang, Lipan Feng, Yongjian Li, G. Cai, Wubo Zhang
Quality improvement and trade‐ins are widely used by firms to manage the demand slowdown. However, how these two strategies interact with each other is unclear. In this paper, we construct a stylized model where a monopoly sells the new product to a market comprising both new and replacement consumers. We examine and compare the firm's optimal decisions, demands, and profits under four cases with quality improvement and/or trade‐in program. We identify several interesting results. First, quality improvement may lead to a lower retail price, while the trade‐in program consistently results in a higher price. Additionally, the trade‐in program encourages the firm to increase quality improvement level and sell the product with a higher price increase per unit of quality improvement. Second, although the trade‐in program and quality improvement strategy can certainly help increase the new product's demand, they may be partially substitutive under some conditions. Interestingly, their complementary effect in improving the firm's profit always exists. Third, quality improvement constantly improves consumer surplus and social welfare; however, it brings a larger environmental burden. Conversely, although the trade‐in program might reduce consumer surplus and social welfare, it can potentially reduce the environmental impacts when unit production cost is relatively low. Finally, our main findings above are relatively robust when considering the internal competition from remanufactured products, external competition from the secondary market, or the impacts of strategic consumer behaviors.
{"title":"Managing demand slowdown: The interplay between trade‐ins and quality improvement","authors":"W. Wang, Lipan Feng, Yongjian Li, G. Cai, Wubo Zhang","doi":"10.1002/nav.22129","DOIUrl":"https://doi.org/10.1002/nav.22129","url":null,"abstract":"Quality improvement and trade‐ins are widely used by firms to manage the demand slowdown. However, how these two strategies interact with each other is unclear. In this paper, we construct a stylized model where a monopoly sells the new product to a market comprising both new and replacement consumers. We examine and compare the firm's optimal decisions, demands, and profits under four cases with quality improvement and/or trade‐in program. We identify several interesting results. First, quality improvement may lead to a lower retail price, while the trade‐in program consistently results in a higher price. Additionally, the trade‐in program encourages the firm to increase quality improvement level and sell the product with a higher price increase per unit of quality improvement. Second, although the trade‐in program and quality improvement strategy can certainly help increase the new product's demand, they may be partially substitutive under some conditions. Interestingly, their complementary effect in improving the firm's profit always exists. Third, quality improvement constantly improves consumer surplus and social welfare; however, it brings a larger environmental burden. Conversely, although the trade‐in program might reduce consumer surplus and social welfare, it can potentially reduce the environmental impacts when unit production cost is relatively low. Finally, our main findings above are relatively robust when considering the internal competition from remanufactured products, external competition from the secondary market, or the impacts of strategic consumer behaviors.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"48 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78033664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study a discrete‐time queueing network with blocking that is primarily motivated by outpatient network management. To tackle the curse of dimensionality in performance analysis, we develop a refined mean‐field approximation that deals with changing population size, a nonconventional feature that makes the analysis challenging within the existing literature. We explicitly quantify the convergence rate for this approximation as O(1/N)$$ Oleft(1/Nright) $$ with N$$ N $$ being the system size. Not only is this convergence better than the O(1/N)$$ Oleft(1/sqrt{N}right) $$ convergence proven in prior work, but our approximation shows a significant improvement in performance prediction accuracy when the system size is small, compared to the conventional (unrefined) mean‐field approximation. This accuracy makes our approximation appealing to support decision‐making in practice.
{"title":"Refined mean‐field approximation for discrete‐time queueing networks with blocking","authors":"Yangyang Pan, P. Shi","doi":"10.1002/nav.22131","DOIUrl":"https://doi.org/10.1002/nav.22131","url":null,"abstract":"We study a discrete‐time queueing network with blocking that is primarily motivated by outpatient network management. To tackle the curse of dimensionality in performance analysis, we develop a refined mean‐field approximation that deals with changing population size, a nonconventional feature that makes the analysis challenging within the existing literature. We explicitly quantify the convergence rate for this approximation as O(1/N)$$ Oleft(1/Nright) $$ with N$$ N $$ being the system size. Not only is this convergence better than the O(1/N)$$ Oleft(1/sqrt{N}right) $$ convergence proven in prior work, but our approximation shows a significant improvement in performance prediction accuracy when the system size is small, compared to the conventional (unrefined) mean‐field approximation. This accuracy makes our approximation appealing to support decision‐making in practice.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"15 1","pages":"770 - 789"},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89613514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a framework for applying sensitivity analysis to a set of potential hybrid microgrid design options, from which a decision maker can select the most preferred one. In contrast to optimization‐centric models that define an objective and produce a single solution, our goal is to empower the decision maker by providing both a range of options and accessible information that enables the decision maker to easily assess their relative upsides and downsides. Moreover, our decoupled approach allows our framework to be paired with any existing model capable of generating a set of potential hybrid microgrid designs. We introduce metrics for computing risk, stemming from power deficits, over a variety of scenarios relating to weather conditions, power demand fluctuations, and extended time horizons. These factors which are inherently uncertain are all important in military operational contexts. By introducing a design of experiments method for sensitivity analysis, we are able to implement parallel processing and maintain computational tractability.
{"title":"Sensitivity analysis of hybrid microgrids with application to deployed military units","authors":"Daniel Reich, S. Sanchez","doi":"10.1002/nav.22130","DOIUrl":"https://doi.org/10.1002/nav.22130","url":null,"abstract":"We introduce a framework for applying sensitivity analysis to a set of potential hybrid microgrid design options, from which a decision maker can select the most preferred one. In contrast to optimization‐centric models that define an objective and produce a single solution, our goal is to empower the decision maker by providing both a range of options and accessible information that enables the decision maker to easily assess their relative upsides and downsides. Moreover, our decoupled approach allows our framework to be paired with any existing model capable of generating a set of potential hybrid microgrid designs. We introduce metrics for computing risk, stemming from power deficits, over a variety of scenarios relating to weather conditions, power demand fluctuations, and extended time horizons. These factors which are inherently uncertain are all important in military operational contexts. By introducing a design of experiments method for sensitivity analysis, we are able to implement parallel processing and maintain computational tractability.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"141 1","pages":"753 - 769"},"PeriodicalIF":0.0,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73432748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the context of fast‐fashion business, we study the joint control of production, inventory, and unilateral transshipment in dual supply chains in which one supply chain is a responsive supply chain for fashion products and the other is an efficient supply chain for basic products in a fluctuating demand environment (FDE). Our research focuses on: (1) formulating an appropriate model for this complex problem; (2) characterizing the structured optimal policy, which can be used to develop effective heuristic policies; and (3) generalizing our studies for more applications. To address these issues, we formulate a discrete‐time finite‐horizon stochastic dynamic program model in which FDE is represented by a world state evolving in accordance with the discrete‐time Markov chain. The supply chain for the fashion product is modeled by a two‐stage tandem production system with a make‐to‐stock (MTS) stage for the fabric and a subsequent MTS stage for finished fashions. In parallel, the supply chain for the basic products is also modeled by a two‐stage tandem production system with a MTS stage for the fabric and a subsequent make‐to‐order (MTO) stage for finished basics. Further, the two supply chains are coupled via the unilateral transshipment of fabric with random transshipment time. By value iteration, we characterize the optimal policy for the single‐product problem with a set of monotone switching surfaces. The results are extended to the multi‐product multi‐supplier case. Further, based on the structure of the optimal policy, we develop a heuristic policy for the multi‐dimensional dynamic program model. From a practice perspective, we demonstrate the value of transshipment and controlled transshipment, analytically and numerically, and therefore justify the establishment of two separate local manufacturing bases in dual supply chains. Additionally, to achieve both quick response and efficiency, we show that the total cost can be reduced significantly if sufficient fabric is prepared just in time (JIT) for in‐season production at the beginning of a season.
{"title":"Optimal and heuristic policies for production and inventory controls in dual supply chains with fluctuating demands","authors":"Bing Lin, Shaoxiang Chen, R. Bhatnagar","doi":"10.1002/nav.22119","DOIUrl":"https://doi.org/10.1002/nav.22119","url":null,"abstract":"In the context of fast‐fashion business, we study the joint control of production, inventory, and unilateral transshipment in dual supply chains in which one supply chain is a responsive supply chain for fashion products and the other is an efficient supply chain for basic products in a fluctuating demand environment (FDE). Our research focuses on: (1) formulating an appropriate model for this complex problem; (2) characterizing the structured optimal policy, which can be used to develop effective heuristic policies; and (3) generalizing our studies for more applications. To address these issues, we formulate a discrete‐time finite‐horizon stochastic dynamic program model in which FDE is represented by a world state evolving in accordance with the discrete‐time Markov chain. The supply chain for the fashion product is modeled by a two‐stage tandem production system with a make‐to‐stock (MTS) stage for the fabric and a subsequent MTS stage for finished fashions. In parallel, the supply chain for the basic products is also modeled by a two‐stage tandem production system with a MTS stage for the fabric and a subsequent make‐to‐order (MTO) stage for finished basics. Further, the two supply chains are coupled via the unilateral transshipment of fabric with random transshipment time. By value iteration, we characterize the optimal policy for the single‐product problem with a set of monotone switching surfaces. The results are extended to the multi‐product multi‐supplier case. Further, based on the structure of the optimal policy, we develop a heuristic policy for the multi‐dimensional dynamic program model. From a practice perspective, we demonstrate the value of transshipment and controlled transshipment, analytically and numerically, and therefore justify the establishment of two separate local manufacturing bases in dual supply chains. Additionally, to achieve both quick response and efficiency, we show that the total cost can be reduced significantly if sufficient fabric is prepared just in time (JIT) for in‐season production at the beginning of a season.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"2 1","pages":"708 - 734"},"PeriodicalIF":0.0,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85228457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stephen M. Henry, Matthew J. Hoffman, Lucas A. Waddell, Frank M. Muldoon
The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real‐world system design optimization and fleet‐level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. This means that fleet‐level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio‐level considerations. In reality, these two problems are highly interconnected. To properly address this system‐fleet design interdependence, we present a general method for efficiently incorporating multi‐objective system design trade‐off information into a mixed‐integer linear programming (MILP) fleet‐level optimization. This work is motivated by the authors' experience with large‐scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet‐level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet‐level MILP.
{"title":"Holistic fleet optimization incorporating system design considerations","authors":"Stephen M. Henry, Matthew J. Hoffman, Lucas A. Waddell, Frank M. Muldoon","doi":"10.1002/nav.22115","DOIUrl":"https://doi.org/10.1002/nav.22115","url":null,"abstract":"The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real‐world system design optimization and fleet‐level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. This means that fleet‐level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio‐level considerations. In reality, these two problems are highly interconnected. To properly address this system‐fleet design interdependence, we present a general method for efficiently incorporating multi‐objective system design trade‐off information into a mixed‐integer linear programming (MILP) fleet‐level optimization. This work is motivated by the authors' experience with large‐scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet‐level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet‐level MILP.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"3 1","pages":"675 - 690"},"PeriodicalIF":0.0,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79588689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the assortment optimization problem in an online setting where a retailer uses multiple distribution centers (DC) to fulfill orders from multiple regions. Customer choice in each region follows a multinomial logit model. Each DC can carry up to a pre‐specified number of products. Outbound shipping cost to a region depends on the DC that ships the order. The problem is to determine which products to carry in each DC and which products to offer for sale in each region to maximize the expected profit. We first show that the problem is NP‐complete. We develop a conic quadratic mixed integer programming formulation and suggest a family of valid inequalities. We also show that a special case with identical choice models can be solved as a linear program. This LP solution approach can be used to develop heuristics for the general case. Numerical experiments show that our conic approach outperforms the mixed integer linear programming formulation and enables us to solve moderately sized instances optimally. The experiments also show that not allowing cross‐shipments or not considering them in assortment decisions may lead to substantial losses and LP‐based heuristics can be effective in practice.
{"title":"Constrained multi‐location assortment optimization under the multinomial logit model","authors":"Başak Bebitoğlu, Alper Şen, Philip Kaminsky","doi":"10.1002/nav.22116","DOIUrl":"https://doi.org/10.1002/nav.22116","url":null,"abstract":"We study the assortment optimization problem in an online setting where a retailer uses multiple distribution centers (DC) to fulfill orders from multiple regions. Customer choice in each region follows a multinomial logit model. Each DC can carry up to a pre‐specified number of products. Outbound shipping cost to a region depends on the DC that ships the order. The problem is to determine which products to carry in each DC and which products to offer for sale in each region to maximize the expected profit. We first show that the problem is NP‐complete. We develop a conic quadratic mixed integer programming formulation and suggest a family of valid inequalities. We also show that a special case with identical choice models can be solved as a linear program. This LP solution approach can be used to develop heuristics for the general case. Numerical experiments show that our conic approach outperforms the mixed integer linear programming formulation and enables us to solve moderately sized instances optimally. The experiments also show that not allowing cross‐shipments or not considering them in assortment decisions may lead to substantial losses and LP‐based heuristics can be effective in practice.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"26 1","pages":"653 - 674"},"PeriodicalIF":0.0,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80980968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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