We consider dynamic assortment optimization with incomplete information under the uncapacitated multinomial logit choice model. We propose an anytime stochastic approximation policy and prove that the regret—the cumulative expected revenue loss caused by offering suboptimal assortments—after T$$ T $$ time periods is bounded by T$$ sqrt{T} $$ times a constant that is independent of the number of products. In addition, we prove a matching lower bound on the regret for any policy that is valid for arbitrary model parameters—slightly generalizing a recent regret lower bound derived for specific revenue parameters. Numerical illustrations suggest that our policy outperforms alternatives by a significant margin when T$$ T $$ and the number of products N$$ N $$ are not too small.
在无能力多项logit选择模型下，研究了具有不完全信息的动态分类优化问题。我们提出了一个随时随机逼近策略，并证明了T $$ T $$时间段后的遗憾-由提供次优分类引起的累积预期收入损失由T $$ sqrt{T} $$乘以一个与产品数量无关的常数所限制。此外，我们证明了对任意模型参数有效的任何策略的后悔下界的匹配下界-稍微推广了最近为特定收益参数导出的后悔下界。数值实例表明，当T $$ T $$和产品数量N $$ N $$不是太小时，我们的政策明显优于替代方案。
{"title":"Stochastic approximation for uncapacitated assortment optimization under the multinomial logit model","authors":"Yannik Peeters, Arnoud V. den Boer","doi":"10.1002/nav.22068","DOIUrl":"https://doi.org/10.1002/nav.22068","url":null,"abstract":"We consider dynamic assortment optimization with incomplete information under the uncapacitated multinomial logit choice model. We propose an anytime stochastic approximation policy and prove that the regret—the cumulative expected revenue loss caused by offering suboptimal assortments—after T$$ T $$ time periods is bounded by T$$ sqrt{T} $$ times a constant that is independent of the number of products. In addition, we prove a matching lower bound on the regret for any policy that is valid for arbitrary model parameters—slightly generalizing a recent regret lower bound derived for specific revenue parameters. Numerical illustrations suggest that our policy outperforms alternatives by a significant margin when T$$ T $$ and the number of products N$$ N $$ are not too small.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"31 1","pages":"927 - 938"},"PeriodicalIF":0.0,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78687604","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}
Perpetuities (i.e., random variables of the form D=∫0∞e−Γ(t−)dΛ(t)$$ D={int}_0^{infty }{e}^{-Gamma left(t-right)}dLambda (t) $$ play an important role in many application settings. We develop approximations for the distribution of D$$ D $$ when the “accumulated short rate process”, Γ$$ Gamma $$ , is small. We provide: (1) characterizations for the distribution of D$$ D $$ when Γ$$ Gamma $$ and Λ$$ Lambda $$ are driven by Markov processes; (2) general sufficient conditions under which weak convergence results can be derived for D$$ D $$ , and (3) Edgeworth expansions for the distribution of D$$ D $$ in the iid case and the case in which Λ$$ Lambda $$ is a Levy process and the interest rate is a function of an ergodic Markov process.
永续性(即D=∫0∞e−Γ(t−)dΛ(t) $$ D={int}_0^{infty }{e}^{-Gamma left(t-right)}dLambda (t) $$形式的随机变量)在许多应用设置中起重要作用。当“累积短期利率过程”Γ $$ Gamma $$很小时，我们对D $$ D $$的分布进行了近似。(1)给出了Γ $$ Gamma $$和Λ $$ Lambda $$受马尔可夫过程驱动时D $$ D $$的分布特征;(2)推导出D $$ D $$弱收敛结果的一般充分条件;(3)在iid情况和Λ $$ Lambda $$是Levy过程且利率是遍历马尔可夫过程的函数的情况下，D $$ D $$分布的Edgeworth展开式。
{"title":"Approximations for the distribution of perpetuities with small discount rates","authors":"J. Blanchet, Peter W. Glynn","doi":"10.1002/nav.22058","DOIUrl":"https://doi.org/10.1002/nav.22058","url":null,"abstract":"Perpetuities (i.e., random variables of the form D=∫0∞e−Γ(t−)dΛ(t)$$ D={int}_0^{infty }{e}^{-Gamma left(t-right)}dLambda (t) $$ play an important role in many application settings. We develop approximations for the distribution of D$$ D $$ when the “accumulated short rate process”, Γ$$ Gamma $$ , is small. We provide: (1) characterizations for the distribution of D$$ D $$ when Γ$$ Gamma $$ and Λ$$ Lambda $$ are driven by Markov processes; (2) general sufficient conditions under which weak convergence results can be derived for D$$ D $$ , and (3) Edgeworth expansions for the distribution of D$$ D $$ in the iid case and the case in which Λ$$ Lambda $$ is a Levy process and the interest rate is a function of an ergodic Markov process.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"163 1","pages":"454 - 471"},"PeriodicalIF":0.0,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74158106","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}
M. R. Bowers, Bogdan C. Bichescu, Nana Bryan, G. Polak, K. Gilbert, D. Keene
The maintenance conversion scheduling problem (MCSP) is faced by organizations such as those in the airline, defense, heavy equipment, and transportation industries switching from an asset maintenance program with longer, less‐frequent service visits to one with shorter, more frequent visits. One example is the United States Air Force (USAF) High Velocity Maintenance program piloted at the Warner Robbins Air Logistics Center on the C‐130 aircraft line. The USAF MCSP is complex, as planners must schedule significantly more aircraft depot maintenance visits during the conversion period and must determine the timing and specific order in which each aircraft completes a repetitive sequence of maintenance visits. The conversion is expected to yield a stable long‐term maintenance schedule, while balancing annual depot workload and operating within reasonable flow times and work‐in‐process levels. While practically important, this problem has received little to no attention in the literature. Therefore, this research formalizes the general MCSP within an optimization framework, shows the MCSP is NP‐complete, proposes a computationally effective solution approach, and shows that a balanced long‐term schedule depends critically on the conversion period schedule. Our solutions are markedly better than USAF proposed schedules and underscore the value of leveraging synergies between asset availability and maintenance efficiency. Our approach moves the focus away from batch scheduling toward a smoother, more uniform, mixed‐model type schedule that yields more stable maintenance operations and a more consistent, predictable level of aircraft readiness. The manuscript concludes with a discussion of the main theoretical and practical implications of our work.
{"title":"The maintenance conversion scheduling problem: Models and insights","authors":"M. R. Bowers, Bogdan C. Bichescu, Nana Bryan, G. Polak, K. Gilbert, D. Keene","doi":"10.1002/nav.22059","DOIUrl":"https://doi.org/10.1002/nav.22059","url":null,"abstract":"The maintenance conversion scheduling problem (MCSP) is faced by organizations such as those in the airline, defense, heavy equipment, and transportation industries switching from an asset maintenance program with longer, less‐frequent service visits to one with shorter, more frequent visits. One example is the United States Air Force (USAF) High Velocity Maintenance program piloted at the Warner Robbins Air Logistics Center on the C‐130 aircraft line. The USAF MCSP is complex, as planners must schedule significantly more aircraft depot maintenance visits during the conversion period and must determine the timing and specific order in which each aircraft completes a repetitive sequence of maintenance visits. The conversion is expected to yield a stable long‐term maintenance schedule, while balancing annual depot workload and operating within reasonable flow times and work‐in‐process levels. While practically important, this problem has received little to no attention in the literature. Therefore, this research formalizes the general MCSP within an optimization framework, shows the MCSP is NP‐complete, proposes a computationally effective solution approach, and shows that a balanced long‐term schedule depends critically on the conversion period schedule. Our solutions are markedly better than USAF proposed schedules and underscore the value of leveraging synergies between asset availability and maintenance efficiency. Our approach moves the focus away from batch scheduling toward a smoother, more uniform, mixed‐model type schedule that yields more stable maintenance operations and a more consistent, predictable level of aircraft readiness. The manuscript concludes with a discussion of the main theoretical and practical implications of our work.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"17 1","pages":"1027 - 1044"},"PeriodicalIF":0.0,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82794041","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}
When competing firms embark and explore a new market, two salient features are often observed. On the one hand, the firms need to improve their quality by accumulating more experience and climbing up the learning curve. On the other hand, their quality may jointly expand the brand awareness of all competing products. In this article, we study a two‐period duopoly price competition where firms can improve their quality based on the accumulated demand (learn‐by‐doing effect) and their potential market size is positively affected by both firms' quality levels (quality spillover effect). In addition, we investigate two pricing schemes, namely, committed pricing and dynamic pricing, and their impact on the equilibrium outcomes. Assuming the two firms are symmetric in every aspect, our main findings include the following. First, we establish the existence and uniqueness of the pure Nash equilibrium for the dynamic game under either pricing scheme, and show that firms always set a low price in the first period to leverage quality improvement. As the quality spillover effect gets stronger, firms tend to raise their first‐period price, leading to a lower individual quality improvement and a non‐monotonic impact on firms' profit. Moreover, we find that committed pricing scheme benefits the duopoly when the spillover effect is strong, otherwise dynamic pricing scheme brings more profits. Finally, we examine two asymmetric cases where the firms are different in certain attributes pertaining to their learning speed and the quality spillover strength. Our analysis shows that the findings in the symmetric case still hold qualitatively. Useful managerial insights are derived from these studies.
{"title":"Duopoly price competition with quality improvement spillover","authors":"Xin Geng, Zepeng Chen, Xiaomeng Guo, Guang Xiao","doi":"10.1002/nav.22057","DOIUrl":"https://doi.org/10.1002/nav.22057","url":null,"abstract":"When competing firms embark and explore a new market, two salient features are often observed. On the one hand, the firms need to improve their quality by accumulating more experience and climbing up the learning curve. On the other hand, their quality may jointly expand the brand awareness of all competing products. In this article, we study a two‐period duopoly price competition where firms can improve their quality based on the accumulated demand (learn‐by‐doing effect) and their potential market size is positively affected by both firms' quality levels (quality spillover effect). In addition, we investigate two pricing schemes, namely, committed pricing and dynamic pricing, and their impact on the equilibrium outcomes. Assuming the two firms are symmetric in every aspect, our main findings include the following. First, we establish the existence and uniqueness of the pure Nash equilibrium for the dynamic game under either pricing scheme, and show that firms always set a low price in the first period to leverage quality improvement. As the quality spillover effect gets stronger, firms tend to raise their first‐period price, leading to a lower individual quality improvement and a non‐monotonic impact on firms' profit. Moreover, we find that committed pricing scheme benefits the duopoly when the spillover effect is strong, otherwise dynamic pricing scheme brings more profits. Finally, we examine two asymmetric cases where the firms are different in certain attributes pertaining to their learning speed and the quality spillover strength. Our analysis shows that the findings in the symmetric case still hold qualitatively. Useful managerial insights are derived from these studies.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"3 1","pages":"958 - 973"},"PeriodicalIF":0.0,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81441605","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}
Ankit Bansal, Osman Y. Özaltın, R. Uzsoy, K. Kempf
Product transitions involve the replacement of products currently being produced and distributed by a firm with new products throughout the firm's supply chain. In high technology industries effective management of product transitions is crucial to long‐term success, and involves the coordination of multiple product development units and a manufacturing unit by a product division serving a particular market. Since the different units are organizationally autonomous, and the product division does not have access to their detailed technological constraints and internal operating policies, a decentralized solution is required. We develop a price‐based coordination framework using the subadditive dual of a mixed‐integer linear program that seeks to maximize the number of units whose proposed plans are included in the final solution. The proposed approach yields superior solutions to a linear‐programming‐based branch‐and‐price approach within the same computing budget. We discuss the broader applicability of this integer column generation approach, and suggest directions for future work.
{"title":"Coordination of manufacturing and engineering activities during product transitions","authors":"Ankit Bansal, Osman Y. Özaltın, R. Uzsoy, K. Kempf","doi":"10.1002/nav.22056","DOIUrl":"https://doi.org/10.1002/nav.22056","url":null,"abstract":"Product transitions involve the replacement of products currently being produced and distributed by a firm with new products throughout the firm's supply chain. In high technology industries effective management of product transitions is crucial to long‐term success, and involves the coordination of multiple product development units and a manufacturing unit by a product division serving a particular market. Since the different units are organizationally autonomous, and the product division does not have access to their detailed technological constraints and internal operating policies, a decentralized solution is required. We develop a price‐based coordination framework using the subadditive dual of a mixed‐integer linear program that seeks to maximize the number of units whose proposed plans are included in the final solution. The proposed approach yields superior solutions to a linear‐programming‐based branch‐and‐price approach within the same computing budget. We discuss the broader applicability of this integer column generation approach, and suggest directions for future work.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"8 1","pages":"841 - 855"},"PeriodicalIF":0.0,"publicationDate":"2022-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88797729","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 this paper, we propose a copula‐based approach to study the allocation problem of hot standbys in series systems composed of two heterogeneous and dependent components. By assuming that the lifetimes of components and spares are dependent and linked via a general survival copula, optimal allocation strategies are presented for the case of one and two redundancies at the component level. Further, redundancies allocation mechanisms are also compared between the allocations at the component level and the system level. For the case of one hot standby, we find that the performance of the redundant system at the component level is always worse than that at the system level. For the case of two hot standbys, the reversed allocation principle (i.e., Barlow–Proschan principle) is valid. Numerical examples and applications are also provided as illustrations. A real application on improving tensile strength of cables in high voltage electricity transmission network systems is presented for showing the applicability of our results.
{"title":"A copula‐based approach on optimal allocation of hot standbys in series systems","authors":"Jiandong Zhang, Yiying Zhang","doi":"10.1002/nav.22055","DOIUrl":"https://doi.org/10.1002/nav.22055","url":null,"abstract":"In this paper, we propose a copula‐based approach to study the allocation problem of hot standbys in series systems composed of two heterogeneous and dependent components. By assuming that the lifetimes of components and spares are dependent and linked via a general survival copula, optimal allocation strategies are presented for the case of one and two redundancies at the component level. Further, redundancies allocation mechanisms are also compared between the allocations at the component level and the system level. For the case of one hot standby, we find that the performance of the redundant system at the component level is always worse than that at the system level. For the case of two hot standbys, the reversed allocation principle (i.e., Barlow–Proschan principle) is valid. Numerical examples and applications are also provided as illustrations. A real application on improving tensile strength of cables in high voltage electricity transmission network systems is presented for showing the applicability of our results.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"118 1","pages":"902 - 913"},"PeriodicalIF":0.0,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79261906","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 formulate and solve a robust dynamic pricing problem for an ambiguity‐averse agent who faces an uncertain probabilistic law governing the realized demand for a single product. Specifically, the pricing problem is framed as a stochastic game that involves a maximizing player (the “agent”) and a minimizing player (“nature”) who promotes robustness by distorting the agent's beliefs within prescribed limits. Our methodology builds on the commonly used entropic approach in the literature but can be utilized to generate a much more versatile class of uncertainty sets. We derive the optimal pricing strategy and the corresponding value function by applying stochastic dynamic programming and solving a version of the Bellman–Isaacs equation. The usefulness of our framework is illustrated by two special cases. Finally, a carefully designed numerical example exposes the value of model robustness.
{"title":"On dynamic pricing under model uncertainty","authors":"Xiao-hai Zhu, Xueqing Sun","doi":"10.1002/nav.22054","DOIUrl":"https://doi.org/10.1002/nav.22054","url":null,"abstract":"We formulate and solve a robust dynamic pricing problem for an ambiguity‐averse agent who faces an uncertain probabilistic law governing the realized demand for a single product. Specifically, the pricing problem is framed as a stochastic game that involves a maximizing player (the “agent”) and a minimizing player (“nature”) who promotes robustness by distorting the agent's beliefs within prescribed limits. Our methodology builds on the commonly used entropic approach in the literature but can be utilized to generate a much more versatile class of uncertainty sets. We derive the optimal pricing strategy and the corresponding value function by applying stochastic dynamic programming and solving a version of the Bellman–Isaacs equation. The usefulness of our framework is illustrated by two special cases. Finally, a carefully designed numerical example exposes the value of model robustness.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"13 1","pages":"856 - 868"},"PeriodicalIF":0.0,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79621684","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}
Truck–drone technology that enables drones to launch from or land on a moving truck without the need for the truck to stop is the focus of this study. We define the truck and drone routing problem with synchronization on arcs (TDRP‐SA). The TDRP‐SA is characterized by synchronization on arcs, time windows, classified customers, direct delivery, multiple trucks, and multiple drones carried by each truck. The TDRP‐SA involves synchronization on arcs to permit trucks to dispatch and retrieve drones at suitable moving‐LRLs (drone launch/retrieval locations) on arcs of truck routes. A moving‐LRL is essentially a drone launch/retrieval location with a moving truck, and the drone launch/retrieval operations do not need special parking for the trucks. We develop a mixed integer nonlinear programming model to address the TDRP‐SA. We propose a mathematical analysis method to locate moving‐LRLs and to estimate the drone's arrival time at the customers. We develop boundary models through introducing linear piecewise functions to locate moving‐LRLs. We provide an adaptive large neighborhood search (ALNS) heuristic. Through computational experiments, the effectiveness of the boundary models, the TDRP‐SA model and ALNS‐based heuristic are evaluated.
{"title":"Truck and drone routing problem with synchronization on arcs","authors":"Hong-qi Li, Jun Chen, Feilong Wang, Yibin Zhao","doi":"10.1002/nav.22053","DOIUrl":"https://doi.org/10.1002/nav.22053","url":null,"abstract":"Truck–drone technology that enables drones to launch from or land on a moving truck without the need for the truck to stop is the focus of this study. We define the truck and drone routing problem with synchronization on arcs (TDRP‐SA). The TDRP‐SA is characterized by synchronization on arcs, time windows, classified customers, direct delivery, multiple trucks, and multiple drones carried by each truck. The TDRP‐SA involves synchronization on arcs to permit trucks to dispatch and retrieve drones at suitable moving‐LRLs (drone launch/retrieval locations) on arcs of truck routes. A moving‐LRL is essentially a drone launch/retrieval location with a moving truck, and the drone launch/retrieval operations do not need special parking for the trucks. We develop a mixed integer nonlinear programming model to address the TDRP‐SA. We propose a mathematical analysis method to locate moving‐LRLs and to estimate the drone's arrival time at the customers. We develop boundary models through introducing linear piecewise functions to locate moving‐LRLs. We provide an adaptive large neighborhood search (ALNS) heuristic. Through computational experiments, the effectiveness of the boundary models, the TDRP‐SA model and ALNS‐based heuristic are evaluated.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"37 1","pages":"884 - 901"},"PeriodicalIF":0.0,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75484070","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}
Shuen Guo, Lingfa Lu, Jinjiang Yuan, C. T. Ng, T. Cheng
We consider the single‐machine Pareto‐scheduling problem to minimize the weighted number of tardy jobs and total weighted late work simultaneously. The problem is to find the set of all the Pareto‐optimal points, that is, the Pareto frontier, and their corresponding Pareto‐optimal schedules. We consider the corresponding weighted‐sum scheduling problem and primary‐secondary scheduling problems, being subproblems of the general Pareto‐scheduling problem. The NP‐hardness of the general problem follows directly from the NP‐hardness of the two constituent single‐criterion problems. We present a pseudo‐polynomial algorithm and a fully polynomial‐time approximation scheme (FPTAS) running in weakly polynomial time to deal with the general problem. When all the jobs have a common due date, we further provide an FPTAS running in strongly polynomial time. We also study some special cases of the general problem where the jobs have equal processing times, a common due date, or a common weight, and analyze their computational complexity status.
{"title":"Pareto‐scheduling with double‐weighted jobs to minimize the weighted number of tardy jobs and total weighted late work","authors":"Shuen Guo, Lingfa Lu, Jinjiang Yuan, C. T. Ng, T. Cheng","doi":"10.1002/nav.22050","DOIUrl":"https://doi.org/10.1002/nav.22050","url":null,"abstract":"We consider the single‐machine Pareto‐scheduling problem to minimize the weighted number of tardy jobs and total weighted late work simultaneously. The problem is to find the set of all the Pareto‐optimal points, that is, the Pareto frontier, and their corresponding Pareto‐optimal schedules. We consider the corresponding weighted‐sum scheduling problem and primary‐secondary scheduling problems, being subproblems of the general Pareto‐scheduling problem. The NP‐hardness of the general problem follows directly from the NP‐hardness of the two constituent single‐criterion problems. We present a pseudo‐polynomial algorithm and a fully polynomial‐time approximation scheme (FPTAS) running in weakly polynomial time to deal with the general problem. When all the jobs have a common due date, we further provide an FPTAS running in strongly polynomial time. We also study some special cases of the general problem where the jobs have equal processing times, a common due date, or a common weight, and analyze their computational complexity status.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"1 1","pages":"816 - 837"},"PeriodicalIF":0.0,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88823061","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 examine buyback contracts in a dyadic supply chain where a retailer orders from a supplier before observing the random demand and sets a retail price after observing it (a.k.a. price postponement). We focus on the case with linear additive demand, which is well known to be less tractable than the case with linear multiplicative demand. With mild conditions on the distribution of demand uncertainty, we derive the supplier's optimal buyback contract and show the following results. The supplier strictly prefers buyback contracts to wholesale price‐only contracts if and only if the unit production cost is lower than a threshold that depends on the dispersion of demand uncertainty; the optimal buyback rate is decreasing in the unit production cost; the profit allocation within the supply chain and channel efficiency depend on the dispersion of demand uncertainty. These results are in stark contrast to those in the case with linear multiplicative demand. Nevertheless, the relation between the operational decisions under the optimal buyback contract and those under the optimal wholesale price‐only contract is consistent with the case of multiplicative demand. We further extend the analysis to two related scenarios. On one hand, our results continue to hold in a supply chain where one supplier sells to two competing retailers. On the other hand, when the retailer does not postpone retail pricing decisions, we establish three distinctive properties of the optimal buyback contract: the supplier strictly prefers buyback contracts to wholesale price‐only contracts if and only if the unit production cost is intermediate; the optimal buyback rate is increasing in the unit production cost in the region where the supplier strictly prefers buyback contracts to wholesale price‐only contracts; price postponement benefits both the retailer and the supply chain but does not always benefit the supplier. The above analysis shows that the supplier's preference between buyback and wholesale price‐only contracts can swing either way when the retailer starts to practice price postponement.
{"title":"Buyback and price postponement in a decentralized supply chain with additive and price‐dependent demand","authors":"Kairen Zhang, Weixin Shang, Weihua Zhou","doi":"10.1002/nav.22052","DOIUrl":"https://doi.org/10.1002/nav.22052","url":null,"abstract":"We examine buyback contracts in a dyadic supply chain where a retailer orders from a supplier before observing the random demand and sets a retail price after observing it (a.k.a. price postponement). We focus on the case with linear additive demand, which is well known to be less tractable than the case with linear multiplicative demand. With mild conditions on the distribution of demand uncertainty, we derive the supplier's optimal buyback contract and show the following results. The supplier strictly prefers buyback contracts to wholesale price‐only contracts if and only if the unit production cost is lower than a threshold that depends on the dispersion of demand uncertainty; the optimal buyback rate is decreasing in the unit production cost; the profit allocation within the supply chain and channel efficiency depend on the dispersion of demand uncertainty. These results are in stark contrast to those in the case with linear multiplicative demand. Nevertheless, the relation between the operational decisions under the optimal buyback contract and those under the optimal wholesale price‐only contract is consistent with the case of multiplicative demand. We further extend the analysis to two related scenarios. On one hand, our results continue to hold in a supply chain where one supplier sells to two competing retailers. On the other hand, when the retailer does not postpone retail pricing decisions, we establish three distinctive properties of the optimal buyback contract: the supplier strictly prefers buyback contracts to wholesale price‐only contracts if and only if the unit production cost is intermediate; the optimal buyback rate is increasing in the unit production cost in the region where the supplier strictly prefers buyback contracts to wholesale price‐only contracts; price postponement benefits both the retailer and the supply chain but does not always benefit the supplier. The above analysis shows that the supplier's preference between buyback and wholesale price‐only contracts can swing either way when the retailer starts to practice price postponement.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"68 1","pages":"869 - 883"},"PeriodicalIF":0.0,"publicationDate":"2022-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79044517","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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