We study new types of dynamic allocation problems the Halting Bandit models. As an application, we obtain new proofs for the classic Gittins index decomposition result compare Gittins (Journal of the Royal Statistical Society, Series B, 1979, 41, 148–177), and recent results of the authors in Cowan and Katehakis (Probability in the Engineering and Informational Sciences, 2015, 29, 51–76).
本文研究了一类新的动态分配问题，即暂停班迪模型。作为应用，我们比较了Gittins (Journal of the Royal Statistical Society, Series B, 1979,41, 148-177)和Cowan and Katehakis (Probability in the Engineering and information Sciences, 2015,29, 51-76)的最新结果，获得了经典Gittins指数分解结果的新证明。
{"title":"Optimal activation of halting multi‐armed bandit models","authors":"Wesley Cowan, M. Katehakis, S. Ross","doi":"10.1002/nav.22145","DOIUrl":"https://doi.org/10.1002/nav.22145","url":null,"abstract":"We study new types of dynamic allocation problems the Halting Bandit models. As an application, we obtain new proofs for the classic Gittins index decomposition result compare Gittins (Journal of the Royal Statistical Society, Series B, 1979, 41, 148–177), and recent results of the authors in Cowan and Katehakis (Probability in the Engineering and Informational Sciences, 2015, 29, 51–76).","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"191 1","pages":"639 - 652"},"PeriodicalIF":0.0,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76936426","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 consider an infinite‐horizon periodic‐review inventory system with dual delivery modes, each with a minimum order quantity (MOQ). The expedited mode provides a shorter lead time than the regular mode but has a higher unit ordering cost. As the optimal ordering policy for a system with dual delivery modes and MOQ requirements is unknown and expected to be very complicated, we propose a class of simple policies called single‐index (M,S)$$ left(M,Sright) $$ policies, and we provide an exact procedure to compute the expected long‐run average total cost. Specifically, we first analyze the steady‐state distribution of the inventory position. Then we develop a recursive procedure to determine the steady‐state distribution of the inventory level. In addition, for a special case where ordering from the regular mode follows a base‐stock policy, we apply normal approximation to simplify the exact calculation of the cost. We also study a more complicated class of policies called dual‐index (M,S)$$ left(M,Sright) $$ policies. In numerical studies, we first compare the average cost of the single‐index (M,S)$$ left(M,Sright) $$ policy with that of a modified single‐index policy without MOQ consideration and the (M,S)$$ left(M,Sright) $$ policy for the single‐mode system respectively to investigate the value of the single‐index (M,S)$$ left(M,Sright) $$ policy. In addition, we find that the simpler single‐index (M,S)$$ left(M,Sright) $$ policy performs close to the dual‐index (M,S)$$ left(M,Sright) $$ policy and the optimal policy computed via dynamic programming. Finally, to assess the effectiveness of the normal approximation in the special case, we numerically compare the cost and policy parameters of the exact calculation with those of the normal approximation. The results illustrate that normal approximation not only improves the calculation speed, but also has near‐optimal solutions.
{"title":"Managing inventory systems with dual delivery modes and minimum order quantities","authors":"Yiran Li, Chaolin Yang","doi":"10.1002/nav.22113","DOIUrl":"https://doi.org/10.1002/nav.22113","url":null,"abstract":"We consider an infinite‐horizon periodic‐review inventory system with dual delivery modes, each with a minimum order quantity (MOQ). The expedited mode provides a shorter lead time than the regular mode but has a higher unit ordering cost. As the optimal ordering policy for a system with dual delivery modes and MOQ requirements is unknown and expected to be very complicated, we propose a class of simple policies called single‐index (M,S)$$ left(M,Sright) $$ policies, and we provide an exact procedure to compute the expected long‐run average total cost. Specifically, we first analyze the steady‐state distribution of the inventory position. Then we develop a recursive procedure to determine the steady‐state distribution of the inventory level. In addition, for a special case where ordering from the regular mode follows a base‐stock policy, we apply normal approximation to simplify the exact calculation of the cost. We also study a more complicated class of policies called dual‐index (M,S)$$ left(M,Sright) $$ policies. In numerical studies, we first compare the average cost of the single‐index (M,S)$$ left(M,Sright) $$ policy with that of a modified single‐index policy without MOQ consideration and the (M,S)$$ left(M,Sright) $$ policy for the single‐mode system respectively to investigate the value of the single‐index (M,S)$$ left(M,Sright) $$ policy. In addition, we find that the simpler single‐index (M,S)$$ left(M,Sright) $$ policy performs close to the dual‐index (M,S)$$ left(M,Sright) $$ policy and the optimal policy computed via dynamic programming. Finally, to assess the effectiveness of the normal approximation in the special case, we numerically compare the cost and policy parameters of the exact calculation with those of the normal approximation. The results illustrate that normal approximation not only improves the calculation speed, but also has near‐optimal solutions.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"64 5 1","pages":"617 - 636"},"PeriodicalIF":0.0,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76383755","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}
External environmental factors can deeply shape customer behavior and contribute to uncertainty in retail operations. In this study, we use field data from a national fashion sporting goods retail chain to empirically study the effect on retail store performance from one important but underappreciated external environmental factor, air pollution; and investigate the potential mechanism of this air pollution's impact. We find that air pollution has an inverted U‐shaped effect on store traffic, which is attributed to a shift of customers between offline shopping and other activities with different air pollution exposure levels. The variation in store traffic caused by air pollution further leads to a U‐shaped relationship between air pollution and the retail conversion rate. In addition, air pollution can affect customer composition as well as the perceived utility of products, reflected by more men's wear and less sportswear sold in hazy weather. In view of the globally increasing air pollution problem, especially in the context of climate change, our findings highlight the importance and value of taking air pollution into account in operations and marketing management.
{"title":"Potential value of air: Effect of air pollution on retail store performance and customer behavior","authors":"Weixin Liu, Jia Li, S. Huang, Yitong Wang","doi":"10.1002/nav.22110","DOIUrl":"https://doi.org/10.1002/nav.22110","url":null,"abstract":"External environmental factors can deeply shape customer behavior and contribute to uncertainty in retail operations. In this study, we use field data from a national fashion sporting goods retail chain to empirically study the effect on retail store performance from one important but underappreciated external environmental factor, air pollution; and investigate the potential mechanism of this air pollution's impact. We find that air pollution has an inverted U‐shaped effect on store traffic, which is attributed to a shift of customers between offline shopping and other activities with different air pollution exposure levels. The variation in store traffic caused by air pollution further leads to a U‐shaped relationship between air pollution and the retail conversion rate. In addition, air pollution can affect customer composition as well as the perceived utility of products, reflected by more men's wear and less sportswear sold in hazy weather. In view of the globally increasing air pollution problem, especially in the context of climate change, our findings highlight the importance and value of taking air pollution into account in operations and marketing management.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"30 1","pages":"601 - 616"},"PeriodicalIF":0.0,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84158131","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}
Software debugging is the process of detecting and removing bugs during software development. Although the intent of modifications to the software is to remove bugs, one cannot rule out the possibility of introducing new bugs as a result of these modifications. We consider a self‐exciting point process, which can incorporate the case of reliability deterioration due to the potential introduction of new bugs to the software during the development phase. In order to account for the unobservable process of introducing bugs, latent variables are incorporated into the self‐exciting point process models. The models are then applied to two data sets in software reliability and additional insights that can be obtained from these models are discussed. Our results suggest that the self‐exciting processes with latent factors perform better than the standard point process models in describing the behavior of software failures during the debugging process.
{"title":"A latent‐factor self‐exciting point process for software failures","authors":"Atilla Ay, Joshua Landon, F. Ruggeri, R. Soyer","doi":"10.1002/nav.22107","DOIUrl":"https://doi.org/10.1002/nav.22107","url":null,"abstract":"Software debugging is the process of detecting and removing bugs during software development. Although the intent of modifications to the software is to remove bugs, one cannot rule out the possibility of introducing new bugs as a result of these modifications. We consider a self‐exciting point process, which can incorporate the case of reliability deterioration due to the potential introduction of new bugs to the software during the development phase. In order to account for the unobservable process of introducing bugs, latent variables are incorporated into the self‐exciting point process models. The models are then applied to two data sets in software reliability and additional insights that can be obtained from these models are discussed. Our results suggest that the self‐exciting processes with latent factors perform better than the standard point process models in describing the behavior of software failures during the debugging process.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"7 2 1","pages":"584 - 600"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79520864","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}
Jingxian Chen, Liang Liang, S. Mukhopadhyay, Dong-qing Yao
Gray markets, a double‐edged sword for the multinational firms' profitability, can boost the sales revenues of low‐end subsidiaries while cannibalizing the demands of high‐end arms. To counter the adverse effects of the gray market, firms can flexibly adjust between the two strategies of setting prices (the price strategy) and choosing quantity (the quantity strategy) for its products. This paper investigates the best strategy for responding to gray markets. We consider a firm that produces two substitute products, each sold in an independent market (country). A gray marketer purchases the product sold in the low‐priced market and resells it in the high‐priced market, thereby starting a gray market. By studying the conditions of determining when and which strategy is more profitable, we establish several findings that are absent in the current literature. For instance, we find that it is likely that the quantity strategy could also be the best one in the presence of the gray competition. Moreover, implementing the quantity strategy can even automatically eliminate the gray market, which will not happen if the price strategy is employed. In addition, we identify special cases in which implementing one of the two strategies can lead to profit improvements while employing the other will cause the firm to suffer in case a gray market exists. We also examine the robustness of these findings in several cases of extensions of our model.
{"title":"Price or quantity? An analysis of strategies in the presence of gray markets","authors":"Jingxian Chen, Liang Liang, S. Mukhopadhyay, Dong-qing Yao","doi":"10.1002/nav.22109","DOIUrl":"https://doi.org/10.1002/nav.22109","url":null,"abstract":"Gray markets, a double‐edged sword for the multinational firms' profitability, can boost the sales revenues of low‐end subsidiaries while cannibalizing the demands of high‐end arms. To counter the adverse effects of the gray market, firms can flexibly adjust between the two strategies of setting prices (the price strategy) and choosing quantity (the quantity strategy) for its products. This paper investigates the best strategy for responding to gray markets. We consider a firm that produces two substitute products, each sold in an independent market (country). A gray marketer purchases the product sold in the low‐priced market and resells it in the high‐priced market, thereby starting a gray market. By studying the conditions of determining when and which strategy is more profitable, we establish several findings that are absent in the current literature. For instance, we find that it is likely that the quantity strategy could also be the best one in the presence of the gray competition. Moreover, implementing the quantity strategy can even automatically eliminate the gray market, which will not happen if the price strategy is employed. In addition, we identify special cases in which implementing one of the two strategies can lead to profit improvements while employing the other will cause the firm to suffer in case a gray market exists. We also examine the robustness of these findings in several cases of extensions of our model.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"23 1","pages":"558 - 573"},"PeriodicalIF":0.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86267032","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}
A common network security approach is to create a De‐Militarized Zone (DMZ) comprising two layers of network defense. The DMZ structure provides an extra layer of security between the sensitive information in a network (e.g., research and development files) and the component of the network that must interface with the general internet (e.g., the mail server). We consider a cyber‐attack on a DMZ network where both attacker and defender have limited resources and capabilities to attack and defend, respectively. We study two optimization problems and one game‐theoretic problem. Given that the attacker (defender) knows the potential capabilities of the defender (attacker) in the two layers, we obtain the optimal allocation of resources for the attacker (defender). The two‐optimization problems are not symmetrical. Absent any knowledge regarding the allocation of the adversary's resources, we solve a game‐theoretic problem and obtain some operational insights regarding the effect of combat (e.g., cyber) capabilities and their optimal allocation.
{"title":"Resource allocation in two‐layered cyber‐defense","authors":"Michael P. Atkinson, M. Kress","doi":"10.1002/nav.22106","DOIUrl":"https://doi.org/10.1002/nav.22106","url":null,"abstract":"A common network security approach is to create a De‐Militarized Zone (DMZ) comprising two layers of network defense. The DMZ structure provides an extra layer of security between the sensitive information in a network (e.g., research and development files) and the component of the network that must interface with the general internet (e.g., the mail server). We consider a cyber‐attack on a DMZ network where both attacker and defender have limited resources and capabilities to attack and defend, respectively. We study two optimization problems and one game‐theoretic problem. Given that the attacker (defender) knows the potential capabilities of the defender (attacker) in the two layers, we obtain the optimal allocation of resources for the attacker (defender). The two‐optimization problems are not symmetrical. Absent any knowledge regarding the allocation of the adversary's resources, we solve a game‐theoretic problem and obtain some operational insights regarding the effect of combat (e.g., cyber) capabilities and their optimal allocation.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"20 1","pages":"574 - 583"},"PeriodicalIF":0.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85281214","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}
Yajie Duan, C. Lin, D. Sargsyan, Javier Cabrera, Christine M Livingston, R. Vogel, J. Sendecki, W. Talloen, H. Geys, Surya Mohanty
Estimation of microorganism concentration in samples (bacterial cells or viral particles) has been a focal point in biomedical experiments for more than a century. Serial dilution of the samples is often used to estimate the target concentrations in immunology, virology, and pharmaceutical industry. A new methodology, called joint likelihood estimation (JLE), is proposed to estimate particles such as the number of microorganisms in a sample from counts obtained by serially diluting the sample. It models count data from the entire single dilution series rather than using only specific dilutions. The theoretical framework is based on the binomial and the Poisson distributions and is consistent with the actual experimental process. The estimator of the target concentration is obtained by MLE with derived joint likelihood functions of the observed counts including right‐censored values. Simulations demonstrated that the new JLE method significantly increases precision and accuracy of the estimate compared to the existing methods. It can be applied to a variety of studies with similar experimental designs, especially when the number of particles in the neat sample is very large.
{"title":"Particle count estimation in dilution series experiments","authors":"Yajie Duan, C. Lin, D. Sargsyan, Javier Cabrera, Christine M Livingston, R. Vogel, J. Sendecki, W. Talloen, H. Geys, Surya Mohanty","doi":"10.1002/nav.22104","DOIUrl":"https://doi.org/10.1002/nav.22104","url":null,"abstract":"Estimation of microorganism concentration in samples (bacterial cells or viral particles) has been a focal point in biomedical experiments for more than a century. Serial dilution of the samples is often used to estimate the target concentrations in immunology, virology, and pharmaceutical industry. A new methodology, called joint likelihood estimation (JLE), is proposed to estimate particles such as the number of microorganisms in a sample from counts obtained by serially diluting the sample. It models count data from the entire single dilution series rather than using only specific dilutions. The theoretical framework is based on the binomial and the Poisson distributions and is consistent with the actual experimental process. The estimator of the target concentration is obtained by MLE with derived joint likelihood functions of the observed counts including right‐censored values. Simulations demonstrated that the new JLE method significantly increases precision and accuracy of the estimate compared to the existing methods. It can be applied to a variety of studies with similar experimental designs, especially when the number of particles in the neat sample is very large.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"55 1","pages":"472 - 479"},"PeriodicalIF":0.0,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88999373","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 article investigates whether and how competing retailers should transship to each other in overlapping markets where customers encountering stock‐out at one retailer may switch to another. A two‐stage game model is used to examine the inventory and end‐of‐season transshipment decisions. We show that, instead of unconditional full‐transshipment for the case of non‐competing retailers, the stage‐2 optimal transshipment policy consists of no‐transshipment, partial‐transshipment, and full‐transshipment, determined by the interplay of switching probability, transshipment price, and remaining inventory. We find that transshipment dampens (respectively, intensifies) the inventory competition when the transshipment price is viable and below (respectively, above) a threshold. In addition to its inventory pooling effect, transshipment under competition also has a competition effect which is positive when transshipment dampens inventory competition but not too strongly. The option of bilateral transshipment leads to a Pareto improvement for competing retailers, when the competition effect is positive; but even when it is negative, Pareto improvement is still achievable for a wider transshipment price range in which the combined pooling and competition effect is positive. We identify explicitly the necessary and sufficient conditions for the existence of a unique pair of coordinating transshipment prices and provide formulas to compute them.
{"title":"Bilateral transshipment between competing retailers","authors":"Qi Fu, Liming Liu, Weixin Shang","doi":"10.1002/nav.22105","DOIUrl":"https://doi.org/10.1002/nav.22105","url":null,"abstract":"This article investigates whether and how competing retailers should transship to each other in overlapping markets where customers encountering stock‐out at one retailer may switch to another. A two‐stage game model is used to examine the inventory and end‐of‐season transshipment decisions. We show that, instead of unconditional full‐transshipment for the case of non‐competing retailers, the stage‐2 optimal transshipment policy consists of no‐transshipment, partial‐transshipment, and full‐transshipment, determined by the interplay of switching probability, transshipment price, and remaining inventory. We find that transshipment dampens (respectively, intensifies) the inventory competition when the transshipment price is viable and below (respectively, above) a threshold. In addition to its inventory pooling effect, transshipment under competition also has a competition effect which is positive when transshipment dampens inventory competition but not too strongly. The option of bilateral transshipment leads to a Pareto improvement for competing retailers, when the competition effect is positive; but even when it is negative, Pareto improvement is still achievable for a wider transshipment price range in which the combined pooling and competition effect is positive. We identify explicitly the necessary and sufficient conditions for the existence of a unique pair of coordinating transshipment prices and provide formulas to compute them.","PeriodicalId":19120,"journal":{"name":"Naval Research Logistics (NRL)","volume":"270 1","pages":"509 - 521"},"PeriodicalIF":0.0,"publicationDate":"2023-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85193676","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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