Recently, the problem of multitasking scheduling has raised a lot of interest in the service industries. Hall et al. (Discrete Applied Mathematics, 2016) proposed a shared processing multitasking scheduling model which allows a team to continue to work on the primary tasks while processing the routinely scheduled activities as they occur. With a team being modeled as a single machine, the processing sharing of the machine is achieved by allocating a fraction of the processing capacity to routine jobs and the remaining fraction, which we denote as sharing ratio, to the primary jobs. In this paper, we generalize this model to parallel machines and allow the fraction of the processing capacity assigned to routine jobs to vary from one to another. The objectives are minimizing makespan and minimizing the total completion time of primary jobs. We show that for both objectives, there is no polynomial time approximation algorithm unless P=NP if the sharing ratios are arbitrary for all machines. Then we consider the problems where the sharing ratios on some machines have a constant lower bound. For each objective, we analyze the performance of the classical scheduling algorithms and their variations and then develop a polynomial time approximation scheme when the number of machines is a constant.
{"title":"Multitasking scheduling with shared processing","authors":"Bin Fu, Yumei Huo, Hairong Zhao","doi":"10.1002/nav.22167","DOIUrl":"https://doi.org/10.1002/nav.22167","url":null,"abstract":"Recently, the problem of multitasking scheduling has raised a lot of interest in the service industries. Hall et al. (Discrete Applied Mathematics, 2016) proposed a shared processing multitasking scheduling model which allows a team to continue to work on the primary tasks while processing the routinely scheduled activities as they occur. With a team being modeled as a single machine, the processing sharing of the machine is achieved by allocating a fraction of the processing capacity to routine jobs and the remaining fraction, which we denote as sharing ratio, to the primary jobs. In this paper, we generalize this model to parallel machines and allow the fraction of the processing capacity assigned to routine jobs to vary from one to another. The objectives are minimizing makespan and minimizing the total completion time of primary jobs. We show that for both objectives, there is no polynomial time approximation algorithm unless P=NP if the sharing ratios are arbitrary for all machines. Then we consider the problems where the sharing ratios on some machines have a constant lower bound. For each objective, we analyze the performance of the classical scheduling algorithms and their variations and then develop a polynomial time approximation scheme when the number of machines is a constant.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138580342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motivated by mounting pressures to achieve environmental sustainability, and the emergence of online waste exchange platforms, in this work we propose an optimization-based framework for studying waste-to-resource formation in the industry. We first develop a linear programming market clearing model comprising self-interested agents participating in waste-to-resource trading. We then embed this in a bi-level capacity optimization problem under uncertainties in the agents' reserve prices, the goal of which is to maximize the economic savings achieved by waste-to-resource. We show that the resulting robust optimization models admit linear mixed integer programming formulations that can be readily computed using available solvers. Furthermore, we provide the formulas for applying an equitable levy and incentive scheme, to enable capacity cost-sharing among the agents. Numerical studies based on a case of organic waste streams demonstrate the usefulness of the proposed models in generating valuable insights for decision support in the design of waste-to-resource markets.
{"title":"Towards a circular economy with waste-to-resource system optimization","authors":"Tsan Sheng Adam Ng, Angel Xin Yee Mah, Kena Zhao","doi":"10.1002/nav.22163","DOIUrl":"https://doi.org/10.1002/nav.22163","url":null,"abstract":"Motivated by mounting pressures to achieve environmental sustainability, and the emergence of online waste exchange platforms, in this work we propose an optimization-based framework for studying waste-to-resource formation in the industry. We first develop a linear programming market clearing model comprising self-interested agents participating in waste-to-resource trading. We then embed this in a bi-level capacity optimization problem under uncertainties in the agents' reserve prices, the goal of which is to maximize the economic savings achieved by waste-to-resource. We show that the resulting robust optimization models admit linear mixed integer programming formulations that can be readily computed using available solvers. Furthermore, we provide the formulas for applying an equitable levy and incentive scheme, to enable capacity cost-sharing among the agents. Numerical studies based on a case of organic waste streams demonstrate the usefulness of the proposed models in generating valuable insights for decision support in the design of waste-to-resource markets.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ran Chen, René De Koster, Yugang Yu, Xiaolong Guo, Hu Yu
Autonomous vehicle storage and retrieval systems have greatly increased in popularity in the last decade. In such a system, at each tier multiple roaming vehicles transport totes between the storage locations and the lifts. However, this may lead to vehicle interference. We study in which order and by which vehicle the storage and retrieval requests should be executed to minimize the makespan, without vehicle interference. The optimal storage locations for incoming totes are also determined. A blocking mitigation protocol is proposed to address vehicle interference. We propose a two-phase matheuristic, where in the first phase, the tier is divided into zones, with each zone assigned its own vehicle. The second phase focuses on reassigning requests between adjacent vehicles to obtain improved solutions. The models proposed in both phases are solved to optimality in polynomial time and pseudo-polynomial time, respectively. Computational experiments show that the matheuristic produces high-quality solutions within a few seconds, even for large-sized instances, making it suitable for real-time decisions. Compared to methods commonly used in practice, our matheuristic can reduce the makespan by up to 15%. Our results show that making integrated decisions that combine storage assignment and request scheduling, is more beneficial than sequential optimization in terms of throughput performance, space utilization and overall system cost. We also find that increasing the number of vehicles has a diminishing return effect on the makespan. Another finding is that the system with a large number of short storage aisles leads to higher throughput capacity than that with a small number of long storage aisles.
{"title":"Blockage-free storage assignment and storage/retrieval scheduling in autonomous vehicle storage and retrieval systems","authors":"Ran Chen, René De Koster, Yugang Yu, Xiaolong Guo, Hu Yu","doi":"10.1002/nav.22166","DOIUrl":"https://doi.org/10.1002/nav.22166","url":null,"abstract":"Autonomous vehicle storage and retrieval systems have greatly increased in popularity in the last decade. In such a system, at each tier multiple roaming vehicles transport totes between the storage locations and the lifts. However, this may lead to vehicle interference. We study in which order and by which vehicle the storage and retrieval requests should be executed to minimize the makespan, without vehicle interference. The optimal storage locations for incoming totes are also determined. A blocking mitigation protocol is proposed to address vehicle interference. We propose a two-phase matheuristic, where in the first phase, the tier is divided into zones, with each zone assigned its own vehicle. The second phase focuses on reassigning requests between adjacent vehicles to obtain improved solutions. The models proposed in both phases are solved to optimality in polynomial time and pseudo-polynomial time, respectively. Computational experiments show that the matheuristic produces high-quality solutions within a few seconds, even for large-sized instances, making it suitable for real-time decisions. Compared to methods commonly used in practice, our matheuristic can reduce the makespan by up to 15%. Our results show that making integrated decisions that combine storage assignment and request scheduling, is more beneficial than sequential optimization in terms of throughput performance, space utilization and overall system cost. We also find that increasing the number of vehicles has a diminishing return effect on the makespan. Another finding is that the system with a large number of short storage aisles leads to higher throughput capacity than that with a small number of long storage aisles.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In multi-agent search planning for a randomly moving and camouflaging target, we examine heterogeneous searchers that differ in terms of their endurance level, travel speed, and detection ability. This leads to a convex mixed-integer nonlinear program, which we reformulate using three linearization techniques. We develop preprocessing steps, outer approximations via lazy constraints, and bundle-based cutting plane methods to address large-scale instances. Further specializations emerge when the target moves according to a Markov chain. We carry out an extensive numerical study to show the computational efficiency of our methods and to derive insights regarding which approach should be favored for which type of problem instance.
{"title":"Multi-agent search for a moving and camouflaging target","authors":"Miguel Lejeune, Johannes O. Royset, Wenbo Ma","doi":"10.1002/nav.22160","DOIUrl":"https://doi.org/10.1002/nav.22160","url":null,"abstract":"In multi-agent search planning for a randomly moving and camouflaging target, we examine heterogeneous searchers that differ in terms of their endurance level, travel speed, and detection ability. This leads to a convex mixed-integer nonlinear program, which we reformulate using three linearization techniques. We develop preprocessing steps, outer approximations via lazy constraints, and bundle-based cutting plane methods to address large-scale instances. Further specializations emerge when the target moves according to a Markov chain. We carry out an extensive numerical study to show the computational efficiency of our methods and to derive insights regarding which approach should be favored for which type of problem instance.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A supplier sells a product through a retailer to the market with uncertain demand. The retailer has a signal useful for updating the forecast of market uncertainty, while the supplier can offer a payment to acquire the retailer's signal, termed information sharing. Due to differential means of market access and methods of data analysis, the supplier and the retailer hold diverse beliefs about market conditions. A firm is more confident about market conditions as it perceives the market to be less uncertain. The supplier can be either aware or unaware of the retailer's market belief. In the former case, the supplier correctly predicts the retailer's belief-based response and makes decision accordingly. In the latter case, the supplier infers the retailer's market belief from the retailer's decision about signal disclosure. We unveil the concrete circumstances where the supplier gains access to the retailer's signal, which would not occur when they held the same accurate market belief. Moreover, with the actual profit performance as the measure, the firms can benefit from holding diverse market beliefs, albeit not simultaneously. The supplier's knowledge of the retailer's market belief can facilitate information sharing but can have detrimental effects on the firms' actual profit performance. Given the opportunity, the retailer may report a market belief that is less confident than its real market belief in communicating with the supplier, which can deter information sharing but has intricate effects on the firms' profits.
{"title":"Firms' diverse market beliefs can facilitate information sharing and improve profit performance","authors":"Li Jiang, Zhongyuan Hao","doi":"10.1002/nav.22165","DOIUrl":"https://doi.org/10.1002/nav.22165","url":null,"abstract":"A supplier sells a product through a retailer to the market with uncertain demand. The retailer has a signal useful for updating the forecast of market uncertainty, while the supplier can offer a payment to acquire the retailer's signal, termed information sharing. Due to differential means of market access and methods of data analysis, the supplier and the retailer hold diverse beliefs about market conditions. A firm is more confident about market conditions as it perceives the market to be less uncertain. The supplier can be either aware or unaware of the retailer's market belief. In the former case, the supplier correctly predicts the retailer's belief-based response and makes decision accordingly. In the latter case, the supplier infers the retailer's market belief from the retailer's decision about signal disclosure. We unveil the concrete circumstances where the supplier gains access to the retailer's signal, which would not occur when they held the same accurate market belief. Moreover, with the actual profit performance as the measure, the firms can benefit from holding diverse market beliefs, albeit not simultaneously. The supplier's knowledge of the retailer's market belief can facilitate information sharing but can have detrimental effects on the firms' actual profit performance. Given the opportunity, the retailer may report a market belief that is less confident than its real market belief in communicating with the supplier, which can deter information sharing but has intricate effects on the firms' profits.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Degradation models based on heterogeneous Wiener processes are commonly used to assess information on the lifetime of highly reliable products. An optimal test plan given limited resources is generally obtained using numerical methods for heterogeneous Wiener processes. However, numerical searches for optimal test plans have the disadvantage of being time-consuming and may provide unclear explanations for the findings. To overcome these difficulties, we derive an explicit expression for decision variables (such as the termination time, number of measurements, and sample size) of - and -optimal test plans with cost constraints. The theoretical results not only ensure that the optimal test plan is found, but also provide clear insights into the decision variables affected by model parameters and experimental costs. Some numerical examples are presented to support the efficiency and applicability of the optimal test plans.
基于异质维纳过程的退化模型通常用于评估高可靠性产品的寿命信息。对于非均质维纳过程，通常采用数值方法得到资源有限的最优试验方案。然而，数值搜索最优测试方案的缺点是耗时，并且可能对结果提供不明确的解释。为了克服这些困难，我们推导出具有成本约束的D $$ D $$ -和V $$ V $$ -最优测试计划的决策变量(如终止时间、测量次数和样本量)的显式表达式。理论结果不仅保证了找到最优的试验方案，而且对受模型参数和试验成本影响的决策变量提供了清晰的认识。数值算例验证了优化方案的有效性和适用性。
{"title":"Optimal test planning for heterogeneous Wiener processes","authors":"Ya-Shan Cheng, Chien-Yu Peng","doi":"10.1002/nav.22164","DOIUrl":"https://doi.org/10.1002/nav.22164","url":null,"abstract":"Degradation models based on heterogeneous Wiener processes are commonly used to assess information on the lifetime of highly reliable products. An optimal test plan given limited resources is generally obtained using numerical methods for heterogeneous Wiener processes. However, numerical searches for optimal test plans have the disadvantage of being time-consuming and may provide unclear explanations for the findings. To overcome these difficulties, we derive an explicit expression for decision variables (such as the termination time, number of measurements, and sample size) of <math altimg=\"urn:x-wiley:nav:media:nav22164:nav22164-math-0001\" display=\"inline\" location=\"graphic/nav22164-math-0001.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>D</mi>\u0000</mrow>\u0000$$ D $$</annotation>\u0000</semantics></math>- and <math altimg=\"urn:x-wiley:nav:media:nav22164:nav22164-math-0002\" display=\"inline\" location=\"graphic/nav22164-math-0002.png\" overflow=\"scroll\">\u0000<semantics>\u0000<mrow>\u0000<mi>V</mi>\u0000</mrow>\u0000$$ V $$</annotation>\u0000</semantics></math>-optimal test plans with cost constraints. The theoretical results not only ensure that the optimal test plan is found, but also provide clear insights into the decision variables affected by model parameters and experimental costs. Some numerical examples are presented to support the efficiency and applicability of the optimal test plans.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The internationalization of production requires multinational firms to determine a local content rate for their products made and sold in a foreign country. In this paper, we investigate the impact of a government's local content requirement (LCR) on the local content rate and pricing decisions of a multinational firm who competes with a local firm in a market. In an emerging market, the multinational firm increases his local content rate to comply with an LCR if the LCR involves a moderate threshold and a sufficiently large penalty tariff rate. Although a small penalty tariff rate cannot induce the multinational firm's compliance, a larger penalty tariff leads the firm to adopt a higher local content rate. When the multinational firm complies with the LCR, a higher LCR threshold or penalty tariff rate shifts away the multinational firm's demand and profit but may not benefit the local firm if the two firms' price competition is fiercer than their quality competition. In addition, if the two firms' quality competition is fiercer than their price competition, a large LCR threshold may still not benefit the local firm. In contrast, in a developed market, the multinational firm should increase his local content rate as the quality‐cost tradeoff ratio increases. The LCR plays the same effect on the multinational firm as that in an emerging market, whereas its effect on the local firm still depends on the relative intensity of the two firms' price competition versus quality competition, but under reverse conditions.
{"title":"Penetrating a market with local‐content and pricing decisions: Implications for a multinational firm in the competition with a local firm","authors":"Zhenning Dong, Liping Liang, Nanqin Liu, Mingming Leng","doi":"10.1002/nav.22161","DOIUrl":"https://doi.org/10.1002/nav.22161","url":null,"abstract":"Abstract The internationalization of production requires multinational firms to determine a local content rate for their products made and sold in a foreign country. In this paper, we investigate the impact of a government's local content requirement (LCR) on the local content rate and pricing decisions of a multinational firm who competes with a local firm in a market. In an emerging market, the multinational firm increases his local content rate to comply with an LCR if the LCR involves a moderate threshold and a sufficiently large penalty tariff rate. Although a small penalty tariff rate cannot induce the multinational firm's compliance, a larger penalty tariff leads the firm to adopt a higher local content rate. When the multinational firm complies with the LCR, a higher LCR threshold or penalty tariff rate shifts away the multinational firm's demand and profit but may not benefit the local firm if the two firms' price competition is fiercer than their quality competition. In addition, if the two firms' quality competition is fiercer than their price competition, a large LCR threshold may still not benefit the local firm. In contrast, in a developed market, the multinational firm should increase his local content rate as the quality‐cost tradeoff ratio increases. The LCR plays the same effect on the multinational firm as that in an emerging market, whereas its effect on the local firm still depends on the relative intensity of the two firms' price competition versus quality competition, but under reverse conditions.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135429956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we provide a semi‐analytical approach to determine the optimal designs for two‐variable gamma accelerated degradation tests under three criteria: ‐optimality, ‐optimality, and ‐optimality. We first use general equivalence theorem to prove that the optimal approximate designs only allocate test units at the four vertices of a rectangular design region, and the corresponding optimal proportion of total number of measurements at each stress level is derived. Next, we apply the concept of prescribed accuracy level and total experimental cost to further determine optimal integer designs. More specifically, a numerical approach is used to resolve the number of test units and number of measurements at each stress level. Finally, an example is presented to illustrate the proposed procedure and compare the efficiency of optimal designs under three optimal criteria.
{"title":"Optimizing two‐variable gamma accelerated degradation tests with a semi‐analytical approach","authors":"Hung‐Ping Tung","doi":"10.1002/nav.22162","DOIUrl":"https://doi.org/10.1002/nav.22162","url":null,"abstract":"Abstract In this paper, we provide a semi‐analytical approach to determine the optimal designs for two‐variable gamma accelerated degradation tests under three criteria: ‐optimality, ‐optimality, and ‐optimality. We first use general equivalence theorem to prove that the optimal approximate designs only allocate test units at the four vertices of a rectangular design region, and the corresponding optimal proportion of total number of measurements at each stress level is derived. Next, we apply the concept of prescribed accuracy level and total experimental cost to further determine optimal integer designs. More specifically, a numerical approach is used to resolve the number of test units and number of measurements at each stress level. Finally, an example is presented to illustrate the proposed procedure and compare the efficiency of optimal designs under three optimal criteria.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chong Wang, Lixin Miao, Canrong Zhang, Tao Wu, Zhe Liang
Abstract This paper studies the berth allocation and quay crane assignment problem (denoted by BACAP) under uncertainty. We assume that the ships' arrival and operation time is uncertain in this problem. We merge the proactive and reactive strategies to address the two‐stage robust optimization (denoted by RO) model for the BACAP to obtain a complete schedule with robustness. We obtain the berth allocation and quay crane assignment with a proactive strategy in the first stage. In the second stage, we formulate a rescheduling model with a reactive strategy considering the sensitivity towards the change in the complete schedule. The second stage model is based on the prospect theory, a quantitative way to describe the stakeholders' perception, including the port managers and shipowners, of the deviation from the baseline plan. The two stages are iterated until a favorable schedule with high robustness is found. To illustrate the superiority of the two‐stage robust optimization model with the prospect theory for the complete schedule, we give an intuitive example to compare the performance among the related models. The two‐stage RO model with the prospect theory for the complete schedule can generate a lower cost and higher robustness schedule. As for the solution methods, the column and constraint generation (denoted by C&CG) algorithm is applied to obtain the exact solution for the two‐stage RO model. Moreover, we propose the scenario‐constrained C&CG (denoted by SC) algorithm, which can reduce constraints and variables for the master problem to accelerate the solving process of the two‐stage RO model. In addition, the optimality of the SC algorithm is verified by analyzing the pattern of the occurrence of the worst‐case scenarios. Besides, to tackle the large‐scale instances, we propose the schedule‐fixed (denoted by SF) algorithm, in which the results of the previous iterations are treated as fixed. The SF algorithm can increase computing efficiency with a small gap compared to the optimal solution value. Furthermore, extensive numerical experiments are conducted on both real‐life instances and randomly generated instances to verify the superiority and generality of our model and algorithms.
{"title":"Robust optimization for the integrated berth allocation and quay crane assignment problem","authors":"Chong Wang, Lixin Miao, Canrong Zhang, Tao Wu, Zhe Liang","doi":"10.1002/nav.22159","DOIUrl":"https://doi.org/10.1002/nav.22159","url":null,"abstract":"Abstract This paper studies the berth allocation and quay crane assignment problem (denoted by BACAP) under uncertainty. We assume that the ships' arrival and operation time is uncertain in this problem. We merge the proactive and reactive strategies to address the two‐stage robust optimization (denoted by RO) model for the BACAP to obtain a complete schedule with robustness. We obtain the berth allocation and quay crane assignment with a proactive strategy in the first stage. In the second stage, we formulate a rescheduling model with a reactive strategy considering the sensitivity towards the change in the complete schedule. The second stage model is based on the prospect theory, a quantitative way to describe the stakeholders' perception, including the port managers and shipowners, of the deviation from the baseline plan. The two stages are iterated until a favorable schedule with high robustness is found. To illustrate the superiority of the two‐stage robust optimization model with the prospect theory for the complete schedule, we give an intuitive example to compare the performance among the related models. The two‐stage RO model with the prospect theory for the complete schedule can generate a lower cost and higher robustness schedule. As for the solution methods, the column and constraint generation (denoted by C&CG) algorithm is applied to obtain the exact solution for the two‐stage RO model. Moreover, we propose the scenario‐constrained C&CG (denoted by SC) algorithm, which can reduce constraints and variables for the master problem to accelerate the solving process of the two‐stage RO model. In addition, the optimality of the SC algorithm is verified by analyzing the pattern of the occurrence of the worst‐case scenarios. Besides, to tackle the large‐scale instances, we propose the schedule‐fixed (denoted by SF) algorithm, in which the results of the previous iterations are treated as fixed. The SF algorithm can increase computing efficiency with a small gap compared to the optimal solution value. Furthermore, extensive numerical experiments are conducted on both real‐life instances and randomly generated instances to verify the superiority and generality of our model and algorithms.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136033067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This article considers an identical parallel‐machine task scheduling problem motivated by operations management of online services. A task with an integer processing time can be split into sub‐tasks with integer processing times. Each task has multiple integer milestones and at each milestone a nonnegative penalty will occur. The penalty value of a task at a milestone is a convex nonincreasing function of the completed amount by this milestone. Our objective is to determine a feasible schedule for all the tasks on given identical parallel machines, such that the sum of all tasks' total penalty at all milestones is minimized. We prove the NP‐hardness of this problem in the ordinary sense and develop a branch‐and‐price algorithm. Computational experiments utilizing data from an online service operations survey show that this algorithm is singularly efficient and promising.
{"title":"A branch‐and‐price algorithm for identical parallel machine scheduling with multiple milestones","authors":"Weiya Zhong, Jia Cui, Yiwei Jiang","doi":"10.1002/nav.22154","DOIUrl":"https://doi.org/10.1002/nav.22154","url":null,"abstract":"Abstract This article considers an identical parallel‐machine task scheduling problem motivated by operations management of online services. A task with an integer processing time can be split into sub‐tasks with integer processing times. Each task has multiple integer milestones and at each milestone a nonnegative penalty will occur. The penalty value of a task at a milestone is a convex nonincreasing function of the completed amount by this milestone. Our objective is to determine a feasible schedule for all the tasks on given identical parallel machines, such that the sum of all tasks' total penalty at all milestones is minimized. We prove the NP‐hardness of this problem in the ordinary sense and develop a branch‐and‐price algorithm. Computational experiments utilizing data from an online service operations survey show that this algorithm is singularly efficient and promising.","PeriodicalId":49772,"journal":{"name":"Naval Research Logistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135995921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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