Multiple subset sum with inclusive assignment set restrictions

Kellerer, Hans; Leung, Joseph Y.-T.; Li, Chung‐Lun

doi:10.1002/nav.20466

Cited by 9 publications

(5 citation statements)

References 17 publications

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“…To solve the problem, they propose a greedy heuristic with a worst-case performance ratio of 1/3 and two different 1/2-approximation algorithms. Kellerer et al (2011) consider the multiple subset sum problem with inclusive assignment restrictions, meaning that the eligible set of an item must be a subset or superset of that of another item. They propose an efficient 0.6492-approximation algorithm and a polynomial time approximation scheme for the problem.…”

Section: Production and Operations Managementmentioning

confidence: 99%

Fulfillment scheduling for buy‐online‐pickup‐in‐store orders

Chen

2022

Production and Operations Management

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One of the most popular ways of shopping in an omnichannel retailing environment is buy‐online‐pickup‐in‐store (BOPS). Retailers often promise BOPS shoppers short in‐store pickup ready times. We study fulfillment scheduling decisions of BOPS orders destined for a single store of a retailer. There are two fulfillment options for BOPS orders: they can be either processed at a fulfillment center (FC) and delivered to the store or processed at the store without needing delivery. There are two types of trucks available to deliver the BOPS orders fulfilled at the FC: prescheduled trucks that are already committed to replenishing store inventory and have some spare capacity that can be utilized, and additional trucks that can be hired from third‐party logistics providers. There is a fixed cost for using each truck; the cost for using a prescheduled truck is lower than that for using an additional truck. If an order is fulfilled at the store, it incurs a processing cost and a processing time, whereas the processing cost and time are negligible if an order is fulfilled at the FC. The problem is to determine where to fulfill each order (FC vs. the store), how to assign the orders fulfilled at the FC to trucks for delivery, and how to schedule the orders fulfilled at the store for store processing, so as to minimize the total fulfillment cost, including the delivery cost from the FC to the store incurred by the orders processed at the FC, and the processing cost for fulfilling the rest of the orders at the store, subject to the constraint that each order is ready for pickup at the store by its promised pickup ready time. We consider various cases of the problem by clarifying their computational complexity, developing optimal algorithms and heuristics, and analyzing theoretical performance of the heuristics. We also conduct computational experiments to validate the effectiveness of the proposed heuristics in both static and dynamic settings and derive important insights about how the presence of prescheduled trucks and the presence of store fulfillment option impact the fulfillment cost and decisions.

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Section: Production and Operations Managementmentioning

confidence: 99%

Fulfillment scheduling for buy‐online‐pickup‐in‐store orders

Chen

2022

Production and Operations Management

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“…Processing set restrictions do not only appear in scheduling models. Kellerer et al (2011) have studied a problem of packing a given set of items into a given set of bins so that the total weight of the items packed is maximized (i.e., a multiple subset sum problem), where the bins have inclusive processing set restrictions. Interesting extensions of Kellerer et al's model that are worth investigating include (i) problem with heterogeneous bin capacities, (ii) problem with a profit maximization objective where each item is associated with a given profit, and…”

Section: Future Research and Recommendationsmentioning

confidence: 99%

Scheduling with processing set restrictions: A literature update

Leung

2016

International Journal of Production Economics

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“…One special case of processing set restrictions, that has been studied very thoroughly, is the case of nested processing sets . In this case, one and only one of the following four conditions must hold for any two jobs i and j :

\begin{matrix} left \\ (i) M_{i} = M_{j}, \\ (ii) M_{i} \subset M_{j}, \\ (iii) M_{i} \supset M_{j}, \\ (iv) M_{i} and M_{j} are disjoint . \end{matrix}

Scheduling problems with machine eligibility constraints and processing set restrictions are of interest to industrial engineers, operations researchers as well as computer scientists, and have many applications in practice (see, e.g., and the recent surveys ). In this article, we consider the problem

P m | M_{j} (nested) | \sum w_{j} T_{j}

.…”

Section: Introductionmentioning

confidence: 99%

“…In the literature of scheduling with the eligibility constraints, the previous studies are mainly concerned with the inclusive eligibility constraints, that is, one and only one of the following three conditions must hold for any two jobs i and j (see, for instance, Glass and Kellerer , Hwang et al , Keller et al and Zhang ):

\begin{matrix} left \\ (i) M_{i} = M_{j}, \\ (ii) M_{i} \subset M_{j}, \\ (iii) M_{i} \supset M_{j} . \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness

Pinedo

Wan

2017

Naval Research Logistics

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We study a parallel machine scheduling problem, where a job j can only be processed on a specific subset of machines Mj, and the Mj subsets of the n jobs are nested. We develop a two‐phase heuristic for minimizing the total weighted tardiness subject to the machine eligibility constraints. In the first phase, we compute the factors and statistics that characterize a problem instance. In the second phase, we propose a new composite dispatching rule, the Apparent Tardiness Cost with Flexibility considerations (ATCF) rule, which is governed by several scaling parameters of which the values are determined by the factors obtained in the first phase. The ATCF rule is a generalization of the well‐known ATC rule which is very widely used in practice. We further discuss how to improve the dispatching rule using some simple but powerful properties without requiring additional computation time, and the improvement is quite satisfactory. We apply the Sequential Uniform Design Method to design our experiments and conduct an extensive computational study, and we perform tests on the performance of the ATCF rule using a real data set from a large hospital in China. We further compare its performance with that of the classical ATC rule. We also compare the schedules improved by the ATCF rule with what we believe are Near Optimal schedules generated by a general search procedure. The computational results show that especially with a low due date tightness, the ATCF rule performs significantly better than the well‐known ATC rule generating much improved schedules that are close to the Near Optimal schedules. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 249–267, 2017

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Multiple subset sum with inclusive assignment set restrictions

Cited by 9 publications

References 17 publications

Fulfillment scheduling for buy‐online‐pickup‐in‐store orders

Fulfillment scheduling for buy‐online‐pickup‐in‐store orders

Scheduling with processing set restrictions: A literature update

Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness

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