Exact and heuristic algorithms for scheduling jobs with time windows on unrelated parallel machines

Tadumadze, Giorgi; Emde, Simon; Diefenbach, Heiko

doi:10.1007/s00291-020-00586-w

Cited by 12 publications

(4 citation statements)

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“…To make the problem more tractable, we propose a decomposition scheme in the spirit of logic-based and combinatorial Benders decomposition (Codato and Fischetti 2006;Hooker 2007), which has seen success dealing with difficult combinatorial optimization problems (e.g., Kress et al 2019;Tadumadze et al 2020;Fang et al 2021;Huang et al 2021). The general idea consists of splitting the original problem into a master and a slave component.…”

Section: Logic-based Benders Decomposition For the Picker Routing Problemmentioning

confidence: 99%

New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

et al. 2021

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This paper develops new solution procedures for the order picker routing problem in U-shaped order picking zones with a movable depot, which has so far only been solved using simple heuristics. The paper presents the first exact solution approach, based on combinatorial Benders decomposition, as well as a heuristic approach based on dynamic programming that extends the idea of the venerable sweep algorithm. In a computational study, we demonstrate that the exact approach can solve small instances well, while the heuristic dynamic programming approach is fast and exhibits an average optimality gap close to zero in all test instances. Moreover, we investigate the influence of various storage assignment policies from the literature and compare them to a newly derived policy that is shown to be advantageous under certain circumstances. Secondly, we investigate the effects of having a movable depot compared to a fixed one and the influence of the effort to move the depot.

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Section: Logic-based Benders Decomposition For the Picker Routing Problemmentioning

confidence: 99%

New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

et al. 2021

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“…The constraint enforces the set of jobs assigned to the machine with the largest portion in the objective value that must remove a job in the next iteration. Although we considered the cut mentioned in Tadumadze et al [47] to change the set of jobs assigned to every machine by removing a job, the numerical test reports that it does not perform better than the greedy cut (27). We want to point out that constraint (27) does not warrant an optimal solution as it does not consider the impact on the objective function value by removing a job from other machines, which potentially can lead to a better job-to-machine assignment.…”

Section: Proposition 2 Constraint (26) Is a Valid Benders Optimality Cutmentioning

confidence: 99%

“…ibility in solving a sub-problem, LBBD has been used to solve various complex combination optimization problems, including inventory location[52], home healthcare delivery[27], parallel machine scheduling[34,47,49], integrated process planning and scheduling[4], gantry crane scheduling[26] and so on. Furthermore, LBBD, as a decomposition framework, can be easily stretched using heuristics to solve its master problem or sub-problems.We keep the assignment decision in the master problem, and the sequence decision is left to the sub-problems for the problem in question.…”

mentioning

confidence: 99%

Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

Guo

Wang

et al. 2021

Complex Intell. Syst.

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In this paper, an identical parallel machine scheduling problem with step-deteriorating jobs is considered to minimize the weighted sum of tardiness cost and extra energy consumption cost. In particular, the actual processing time of a job is assumed to be a step function of its starting time and its deteriorating threshold. When the starting time of a job is later than its deteriorating threshold, the job faces two choices: (1) maintaining its status in holding equipment and being processed with a base processing time and (2) consuming an extra penalty time to finish its processing. The two work patterns need different amounts of energy consumption. To implement energy-efficient scheduling, the selection of the pre-processing patterns must be carefully considered. In this paper, a mixed integer linear programming (MILP) model is proposed to minimize the total tardiness cost and the extra energy cost. Decomposition approaches based on logic-based Benders decomposition (LBBD) are developed by reformulating the studied problem into a master problem and some independent sub-problems. The master problem is relaxed by only making assignment decisions. The sub-problems are to find optimal schedules in the job-to-machine assignments given by the master problem. Moreover, MILP and heuristic based on Tabu search are used to solve the sub-problems. To evaluate the performance of our methods, three groups of test instances were generated inspired by both real-world applications and benchmarks from the literature. The computational results demonstrate that the proposed decomposition approaches can compute competitive schedules for medium- and large-size problems in terms of solution quality. In particular, the LBBD with Tabu search performs the best among the suggested four methods.

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“…It is well-known that the truck scheduling problem can be modeled as a parallel machine scheduling problem (Tadumadze et al 2019(Tadumadze et al , 2020. Thus, we generate arrival times and (un-)loading times of trucks similarly to the instance generation scheme proposed by Hall and Posner (2001).…”

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confidence: 99%

Robust spotter scheduling in trailer yards

2020

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Spotters (also denoted as switchers) are specialized terminal tractors, which are dedicated to the rapid maneuvering of semitrailers between parking lot and dock doors in large trailer yards. This paper is dedicated to spotter scheduling, i.e., the assignment of predefined trailer movements to a given fleet of spotters. The limited number of dock doors for loading and unloading is often the scarce resource during trailer processing, so that idle time of the bottleneck, e.g., caused by unforeseen delay in the yard, is to be avoided. In this setting, we aim to insert time buffers between any pair of subsequent jobs assigned to the same spotter, so that small delays are not propagated and subsequent jobs can still be executed in a timely manner. We formalize two versions of the resulting robust spotter scheduling problem and provide efficient algorithms for finding optimal solutions in polynomial time. Furthermore, we simulate delays during the execution of spotter schedules and show that the right robustness objective can greatly improve yard performance.

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Exact and heuristic algorithms for scheduling jobs with time windows on unrelated parallel machines

Cited by 12 publications

References 50 publications

New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

New solution procedures for the order picker routing problem in U-shaped pick areas with a movable depot

Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

Robust spotter scheduling in trailer yards

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