New solution approaches for optimization problems with combinatorial aspects in logistics management

Heiko Diefenbach

Publications of Darmstadt Technical University, Institute for Business Studies (BWL) from Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL)

Abstract: This dissertation comprises five papers, which have been published in scientific journals between 2019 and 2022. The papers consider logistic optimization problems from three different subjects with a focus on intra-logistics. All considered optimization problems have strong combinatorial aspects. To solve the considered problems, various solution approaches including different decomposition techniques are employed. Paper 1 investigates the optimization of the layout and storage assignment in warehouses with U-shaped order picking zones. The paper considers two objectives, namely minimizing the order picker's walking distance and physical strain during order picking. To solve the problem, a semantic decomposition approach is proposed, which solves the problem in polynomial time. In a computational study, both considered objectives are found to be mostly complementary. Moreover, suggestions for advantageous layout designs and storage assignments are derived. Paper 2 considers the problem of how to stow bins on tow trains in order to minimize the handling personnel's physical strain for loading and unloading. The problem is shown to be NP-hard and decomposed semantically. Utilising the decomposition, the problem is solved exactly with dynamic programming and heuristically with a greedy randomized adaptive search procedure. A consecutive computational study shows that both procedures perform well. Beyond that, it investigates the influence of the tow train wagons' design on the considered objective. Paper 3 is concerned with the problem of scheduling jobs with time windows on unrelated parallel machines, which is a NP-hard optimization problem that has applications, i.a., in berth allocation and truck dock scheduling. The paper presents an exact logic-based Benders decomposition procedure and a heuristic solution approach based on a set partitioning formulation of the problem. Moreover, three distinct objectives, namely minimizing the makespan, the maximum flow time, and the maximum lateness are considered. Both procedures exhibit good performances in the concluding computational study. Paper 4 addresses the problem of order picker routing in a U-shaped order picking zone with the objective of minimizing the covered walking distance. The problem is proven to be NP-hard. An exact logic-based Benders decomposition procedure as well as a heuristic dynamic programming approach are developed and shown to perform well in computational tests. Beyond that, the paper discusses different storage assignment policies and compares them in a numeric study. Paper 5 studies scheduling electrically powered tow trains in in-plant production logistics. The problem is regarded as an Electric Vehicle Scheduling Problem, where tow trains must be assigned to timetabled service trips. Since the tow trains' range is limited, charging breaks need to be scheduled in-between trips, which require detours and time. The objective consists in minimizing the required fleet size. The problem is shown to be NP-hard. To solve the problem, Paper 5 proposes a branch-and-check approach that is applicable for various charging technologies, including battery swapping and plug-in charging with nonlinear charge increase. In a computational study, the approach's practical applicability is demonstrated. Moreover, influences of the batteries' maximum capacity and employed charging technology are investigated.

Date: 2023
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