Subproblem Separation in Logic-Based Benders\u27 Decomposition for the Vehicle Routing Problem with Local Congestion

Subproblem separation is a common strategy for the acceleration of the logic-based Benders\u27 decomposition (LBBD). However, it has only been applied to problems with an inherently separable subproblem structure. This paper proposes a new method to separate the subproblem using the connected components algorithm. The subproblem separation is applied to the vehicle routing problem with local congestion (VRPLC). Accordingly, new Benders\u27 cuts are derived for the new subproblem formulation. The computational experiments evaluate the effectiveness of subproblem separation for different methods applying new cuts. It is shown that subproblem separation significantly benefits the LBBD scheme

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

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 frst 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 infuence 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 efects of having a movable depot compared to a fxed one and the infuence of the efort to move the depot

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

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

Parallel batching with multi-size jobs and incompatible job families

Parallel batch scheduling has many applications in the industrial sector, like in material and chemical treatments, mold manufacturing and so on. The number of jobs that can be processed on a machine mostly depends on the shape and size of the jobs and of the machine. This work investigates the problem of batching jobs with multiple sizes and multiple incompatible families. A flow formulation of the problem is exploited to solve it through two column generation-based heuristics. First, the column generation finds the optimal solution of the continuous relaxation, then two heuristics are proposed to move from the continuous to the integer solution of the problem: one is based on the price-and-branch heuristic, the other on a variable rounding procedure. Experiments with several combinations of parameters are provided to show the impact of the number of sizes and families on computation times and quality of solutions

Bi-Criteria Batching and Scheduling in Hybrid Flow Shops

In this research, a bi-criteria batching and scheduling problem is investigated in hybrid flow shop environments, where unrelated-parallel machines are run simultaneously with different capacities and eligibilities in processing, in some stages. The objective is to simultaneously minimize a linear combination of the total weighted completion time and total weighted tardiness. The first favors the producer’s interest by minimizing work-in-process inventory, inventory holding cost, and energy consumption as well as maximizing machine utilization, while the second favors the customers’ interest by maximizing customers’ service level and delivery speed. In particular, it disregards the group technology assumptions (GTAs) by allowing for the possibility of splitting pre-determined groups of jobs into inconsistent batches in order to improve the operational efficiency. A comparison between the group scheduling and batch scheduling approaches reveals the outstanding performance of the batch scheduling approach. As a result, contrary to the GTAs, jobs belonging to a group might be processed on more than one machine as batches, but not all machines may be capable of processing all jobs. A sequence- and machine-dependent setup time is required between each of two consecutively scheduled batches belonging to different groups. Based on manufacturing company policy, the desired lower bounds on batch sizes are considered for the number of jobs assigned to batches. Although, the direction in which all jobs move through production line is the same, some jobs may skip some stages. Furthermore, to reflect real industry requirements, the job release times and the machine availability times are considered to be dynamic, which means not all machines and jobs are available at the beginning of the planning horizon.The problem is formulated with the help of four mixed-integer linear programming (MILP) models. Two out of four MILP models are formulated as two integrated phases, i.e., batching and scheduling phases, with respect to the precedence constraints between each pair of jobs batches and or the position concept within batches. The optimal combination between batch compositions of groups are determined in the batching phase, while the optimal assignment and sequence of batches on machines and sequence of jobs within batches are determined in the scheduling phase, with respect to a set of operational constraints. A batch composition of a group corresponding to a particular stage, determined in the batching phase of the MILP model, represents the number of batches assigned to the group as well as the number and type of jobs belonging to each batch of that group. Since the first and second MILP models lead to unmanageable solution space, the relaxed MILP model, which allocates one and only one job to each batch of each group in each stage, can be developed to focus on the non-dominated solution space. The optimal solutions of MILP models and relaxed MILP model are equal, if and only if the optimal solution of the relaxed MILP model does not violate the desired lower bounds on batch sizes. Since the relaxed MILP model cannot guarantee the optimal solution of the MILP models, a third MILP model is developed by integrating batching and scheduling phases. This MILP model eliminates an exhaustive combination enumeration between batch compositions of all groups in all stages. Although the third MILP model converges to the optimal solution slower than the relaxed MILP model, it guarantees finding the optimal solution of the first and second MILP models. A comparison between four MILP models shows the superior performance of the third MILP model. However, since the problem is strongly NP-hard, it is not possible to find its optimal solution within a reasonable time as the problem size increases from small to medium to large, even by the relaxed MILP model or the fourth MILP model. Therefore, several meta-heuristic algorithms based upon basic local search, basic population-based search, and hybridization of local search and population-based searches are developed, which move back and forth between batching and scheduling phases. Tabu Search (TS) is implemented as a basic local search algorithm, while Tabu Search Path-Relinking (TS PR) is implemented as a local search algorithm enhanced with a population-based structure. TS is incorporated into the framework of path-relinking to exploit the information on good solutions. The TS PR algorithm comprises several distinguishing features including relinking procedures to effectively explore trajectories connecting elite solutions and the methods used to choose the reference solution. Particle Swarm Optimization (PSO) is implemented as a basic population-based algorithm, while Particle Swarm Optimization enhanced with a local search algorithm (PSO LSA) is developed to realize the benefits of batching and, consequently, enhance the quality of solutions.Since there is interdependency between positions of a job in different stages of a hybrid flow shop in batch scheduling, a meta-heuristic algorithm is not capable of capturing these interdependencies and, subsequently, its efficacy can be diminished. In order to capture this interdependency, the non-, partial- complete-, and stage-based interdependency strategy are developed. In the stage-based-interdependency strategy, a complete sequence related to all of the stages is gradually determined, stage by stage. An initial solution finding mechanism is developed to trigger the search into the solution space and generate an initial population. The performances of these algorithms are compared to each other in order to identify which algorithm(s) outperforms the others. Nevertheless, the performances of the best algorithm(s) are evaluated with respect to a tight lower bound obtained from a branch-and-price (B&P) algorithm. The B&P algorithm uses Dantzig-Wolfe decomposition (DWD) to divide the original problem into a master problem and several sub-problems (SPs) corresponding to each stage. The original problem is decomposed into the SPs by three DWDs corresponding to the three MILP models. Although, by applying DWD technique in the first and second MILP models, an exhaustive combination enumeration between batch compositions of all groups in all stages is excluded and, as a result, the SPs are easier to solve than the original problem, they are still strongly NP-hard because of an enormous number of combinations between batch compositions of all groups in each stage. However, the DWD technique corresponding to the relaxed MILP model not only drastically reduces the number of variables and constraints in the SPs, but also eliminates the batching phase of the first and second MILP models. Decomposing the original problem based on the relaxed MILP model and implementing the B&P algorithm cannot guarantee optimal solutions or tight lower bounds of problems unless the number of violations in the desired lower bounds on batch sizes is not significant. Therefore, the third MILP model is decomposed by DWD so that the B&P algorithm is capable of finding tight lower bounds even for large-size instances of the problem. A comparison between the lower bounds obtained from the B&P algorithm and CPLEX reveals the impressive performance of the B&P algorithm, particularly for large-size problems. The evaluation of the best algorithms based upon these tight lower bounds developed by the B&P algorithm, uncovers the outstanding performance of hybrid algorithms compared to the results obtained from CPLEX.Keywords: Bi-Criteria Objective, Column Generation, Batch Scheduling, Tabu Search, Batching and Scheduling, Desired Lower Bounds on Batch Sizes, Path-Relinking, Branch-and-Price Optimization Algorithm, Particle Swarm Optimization, Group Scheduling, Hybrid Flow Shop, Dantzig-Wolfe Decomposition, Mixed-Integer Linear Programming Model, Sequence- and Machine-Dependent Setup Tim

Bi-Criteria Batching and Scheduling in Hybrid Flow Shops

In this research, a bi-criteria batching and scheduling problem is investigated in hybrid flow shop environments, where unrelated-parallel machines are run simultaneously with different capacities and eligibilities in processing, in some stages. The objective is to simultaneously minimize a linear combination of the total weighted completion time and total weighted tardiness. The first favors the producer’s interest by minimizing work-in-process inventory, inventory holding cost, and energy consumption as well as maximizing machine utilization, while the second favors the customers’ interest by maximizing customers’ service level and delivery speed. In particular, it disregards the group technology assumptions (GTAs) by allowing for the possibility of splitting pre-determined groups of jobs into inconsistent batches in order to improve the operational efficiency. A comparison between the group scheduling and batch scheduling approaches reveals the outstanding performance of the batch scheduling approach. As a result, contrary to the GTAs, jobs belonging to a group might be processed on more than one machine as batches, but not all machines may be capable of processing all jobs. A sequence- and machine-dependent setup time is required between each of two consecutively scheduled batches belonging to different groups. Based on manufacturing company policy, the desired lower bounds on batch sizes are considered for the number of jobs assigned to batches. Although, the direction in which all jobs move through production line is the same, some jobs may skip some stages. Furthermore, to reflect real industry requirements, the job release times and the machine availability times are considered to be dynamic, which means not all machines and jobs are available at the beginning of the planning horizon.The problem is formulated with the help of four mixed-integer linear programming (MILP) models. Two out of four MILP models are formulated as two integrated phases, i.e., batching and scheduling phases, with respect to the precedence constraints between each pair of jobs batches and or the position concept within batches. The optimal combination between batch compositions of groups are determined in the batching phase, while the optimal assignment and sequence of batches on machines and sequence of jobs within batches are determined in the scheduling phase, with respect to a set of operational constraints. A batch composition of a group corresponding to a particular stage, determined in the batching phase of the MILP model, represents the number of batches assigned to the group as well as the number and type of jobs belonging to each batch of that group. Since the first and second MILP models lead to unmanageable solution space, the relaxed MILP model, which allocates one and only one job to each batch of each group in each stage, can be developed to focus on the non-dominated solution space. The optimal solutions of MILP models and relaxed MILP model are equal, if and only if the optimal solution of the relaxed MILP model does not violate the desired lower bounds on batch sizes. Since the relaxed MILP model cannot guarantee the optimal solution of the MILP models, a third MILP model is developed by integrating batching and scheduling phases. This MILP model eliminates an exhaustive combination enumeration between batch compositions of all groups in all stages. Although the third MILP model converges to the optimal solution slower than the relaxed MILP model, it guarantees finding the optimal solution of the first and second MILP models. A comparison between four MILP models shows the superior performance of the third MILP model. However, since the problem is strongly NP-hard, it is not possible to find its optimal solution within a reasonable time as the problem size increases from small to medium to large, even by the relaxed MILP model or the fourth MILP model. Therefore, several meta-heuristic algorithms based upon basic local search, basic population-based search, and hybridization of local search and population-based searches are developed, which move back and forth between batching and scheduling phases. Tabu Search (TS) is implemented as a basic local search algorithm, while Tabu Search Path-Relinking (TS PR) is implemented as a local search algorithm enhanced with a population-based structure. TS is incorporated into the framework of path-relinking to exploit the information on good solutions. The TS PR algorithm comprises several distinguishing features including relinking procedures to effectively explore trajectories connecting elite solutions and the methods used to choose the reference solution. Particle Swarm Optimization (PSO) is implemented as a basic population-based algorithm, while Particle Swarm Optimization enhanced with a local search algorithm (PSO LSA) is developed to realize the benefits of batching and, consequently, enhance the quality of solutions.Since there is interdependency between positions of a job in different stages of a hybrid flow shop in batch scheduling, a meta-heuristic algorithm is not capable of capturing these interdependencies and, subsequently, its efficacy can be diminished. In order to capture this interdependency, the non-, partial- complete-, and stage-based interdependency strategy are developed. In the stage-based-interdependency strategy, a complete sequence related to all of the stages is gradually determined, stage by stage. An initial solution finding mechanism is developed to trigger the search into the solution space and generate an initial population. The performances of these algorithms are compared to each other in order to identify which algorithm(s) outperforms the others. Nevertheless, the performances of the best algorithm(s) are evaluated with respect to a tight lower bound obtained from a branch-and-price (B&P) algorithm. The B&P algorithm uses Dantzig-Wolfe decomposition (DWD) to divide the original problem into a master problem and several sub-problems (SPs) corresponding to each stage. The original problem is decomposed into the SPs by three DWDs corresponding to the three MILP models. Although, by applying DWD technique in the first and second MILP models, an exhaustive combination enumeration between batch compositions of all groups in all stages is excluded and, as a result, the SPs are easier to solve than the original problem, they are still strongly NP-hard because of an enormous number of combinations between batch compositions of all groups in each stage. However, the DWD technique corresponding to the relaxed MILP model not only drastically reduces the number of variables and constraints in the SPs, but also eliminates the batching phase of the first and second MILP models. Decomposing the original problem based on the relaxed MILP model and implementing the B&P algorithm cannot guarantee optimal solutions or tight lower bounds of problems unless the number of violations in the desired lower bounds on batch sizes is not significant. Therefore, the third MILP model is decomposed by DWD so that the B&P algorithm is capable of finding tight lower bounds even for large-size instances of the problem. A comparison between the lower bounds obtained from the B&P algorithm and CPLEX reveals the impressive performance of the B&P algorithm, particularly for large-size problems. The evaluation of the best algorithms based upon these tight lower bounds developed by the B&P algorithm, uncovers the outstanding performance of hybrid algorithms compared to the results obtained from CPLEX.Keywords: Dantzig-Wolfe Decomposition, Mixed-Integer Linear Programming Model, Branch-and-Price Optimization Algorithm, Sequence- and Machine-Dependent Setup Time, Column Generation, Group Scheduling, Particle Swarm Optimization, Batching and Scheduling, Hybrid Flow Shop, Tabu Search, Desired Lower Bounds on Batch Sizes, Bi-Criteria Objective, Path-Relinkin

Multiperiod Dispatching and Routing for On-Time Delivery in a Dynamic and Stochastic Environment

On-demand delivery has become increasingly popular around the world. Brick-and-mortar grocery stores, restaurants, and pharmacies are providing fast delivery services to satisfy the growing home delivery demand. Motivated by a large meal and grocery delivery company, we model and solve a multiperiod driver dispatching and routing problem for last-mile delivery systems where on-time performance is the main target. The operator of this system needs to dispatch a set of drivers and specify their delivery routes in a stochastic environment, in which random demand arrives over a fixed number of periods. The resulting dynamic program is challenging to solve due to the curse of dimensionality. We propose a novel approximation framework to approximate the value function via a simplified dispatching program. We then develop efficient exact algorithms for this problem based on Benders decomposition and column generation. We validate the superior performance of our framework and algorithms via extensive numerical experiments. Tested on a real-world data set, we quantify the value of adaptive dispatching and routing in on-time delivery and highlight the need of coordinating these two decisions in a dynamic setting. We show that dispatching multiple vehicles with short trips is preferable for on-time delivery, as opposed to sending a few vehicles with long travel times

On the investigation of the large-scale grouping constrained storage location assignment problem

The primary focus of this study is a novel optimisation problem, namely Storage Location Assignment Problem with Grouping Constraint (SLAP-GC). The problem stems from real-world applications and is significant in theoretical values and applicability in resource allocation tasks where groupings must be considered. The aim of this problem is to minimise the total operational cost in a warehouse through stock rearrangement. The problem consists of two interdependent subproblems, grouping same product items and assigning items to minimize picking distance. The interactions between these two subproblems make this problem significantly different from previous Storage Location Assignment Problems (SLAP), a well-studied field in logistics. Existing approaches for SLAP are not directly applicable for SLAP-GC. This dissertation lays a foundation for research on grouping constraints and other optimisation problems with similar interactions between subproblems. Firstly this study presents a formal definition of SLAP-GC. Then it others a formal proof of NP-completeness of SLAP-GC by reducing from a well-known 3-Partition problem to SLAP-GC. This suggests that the real-world instances of SLAP-GC should not be tackled with exact approaches, but with approximation and heuristic approaches. Then, we explored decomposition and modelling techniques for SLAP-GC and developed three types of promising heuristic approaches: a hyperheuristic approach, a metaheuristic approach and a matheuristic approach. Comprehensive experimental studies are conducted on both synthetic benchmark instances and real-world instances to examine their efficiency, efficacy, and scalability. Through the analysis of the experimental results, the suitability of proposed methods is verified on various SLAP-GC scenarios. In addition, we demonstrate in this study that with the proposed decomposition, large-scale SLAP-GC can be handled efficiently by the three proposed heuristic-based approaches