Weighted tardiness minimization for unrelated machines with sequence-dependent and resource-constrained setups

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimization. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component - vital to guarantee the non-violation of the problem's constraints - which optimally allocates resources with respect to tardiness minimization. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure is revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight deadlines, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Review on unrelated parallel machine scheduling problem with additional resources

This study deals with an unrelated parallel machine scheduling problem with additional resources (UPMR). That is one of the important sub-problems in the scheduling. UPMR consists of scheduling a set of jobs on unrelated machines. In addition to that, a number of one or more additional resources are needed. UPMR is very important and its importance comes from the wealth of applications; they are applicable to engineering and scientific situations and manufacturing systems such as industrial robots, nurses, machine operators, bus drivers, tools, assembly plant machines, fixtures, pallets, electricity, mechanics, dies, automated guided vehicles, fuel, and more. The importance also comes from the concern about the limitation of resources that are dedicated for the production process. Therefore, researchers and decision makers are still working on UPMR problem to get an optimum schedule for all instances which have not been obtained to this day. The optimum schedule is able to increase the profits and decrease the costs whilst satisfying the customers’ needs. This research aims to review and discuss studies related to unrelated parallel machines and additional resources. Overall, the review demonstrates the criticality of resolving the UPMR problem. Metaheuristic techniques exhibit significant effectiveness in generating results and surpassing other algorithms. Nevertheless, continued improvement is essential to satisfy the evolving requirements of UPMR, which are subject to operational changes based on customer demand

Quantitative Methods For Select Problems In Facility Location And Facility Logistics

This dissertation presented three logistics problems. The first problem is a parallel machine scheduling problems that considers multiple unique characteristics including release dates, due dates, limited machine availability and job splitting. The objective of is to minimize the total amount of time required to complete work. A mixed integer programming model is presented and a heuristic is developed for solving the problem. The second problem extends the first parallel scheduling problem to include two additional practical considerations. The first is a setup time that occurs when warehouse staff change from one type of task to another. The second is a fixed time window for employee breaks. A simulated annealing (SA) heuristic is developed for its solution. The last problem studied in this dissertation is a new facility location problem variant with application in disaster relief with both verified data and unverified user-generated data are available for consideration during decision making. A total of three decision strategies that can be used by an emergency manager faced with a POD location decision for which both verified and unverified data are available are proposed: Consider Only Verified, Consider All and Consider Minimax Regret. The strategies differ according to how the uncertain user-generated data is incorporated in the planning process. A computational study to compare the performance of the three decision strategies across a range of plausible disaster scenarios is presented

A general Framework for Utilizing Metaheuristic Optimization for Sustainable Unrelated Parallel Machine Scheduling: A concise overview

Sustainable development has emerged as a global priority, and industries are increasingly striving to align their operations with sustainable practices. Parallel machine scheduling (PMS) is a critical aspect of production planning that directly impacts resource utilization and operational efficiency. In this paper, we investigate the application of metaheuristic optimization algorithms to address the unrelated parallel machine scheduling problem (UPMSP) through the lens of sustainable development goals (SDGs). The primary objective of this study is to explore how metaheuristic optimization algorithms can contribute to achieving sustainable development goals in the context of UPMSP. We examine a range of metaheuristic algorithms, including genetic algorithms, particle swarm optimization, ant colony optimization, and more, and assess their effectiveness in optimizing the scheduling problem. The algorithms are evaluated based on their ability to improve resource utilization, minimize energy consumption, reduce environmental impact, and promote socially responsible production practices. To conduct a comprehensive analysis, we consider UPMSP instances that incorporate sustainability-related constraints and objectives

Scheduling on parallel machines with a common server in charge of loading and unloading operations

This paper addresses the scheduling problem on two identical parallel machines with a single server in charge of loading and unloading operations of jobs. Each job has to be loaded by the server before being processed on one of the two machines and unloaded by the same server after its processing. No delay is allowed between loading and processing, and between processing and unloading. The objective function involves the minimization of the makespan. This problem referred to as P2, S1|sj , tj |Cmax generalizes the classical parallel machine scheduling problem with a single server which performs only the loading (i.e., setup) operation of each job. For this NP-hard problem, no solution algorithm was proposed in the literature. Therefore, we present two mixedinteger linear programming (MILP) formulations, one with completion-time variables along with two valid inequalities and one with time-indexed variables. In addition, we propose some polynomial-time solvable cases and a tight theoretical lower bound. In addition, we show that the minimization of the makespan is equivalent to the minimization of the total idle times on the machines. To solve large-sized instances of the problem, an efficient General Variable Neighborhood Search (GVNS) metaheuristic with two mechanisms for finding an initial solution is designed. The GVNS is evaluated by comparing its performance with the results provided by the MILPs and another metaheuristic. The results show that the average percentage deviation from the theoretical lower-bound of GVNS is within 0.642%. Some managerial insights are presented and our results are compared with the related literature.Comment: 40 pages, 4 figures, 16 table

One Benders cut to rule all schedules in the neighbourhood

Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose tighter dual bounds, its application to resource-constrained scheduling remains less explored. Given a position-based Mixed-Integer Linear Programming (MILP) formulation for scheduling on unrelated parallel machines, we notice that certain $k-$OPT neighbourhoods could implicitly be explored by regular local search operators, thus allowing us to integrate Local Branching into Branch-and-Check schemes. After enumerating such neighbourhoods and obtaining their local optima - hence, proving that they are suboptimal - a local branching cut (applied as a Benders cut) eliminates all their solutions at once, thus avoiding an overload of the master problem with thousands of Benders cuts. However, to guarantee convergence to optimality, the constructed neighbourhood should be exhaustively explored, hence this time-consuming procedure must be accelerated by domination rules or selectively implemented on nodes which are more likely to reduce the optimality gap. In this study, the realisation of this idea is limited on the common 'internal (job) swaps' to construct formulation-specific $4$-OPT neighbourhoods. Nonetheless, the experimentation on two challenging scheduling problems (i.e., the minimisation of total completion times and the minimisation of total tardiness on unrelated machines with sequence-dependent and resource-constrained setups) shows that the proposed methodology offers considerable reductions of optimality gaps or faster convergence to optimality. The simplicity of our approach allows its transferability to other neighbourhoods and different sequencing optimisation problems, hence providing a promising prospect to improve Branch-and-Check methods

Theoretical and Computational Research in Various Scheduling Models

Nine manuscripts were published in this Special Issue on “Theoretical and Computational Research in Various Scheduling Models, 2021” of the MDPI Mathematics journal, covering a wide range of topics connected to the theory and applications of various scheduling models and their extensions/generalizations. These topics include a road network maintenance project, cost reduction of the subcontracted resources, a variant of the relocation problem, a network of activities with generally distributed durations through a Markov chain, idea on how to improve the return loading rate problem by integrating the sub-tour reversal approach with the method of the theory of constraints, an extended solution method for optimizing the bi-objective no-idle permutation flowshop scheduling problem, the burn-in (B/I) procedure, the Pareto-scheduling problem with two competing agents, and three preemptive Pareto-scheduling problems with two competing agents, among others. We hope that the book will be of interest to those working in the area of various scheduling problems and provide a bridge to facilitate the interaction between researchers and practitioners in scheduling questions. Although discrete mathematics is a common method to solve scheduling problems, the further development of this method is limited due to the lack of general principles, which poses a major challenge in this research field