A Heuristic Approach for Assembly Scheduling and Transportation Problems with Parallel Machines

Assembly plays an important role in any production system as it constitutes a significant portion of the lead time and cost of a product. Virtual computer-integrated manufacturing (VCIM) system is a modern production system being conceptually developed to extend the application of traditional computer-integrated manufacturing (CIM) system to global level. Assembly scheduling in VCIM systems is quite different from one in traditional production systems because of the difference in the working principles of the two systems. In this article, the assembly scheduling problem in VCIM systems is modeled and then an integrated approach based on genetic algorithm (GA) is proposed to search for a global optimised solution to the problem. Because of dynamic nature of the scheduling problem, a novel GA with unique chromosome representation and modified genetic operations is developed herein. Robustness of the proposed approach is verified by a numerical example.

Production scheduling is a critical requirement in today’s production systems. The production scheduling problem focuses on the rational allocation of production resources, determining the processing order of production tasks and operations, satisfying production constraints arising from the production environment such as the number of machines and task duration, and achieving optimal production goals, such as completing all tasks in the fastest way possible. The Flexible Job Shop Scheduling (FJSP) problem is a classical production scheduling issue, an extension of the Job Shop Scheduling (JSP) problem. The JSP problem involves allocating a set of jobs to a set of machines, where each job consists of multiple operations that must adhere to a precedence order. Each machine can process only one operation at a time for each job, and the time required for each operation on the corresponding machine is predetermined. The challenge in the JSP problem is to determine an appropriate order for processing operations or assignments, based on the production objective. FJSP represents a more complex and flexible variant of this problem, where at least one operation of a task can be performed on a set of alternative machines. Given that FJSP problems are NP-hard, solutions tend to be complex, varied, and often have limited applicability. Many FJSP scenarios require targeted modeling. In this paper, I propose a modeling approach for the static scheduling problem of job shops, considering low flexibility and demonstrating its usability by comparing it with other scheduling approaches, such as those based on genetic algorithm modeling. The paper is organized as follows:The first part of this paper offers a brief introduction to the FJSP problem, including background, research motivation, and main contributions, the second part provides a literature review,including a brief review and introduction of recent solutions to the FJSP problem, the third part describes a specific modeling approach, the fourth part details the test experiments and results of the modeling approach and includes comparisons with some other approaches, the fifth part analyzes the results from the fourth part and discusses the advantages and disadvantages of the modeling approach relative to others, and the sixth part concludes with a summary of findings and recommendations.

In this study, a new and simple alternate routing heuristics, which would be superior to the conventional routing strategies in terms of various system performance measures and easier to apply practically, was presented. Because of the high investment costs of FMSs, it is also definitely worth choosing the best operating policy and system configuration by analyzing the system model, and adapting to changes over time. In future research, the heuristic rule base will be extended to include other supplementary constraints such as dynamic tool allocation and sequence dependent setup times. For practical implementation of the proposed decision support system, additional research in the area of human interfaces could be useful to develop more user friendly system which automatically constructs simulation model of the system from the knowledge base of a production system.

In this paper, we propose a mixed integer programming (MIP) model for the Chicken Flock Sizing, Allocation and Scheduling Problem (CFSASP), which is an important planning problem in the broiler production supply chain. To solve the CFSASP efficiently, two variants of rolling horizon heuristics (RHHs) have been developed and applied on the case of a Norwegian broiler production company. Computational results show that the RHHs successfully obtain high-quality solutions within a reasonable time. The value of optimisation is verified through comparison with the case company's plans, where the solutions from optimisation outperforms the current solutions. Sensitivity analyses are also conducted to provide managerial insights regarding certain strategic decisions, such as how many and which days to use for hatching of chickens. Due to the promising results, the case company is now implementing an optimisation-based decision support system based on the MIP model and solution methods shown in this paper.

Scheduling of single stage assembly with air transportation in a consumer electronic supply chain

Scheduling of multi-component products in a two-stage flexible flow shop

Job shop scheduling, as one of the classical scheduling problems, has been widely studied in literatures, and proved to be mostly NP-hard. Although it is extremely difficult to solve job shop scheduling with no-wait constraint to optimality, the two-machine no-wait job shop scheduling to minimise makespan could be solvable in polynomial time when each job has exactly two equal length operations (proportionate job shop). In the present paper, an extension is attempted by considering a proportionate flexible two-stage no-wait job shop scheduling problem with minimum makespan, and a set-covering formulation is put forward which contains a master problem and a pricing problem. To solve this problem, a column generation (CG)-based approach is implemented. In comparison, a mixed integer programming model is constructed and optimised by Cplex. A series of randomly generated numerical instances are calculated. And the testing result shows that the mixed integer model handled by Cplex can only solve small scale cases, while the proposed CG-based method can conquer larger size problems in acceptable time.

Real-world manufacturing scenarios usually lead to difficult assembly scheduling problems. Besides strict precedence constraints between jobs or operations, such problems incorporate constraints related to maintenance activities on working stations (machines) and specific setup times when different operations are executed on the same machine. This paper analyzes the performance of several approaches, based on mathematical programming and on (meta)heuristics, to solve flexible assembly scheduling problems characterized by an arbitrary tree-like structure of the operation network. In this context, a specific encoding of candidate solutions and some specific perturbation operators are proposed. The encoding and the operators allow the distribution of sub(batches) of operations on several machines which leads, for some assembly scheduling problems, to a significant decrease of the makespan.

Operating room (OR) planning and scheduling is a highly complex combinatorial optimization problem that involves patient assignment, OR allocation, and surgical sequencing within a constrained planning horizon. This study addresses the OR scheduling problem by incorporating downstream bed availability in both hospital wards and intensive care units (ICUs), aiming to improve operational efficiency and patient outcomes. A mixed-integer programming (MIP) model is developed to minimize the total completion time across all operating rooms during the planning period. Given the NP-hard nature of the problem, a novel Genetic Engineering Algorithm (GEA) is proposed as an advanced extension of the traditional Genetic Algorithm (GA). The GEA incorporates three innovative search strategies inspired by genetic engineering principles, refining the crossover and mutation operators to improve solution quality and convergence speed. To evaluate the effectiveness of the proposed algorithm, GEA and its variants are tested on 18 benchmark instances of varying problem sizes for the proposed OR planning and scheduling problem. A real-world case study from a hospital in Pakistan illustrates the practical applicability of the proposed approach using different real-world criteria. The results demonstrate that GEA consistently outperforms state-of-the-art metaheuristic algorithms. Its robustness and accuracy are further validated using 10 standard mathematical benchmark functions. The results confirm the GEA’s effectiveness and efficiency in addressing complex OR planning and scheduling problems and underscore its potential for advancing metaheuristic algorithm design in combinatorial optimization.

A simulation-based scheduling mechanism for photo-reconnaissance satellite is presented in this paper. The satellite scheduling problem belongs to a class of single-machine scheduling problems with time window constraint. It is NP-hard in computational complexity. Based on simulation platform, a mixed integer programming model is used to formulate the problem and an advanced tabu algorithm is adopted to solve the MIP. Numerical results demonstrate that this approach is efficient in the scheduling problems.

A simulation-based scheduling mechanism for photo-reconnaissance satellite is presented in this paper. The satellite scheduling problem belongs to a class of single-machine scheduling problems with time window constraint. It is NP-hard in computational complexity. Based on simulation platform, a mixed integer programming model is used to formulate the problem and an advanced tabu algorithm is adopted to solve the MIP. Numerical results demonstrate that this approach is efficient in the scheduling problems.

A bicriterion single-machine scheduling problem with step-improving processing times

In this paper, motivated by the production process of electronic control modules in the digital electronic detonators industry, we study a multi-objective flexible flow shop scheduling problem. The objective is to find a feasible schedule that minimizes both the makespan and the total tardiness. Considering the constraints imposed by the jobs and the machines throughout the manufacturing process, a mixed integer programming model is formulated. By transforming the scheduling problem into a Markov decision process, the agent state features and the actions are designed based on the processing status of the machines and the jobs, along with heuristic rules. Furthermore, a reward function based on the optimization objectives is designed. Based on the deep reinforcement learning algorithm, the Dueling Double Deep Q-Network (D3QN) algorithm is designed to solve the scheduling problem by incorporating the target network, the dueling network, and the experience replay buffer. The D3QN algorithm is compared with heuristic rules, the genetic algorithm (GA), and the optimal solutions generated by Gurobi. The ablation experiments are designed. The experimental results demonstrate the high performance of the D3QN algorithm with the target network and the dueling network proposed in this paper. The scheduling model and the algorithm proposed in this paper can provide theoretical support to make the production plan of electronic control modules reasonable and improve production efficiency.

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

This application is motivated by a complex real-world scheduling problem found in the bottleneck workstation of the production line of an automotive safety glass manufacturing facility. The scheduling problem consists of scheduling jobs (glass parts) on a number of parallel batch processing machines (furnaces), assigning each job to a batch, and sequencing the batches on each machine. The two main objectives are to maximize the utilization of the parallel machines and to minimize the delay in the completion date of each job in relation to a required due date (specific for each job). Aside from the main objectives, the output batches should also produce a balanced workload on the parallel machines, balanced job due dates within each batch, and minimal capacity loss in the batches. The scheduling problem also considers a batch capacity constraint, sequence-dependent processing times, incompatible product families, additional resources, and machine capability. We propose a two-phase heuristic approach that combines exact methods with search heuristics. The first phase comprises a four-stage mixed-integer linear program for building the batches; the second phase is based on a Greedy Randomized Adaptive Search Procedure for sequencing the batches assigned to each machine. We conducted experiments on instances with up to 100 jobs built with real data from the manufacturing facility. The results are encouraging both in terms of computing time--5 min in average--and quality of the solutions--less than 10 % relative gap from the optimal solution in the first phase and less than 5 % in the second phase. Additional experiments were conducted on randomly generated instances of small, medium, and large size.