A Decentralized Scheduling Method for Flowshop Problems with Resource Constraints

In this paper, the Lagrangian decomposition and coordination technique is applied to flowshop scheduling problems in which the sum of the changeover cost and the tardiness penalty is minimized. The proposed method possesses a feature that the scheduling problem is decomposed not into single job-level subproblems but into single machine-level subproblems. By decomposing the problem into one-machine multi-operation subproblems, the changeover cost and/or changeover time can easily be embedded in the objective function. In the proposed method, each subproblem for a single machine is solved by combining the simulated annealing method and the neighborhood search algorithm. In order to avoid oscillations in multiplier values, a new Lagrangian function is used to solve each subproblem. The effectiveness of the proposed method is verified by comparing the results of the example problems solved by the proposed method with those solved by the simulated annealing method in which a schedule of the entire machine is successively improved.

In the conventional Lagrangian relaxation approach, the scheduling problems are decomposed into job-level sub-problems or operation-level sub-problems. However, these approaches are not applicable to the flowshop problems with the changeover cost which depends on the sequence of operations. In this paper, we propose a machine-oriented decomposition method for the flowshop problems using the Lagrangian decomposition and coordination technique. In the proposed method, each sub-problem for single machine is solved by the simulated annealing method. The solutions of the sub-problems are used to generate a feasible schedule by a heuristic procedure. The effectiveness of the proposed method is verified by comparing the results of the example problems solved by the proposed method with those solved by the conventional method. Furthermore, it has been shown that the proposed approach is easily applicable to the flow hop problem with resource constrains minimizing the changeover costs and due date penalties.

ラグランジュ分解・調整法による生産スケジューリング手法:リエントラントフレキシブルフローショップ問題への適用

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Planning coordination for multiple companies has received much attention from viewpoints of global supply chain management. In practical situations, a plausible plan for multiple companies should be created by mutual negotiation and coordination without sharing such confidential information as inventory costs, setup costs, and due date penalties for each company. In this paper, we propose a framework for distributed optimization of supply chain planning using an augmented Lagrangian decomposition and coordination approach. A feature of the proposed method is that it can derive a near-optimal solution without requiring all of the information. The proposed method is applied to supply chain planning problems for a petroleum complex, and a midterm planning problem for multiple companies. Computational experiments demonstrate that the average gap between a solution derived by the proposed method and the optimal solution is within 3% of the performance index, even though only local information is used to derive a solution for each company. </para>

The impact of neighbourhood size on the process of simulated annealing: Computational experiments on the flowshop scheduling problem

This paper presents the mixed-integer linear programming (MILP) based model to approach the admission control in flow shop scheduling problem with queue time constraints, where there are various upper bounds limit in each queue. The scheduling proposed in this paper iteratively retrieves the real-time status of a production system such as machine failures and recoveries, and job arrivals in each step and generate the most updated scheduling result at each decision time. Our objective function is to minimize the occurrence of queue time violation. We solve the MILP using combinatorial Benders’ cut (CBC), where the MILP model is decomposed into two independent parts: the binary variables as a master problem and the continuous variables as a slave problem. We compare the CBC with the results gained from the CPLEX. The numerical results indicate that the CBC indeed effectively and efficiently reaches the good feasible solution within a reasonable timeframe in the context of timely updating scheduling problem.

The present paper reports on a new approach to applying simulated annealing to the flow shop scheduling problem with early/tardy costs. This approach incorporates the simulated annealing methodology with problem-specific knowledge, which is given in a table called the ‘Backward-Forward Exchange Priority Table’. Performance of the proposed method is tested on randomly generated problems and is compared to those of two formal simulated annealing schemes. Finally, it is shown that solutions obtained by the proposed method are superior to those of formal annealing schemes.

This paper deals with the flow shop scheduling problem. To find the optimal solution is an NP-hard problem. The paper reviews some algorithms from the literature and applies a benchmark dataset to evaluate their efficiency. In this research work, the discrete bacterial memetic evolutionary algorithm (DBMEA) as a global searcher was investigated. The proposed algorithm improves the local search by applying the simulated annealing algorithm (SA). This paper presents the experimental results of solving the no-idle flow shop scheduling problem. To compare the proposed algorithm with other researchers’ work, a benchmark problem set was used. The calculated makespan times were compared against the best-known solutions in the literature. The proposed hybrid algorithm has provided better results than methods using genetic algorithm variants, thus it is a major improvement for the memetic algorithm family solving production scheduling problems.

Production scheduling optimization in foundry using hybrid Particle Swarm Optimization algorithm

As an emerging novel evolutionary technique, the immune algorithm has gained a lot of attention and wide applications in various fields of engineering and management. To our knowledge, this paper first considers the application of immune algorithm for the classic permutation flow shop scheduling problem. We present a hybrid heuristic combining immune algorithm and simulated annealing for the n-job, m-machine permutation flow shop scheduling problem to minimize makespan and total flow time. A heuristically directed population-based construction approach in the immune algorithm and a forward/backward shift neighborhood search heuristic in the simulated annealing of the proposed method is utilized to explore the search process for better schedules of jobs as well to speed up the convergence speed of the proposed algorithm. The proposed method is tested with Taillard’s flow shop scheduling benchmark instances for different problems with job sizes varying from 20 to 500. The computational results demonstrate that the proposed heuristic is very competitive with the state-of-the-art procedures in terms of both solution quality and computational times.

In this paper, simulated annealing (SA) algorithm is employed to solve the flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs. Four variants of the two-phase SA algorithm (SA-I to SA-IV) are proposed to solve flowshop scheduling problem with the objective of minimising the CTV of jobs without considering the right shifting of completion time of jobs on the last machine. The proposed SA algorithms have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed SA variants are compared with the best CTV of jobs reported in the literature, and the proposed SA-III is found to perform well in minimising the chosen performance measure (CTV) particularly in medium and large size problems.

Flow shop scheduling problem has a wide application in the manufacturing and has attracted much attention in academic fields. From other point, on time delivery of products and services is a major necessity of companies’ todays; early and tardy delivery times will result additional cost such as holding or penalty costs. In this paper, just-in-time (JIT) flow shop scheduling problem with preemption and machine idle time assumptions is considered in which objective function is minimizing the sum of weighted earliness and tardiness. A new non-linear mathematical model is formulated for this problem and due to high complexity of the problem meta-heuristic approaches have been applied to solve the problem for finding optimal solution. The parameters of algorithms are set by Taguchi method. Each parameter is tested in three levels. By implementation of many problems with different sizes these levels are determined .The proposed model is solved by three meta-heuristic algorithms: genetic algorithm (GA), imperialist competitive algorithm (ICA) and hybrid of GA and ICA. To evaluate the performance of the proposed algorithms many test problems have been designed. The Computational results indicate the superiority of the performance of hybrid approach than GA and ICA in finding thebest solution in reasonable computational time.

Chapter 6 - Quantum-inspired multi-objective simulated annealing for bilevel image thresholding

In this paper, the no-wait flow shop scheduling problem under makespan and flowtime criteria is addressed. The no-wait flowshop is a variant of the well-known flowshop scheduling problem where all processes follow the previous one without any interruption for operations of a job. Owing to the problem is known to be NP-hard for more than two machines, a hybrid meta-heuristic algorithm based on ant colony optimization (ACO) and simulated annealing (SA) algorithm is improved. First, at each step, due to the characteristic of ACO algorithm that include solution construction and pheromone trail updating, some different areas of search space are checked and best solution is selected. Then, to enhance the quality and diversity of the solution and finding best neighbor of this solution, a novel SA is presented. Moreover, a new principle is applied for global pheromone update based on the probability function like SA algorithm. The proposed approach solution is compared with several the state-of-the-art algorithms in the literature. The reported results show that the proposed algorithms are effective and the new approach for local search in ACO algorithm is efficient for solving the no-wait flow shop problem. Then, we employed another hybrid ACO algorithm based on hybridization of ACO with variable neighborhood search (VNS) and compare the results given by two proposed algorithms. These results show that our new hybrid provides better results than ACO-VNS algorithm.

This paper considers the characteristics of hybrid flow shop with energy saving. First of all, established the model of hybrid flow shop with energy saving problem. Then Lagrangian relaxation was proposed to solve the energy scheduling problem in hybrid flow shop. Lagrangian relaxation algorithm introduced precedence constraints into the objective function, and the original problem was decomposed into a series of parallel machine sub-problems. A dynamic programming algorithm was then designed to solve these sub-problems. The method of updating of multiples was sub-gradient algorithm. Lastly, a two stage heuristic approach was constructed to convert the infeasible solution into a feasible solution. Testing results demonstrated that the proposed method can generate near optimal schedules in an acceptable computational time.