Integrating non-preemptive open shops scheduling with sequence-dependent setup times using advanced metaheuristics

In this article, we consider non-preemptive open shops scheduling problem (OSSP) where setup times are sequence-dependent (SDST) on each machine to minimize makespan. The contributions of this article are threefold. Firstly, we incorporate a very practical assumption in our problem, SDST, which, according to Allahverdi et al. (2008) [Allahverdi, A., Ng, C. T., Cheung, T. C. E., & Kovalyov, Y. M. (2008). A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 187(3), 985–1032], no paper has ever attempted to integrate into OSSP. Secondly, we propose two new advanced metaheuristics: multi-neighborhood search simulated annealing and hybrid simulated annealing to tackle the problem at hand. Thirdly, for the first time, we adapt two well-known constructive heuristics: longest total processing time and longest total remaining processing from the literature so as to consider the case of SDSTs. We also apply genetic algorithm from the literature of OSSP to embrace the concepts of SDST. Since there is no standard SDST-OSSP benchmark, we make certain adaptations on the Taillard’s benchmark [Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285] to include setup times. An experimental design based on foregoing benchmark is conducted to evaluate the competitiveness and robustness of our proposed algorithm against some effective algorithms in the literature. The obtained results strongly support the high performance of our proposed algorithms with respect to other well-known heuristic and metaheuristic algorithms.     

A hybrid genetic algorithm for the single machine scheduling problem with sequence-dependent setup times

This paper presents a hybrid approach based on the integration between a genetic algorithm (GA) and concepts from constraint programming, multi-objective evolutionary algorithms and ant colony optimization for solving a scheduling problem. The main contributions are the integration of these concepts in a GA crossover operator. The proposed methodology is applied to a single machine scheduling problem with sequence-dependent setup times for the objective of minimizing the total tardiness. A sensitivity analysis of the hybrid approach is carried out to compare the performance of the GA and the hybrid genetic algorithm (HGA) approaches on different benchmarks from the literature. The numerical experiments demonstrate the HGA efficiency and effectiveness which generates solutions that approach those of the known reference sets and improves several lower bounds.     

Two-machine robotic cell scheduling problem with sequence-dependent setup times

In this paper, we introduce a new and practical two-machine robotic cell scheduling problem with sequence-dependent setup times (2RCSDST) along with different loading/unloading times for each part. Our objective is to simultaneously determine the sequence of robot moves and the sequence of parts that minimize the total cycle time. The proposed problem is proven to be strongly NP-hard. Using the Gilmore and Gomory (GnG) algorithm, a polynomial-time computable lower bound is provided.     

Multi-agent based approach for single machine scheduling with sequence-dependent setup times and machine maintenance

Scheduling of single machine in manufacturing systems is especially complex when the order arrivals are dynamic. The complexity of the problem increases by considering the sequence-dependent setup times and machine maintenance in dynamic manufacturing environment. Computational experiments in literature showed that even solving the static single machine scheduling problem without considering regular maintenance activities is NP-hard. Multi-agent systems, a branch of artificial intelligence provide a new alternative way for solving dynamic and complex problems. In this paper a collaborative multi-agent based optimization method is proposed for single machine scheduling problem with sequence-dependent setup times and maintenance constraints. The problem is solved under the condition of both regular and irregular maintenance activities. The solutions of multi-agent based approach are compared with some static single machine scheduling problem sets which are available in the literature. The method is also tested under real-time manufacturing environment where computational time plays a critical role during decision making process.     

Hybrid flexible flowshops with sequence-dependent setup times and machine availability constraints

One of the common assumptions in the field of scheduling is that machines are always available in the planning horizon. This may not be true in realistic problems since machines might be busy processing some jobs left from previous production horizon, breakdowns or preventive maintenance activities. Another common assumption is the consideration of setup times as a part of processing times, while in some industries, such as printed circuit board and automobile manufacturing, not only setups are an important factor but also setup magnitude of a job depends on its immediately preceding job on the same machine, known as sequence-dependent setup times. In this paper, we consider hybrid flexible flowshops with sequence-dependent setup times and machine availability constraints caused by preventive maintenance. The optimization criterion is the minimization of makespan. Since this problem is NP-hard in the strong sense, we propose three heuristics, based on SPT, LPT and Johnson rule and two metaheuristics based on genetic algorithm and simulated annealing. Computational experiments are performed to evaluate the efficiencies of the algorithms.     

Bi-criteria flexible job-shop scheduling with sequence-dependent setup times—Variable neighborhood search approach

In scheduling problems, taking the sequence-dependent setup times into account is one of the important issues that have recently been considered by researchers in the production scheduling field. In this paper, we consider flexible job-shop scheduling problem (FJSP) with sequence-dependent setup times to minimize makespan and mean tardiness. The FJSP consists of two sub-problems from which the first one is to assign each operation to a machine out of a set of capable machines, and the second one deals with sequencing the assigned operations on all machines. To solve this problem, a variable neighborhood search (VNS) algorithm based on integrated approach is proposed. In the presented optimization method, the external loop controlled the stop condition of algorithm and the internal loop executed the search process. To search the solution space, the internal loop used two main search engines, i.e. shake and local search procedures. In addition, neighborhood structures related to the sequencing problem and the assignment problem were employed to generate neighboring solutions. To evaluate the performance of the proposed algorithm, 20 test problems in different sizes are randomly generated. Consequently, computational results and comparisons validate the quality of the proposed approach.     

Design of a genetic algorithm for bi-objective unrelated parallel machines scheduling with sequence-dependent setup times and precedence constraints

This paper presents a novel, two-level mixed-integer programming model of scheduling N jobs on M parallel machines that minimizes bi-objectives, namely the number of tardy jobs and the total completion time of all the jobs. The proposed model considers unrelated parallel machines. The jobs have non-identical due dates and ready times, and there are some precedence relations between them. Furthermore, sequence-dependent setup times, which are included in the proposed model, may be different for each machine depending on their characteristics. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time using traditional approaches or optimization tools is extremely difficult. This paper proposes an efficient genetic algorithm (GA) to solve the bi-objective parallel machine scheduling problem. The performance of the presented model and the proposed GA is verified by a number of numerical experiments. The related results show the effectiveness of the proposed model and GA for small and large-sized problems.     

A two-stage heuristic for single machine capacitated lot-sizing and scheduling with sequence-dependent setup costs

This paper considers a single machine capacitated lot-sizing and scheduling problem. The problem is to determine the lot sizes and the sequence of lots while satisfying the demand requirements and the machine capacity in each period of a planning horizon. In particular, we consider sequence-dependent setup costs that depend on the type of the lot just completed and on the lot to be processed. The setup state preservation, i.e., the setup state at the end of a period is carried over to the next period, is also considered. The objective is to minimize the sum of setup and inventory holding costs over the planning horizon. Due to the complexity of the problem, we suggest a two-stage heuristic in which an initial solution is obtained and then it is improved using a backward and forward improvement method that incorporates various priority rules to select the items to be moved. Computational tests were done on randomly generated test instances and the results show that the two-stage heuristic outperforms the best existing algorithm significantly. Also, the heuristics with better priority rule combinations were used to solve case instances and much improvement is reported over the conventional method as well as the best existing algorithm.     

A fuzzy-mixed-integer goal programming model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates

This paper presents a new mixed-integer goal programming (MIGP) model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates. Two objectives are considered in the model to minimize the total weighted flow time and the total weighted tardiness simultaneously. Due to the complexity of the above model and uncertainty involved in real-world scheduling problems, it is sometimes unrealistic or even impossible to acquire exact input data. Hence, we consider the parallel-machine scheduling problem with sequence-dependent set-up times under the hypothesis of fuzzy processing time's knowledge and two fuzzy objectives as the MIGP model. In addition, a quite effective and applicable methodology for solving the above fuzzy model are presented. At the end, the effectiveness of the proposed model and the denoted methodology is demonstrated through some test problems.     

Lot-sizing scheduling with batch setup times

This paper is concerned with scheduling independent jobs on m parallel machines in such a way that the makespan is minimized. Each job j is allowed to split arbitrarily into several parts, which can be individually processed on any machine at any time. However, a setup for uninterrupted s_j time units is required before any split part of job j can be processed on any machine. The problem is strongly NP-hard if the number m of machines is variable and weakly NP-hard otherwise. We give a polynomial-time -approximation algorithm for the former case and a fully polynomial-time approximation scheme for the latter. AMS Subject Classifications: 68M20 · 90B35 · 90C59     

A branch-and-cut algorithm for a production scheduling problem with sequence-dependent and time-dependent setup times

This paper introduces and compares three different formulations of a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The setup is divided into two parts: one that can be performed at any time and another one that is restricted to be performed outside of a given time interval. As a result, the setup time between two jobs is a function of the completion time of the first job. The problem can be formulated as a time-dependent traveling salesman problem, where the travel time between two nodes is a function of the departure time from the first node. We show that the resulting formulation can be strengthened to provide better linear programming relaxation lower bounds. We also introduce several families of valid inequalities which are used within a branch-and-cut algorithm. Computational experiments show that this algorithm can solve some instances with up to 50 jobs within reasonable computing times.     

Job shop scheduling with setup times, deadlines and precedence constraints

In the last 15 years several procedures have been developed that can find solutions of acceptable quality in reasonable computing time to Job Shop Scheduling problems in environments that do not involve sequence-dependent setup times of the machines. The presence of the latter, however, changes the picture dramatically. In this paper we adapt one of the best known heuristics, the Shifting Bottleneck Procedure, to the case when sequence dependent setup times play an important role. This is done by treating the single machine scheduling problems that arise in the process as Traveling Salesman Problems with time windows, and solving the latter by an efficient dynamic programming algorithm. The model treated here also incorporates precedence constraints, release times and deadlines. Computational experience on a vast array of instances, mainly from the semiconductor industry, shows our procedure to advance substantially the state of the art. Paper presented in New York at MISTA 2005. E. Balas supported by the National Science Foundation through grant DMI-9802773 and by the Office of Naval Research through contract #N00014-97-1-0133.     

Minimization of maximum lateness on parallel machines with sequence-dependent setup times and job release dates

In this paper, we consider an identical parallel machine scheduling problem with sequence-dependent setup times and job release dates. An improved iterated greedy heuristic with a sinking temperature is presented to minimize the maximum lateness. To verify the developed heuristic, computational experiments are conducted on a well-known benchmark problem data set. The experimental results show that the proposed heuristic outperforms the basic iterated greedy heuristic and the state-of-art algorithms on the same benchmark problem data set. It is believed that this improved approach will also be helpful for other applications.     

An exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times

This study proposes an exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times. The algorithm is an extension of the authors' previous algorithm for the single-machine scheduling problem without setup times, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. In the first stage of the algorithm, the conjugate subgradient algorithm or the column generation algorithm is applied to a Lagrangian relaxation of the original problem to adjust multipliers. Then, in the second stage, constraints are successively added to the relaxation until the gap between lower and upper bounds becomes zero. The relaxation is solved by dynamic programming and unnecessary dynamic programming states are eliminated to suppress the increase of computation time and memory space. In this study a branching scheme is integrated into the algorithm to manage to solve hard instances. The proposed algorithm is applied to benchmark instances in the literature and almost all of them are optimally solved.     

A bi-objective possibilistic programming model for open shop scheduling problems with sequence-dependent setup times, fuzzy processing times, and fuzzy due dates

We are concerned with an open shop scheduling problem having sequence-dependent setup times. A novel bi-objective possibilistic mixed-integer linear programming model is presented. Sequence-dependent setup times, fuzzy processing times and fuzzy due dates with triangular possibility distributions are the main constraints of this model. An open shop scheduling problem with these considerations is close to the real production scheduling conditions. The objective functions are to minimize total weighted tardiness and total weighted completion times. To solve small-sized instances for Pareto-optimal solutions, an interactive fuzzy multi-objective decision making (FMODM) approach, called TH method proposed by Torabi and Hassini, is applied. Using this method, an equivalent auxiliary single-objective crisp model is obtained and solved optimally by the Lingo software. For medium to large size examples, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed. This algorithm consists of a decoding procedure using a permutation list to reduce the search area in the solution space. Also, a local search algorithm is applied to generate good initial particle positions. Finally, to evaluate the effectiveness of the MOPSO algorithm, the results are compared with the ones obtained by the well-known SPEA-II, using design of experiments (DOE) based on some performance metrics.     

Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times

A scheduling problem with unrelated parallel machines, sequence and machine-dependent setup times, due dates and weighted jobs is considered in this work. A branch-and-bound algorithm (B&B) is developed and a solution provided by the metaheuristic GRASP is used as an upper bound. We also propose a set of instances for this type of problem. The results are compared to the solutions provided by two mixed integer programming models (MIP) with the solver CPLEX 9.0. We carry out computational experiments and the algorithm performs extremely well on instances with up to 30 jobs.     

Criteria selection and analysis for single machine dynamic on-line scheduling with multiple objectives and sequence-dependent setups

Fertile opportunities exist for research involving dynamic and stochastic scheduling with multiple conflicting objectives and sequence-dependent setups as little has been reported in the literature to date. This research focuses on understanding and identifying the criteria that could be combined into a single rule using the linear weighted aggregation approach to consider the contradicting needs of cycle time and delivery accuracy. Eight dispatching criteria are compared and evaluated using discrete event simulation. In most studies, the basic concept is to combine different dispatching criterion that performs the best in each objective into a single rule but this may be insufficient. Simulation results show that it is necessary to take into account not only the criterion’s strength in optimizing a performance objective but also the degree of trade-off it has on the other conflicting performance objectives of interest. A correlation analysis of the objectives used is also presented.     

An iterated local search for the multi-objective permutation flowshop scheduling problem with sequence-dependent setup times

Due to its simplicity yet powerful search ability, iterated local search (ILS) has been widely used to tackle a variety of single-objective combinatorial optimization problems. However, applying ILS to solve multi-objective combinatorial optimization problems is scanty. In this paper we design a multi-objective ILS (MOILS) to solve the multi-objective permutation flowshop scheduling problem with sequence-dependent setup times to minimize the makespan and total weighted tardiness of all jobs. In the MOILS, we design a Pareto-based variable depth search in the multi-objective local search phase. The search depth is dynamically adjusted during the search process of the MOILS to strike a balance between exploration and exploitation. We incorporate an external archive into the MOILS to store the non-dominated solutions and provide initial search points for the MOILS to escape from local optima traps. We compare the MOILS with several multi-objective evolutionary algorithms (MOEAs) shown to be effective for treating the multi-objective permutation flowshop scheduling problem in the literature. The computational results show that the proposed MOILS outperforms the MOEAs.     

A hybridization of simulated annealing and electromagnetic-like mechanism for job shop problems with machine availability and sequence-dependent setup times to minimize total weighted tardiness

In this paper, we explore job shop problems with two recently popular and realistic assumptions, sequence-dependent setup times and machine availability constraints to actualize the problem. The criterion is a minimization of total weighted tardiness. We establish a simple criterion to integrate machine availability constraints and scheduling decisions simultaneously. We propose a hybrid meta-heuristic to tackle the given problem. This meta-heuristic method, called EMSA, is a combination of two meta-heuristics: (1) Electromagnetic-like mechanism (EM); and (2) simulated annealing (SA). The hybridization is done to overcome some existing drawbacks of each of these two algorithms. To evaluate the proposed hybrid meta-heuristic method, we carry out a benchmark by which the proposed EMSA is compared with some existing algorithms as well as simulated annealing and electromagnetic-like mechanism alone in a fixed given computational time. All the related results and analysis obtained through the benchmark illustrate that our proposed EMSA is very effective and supersedes the foregoing algorithms.     

Rescheduling of parallel machines with stochastic processing and setup times

This paper tackles rescheduling for the unrelated parallel machine problem with sequence dependent setup times and different rates of breakdowns or urgent jobs arrivals. The jobs’ processing and setup times are stochastic for better depiction of the real world. A new repair rule which will be referred to as Minimum Weighted C_max Difference (MWCD) is developed and compared to existing algorithms using simulation.