A bi-objective coordination setup problem in a two-stage production system

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Abstract

This paper addresses a problem arising in the coordination between two consecutive departments of a production system, where parts are processed in batches, and each batch is characterized by two distinct attributes. Due to the lack of interstage buffering between the two stages, these departments have to follow the same batch sequence. In the first department, a setup occurs every time the first attribute of a new batch is different from the one of the previous batch. In the downstream department, there is a setup when the second attribute changes in two consecutive batches. The problem consists in finding a batch sequence optimizing the number of setups paid by each department. This case results in a particular bi-objective combinatorial optimization problem. We present a geometrical characterization for the feasible solution set of the problem, and we propose three effective heuristics, as shown by an extensive experimental campaign. The proposed approach can be also used to solve a class of single-objective problems, in which setup costs in the two departments are general increasing functions of the number of setups.

Introduction

This work deals with a problem of real-life manufacturing interest: The coordination of two consecutive production departments. Each department consists of a flexible machine, the first one deals with shaping items of raw wooden panels; the second concerns the painting of the just shaped items. To avoid unnecessary costs, each department works with batches of jobs, in which every job has the same shape and color. Due to limited interstage buffering between the two stages, these departments have to follow the same batch sequence. Hence, this problem belongs to the class of permutation sequencing problems.

When two consecutive jobs with different features have to be processed, at least one department must pay a setup, in order to reconfigure its own machine, i.e., changing tools. The effort needed to accomplish a setup (in terms of manpower, machine reconfiguration, etc.) is almost the same in each department. This implies that the same cost must be paid for a setup in the first and in the second department. Hence, each department have to organize its own operations in order to minimize the number of setups, i.e, the reconfigurations of cutting and painting tools, respectively. This combinatorial problem is inherently bi-objective (Ehrgott, 2000, T’kindt and Billaut, 2002) because each department has to minimize its setup costs, while from a global point of view, the minimization of the total setup cost must be pursued.

Note that, the considered problem can be modeled as a tool switching problem on a single machine with two classes of tools (cutting and painting tools), in which a given set of jobs (each of them requiring exactly one tool of each class) must be sequenced on the machine minimizing the number of tool switching. In this paper, a graph based model, first introduced in Agnetis et al. (2001), is used to obtain a lower bound and an upper bound of the number of setups for each department. At an operational level, the goal is to find a, possible large, set of sequences of batches solving a trade-off between different objectives (i.e., the number of setups paid by each department). We tackled this multi-objective problem using a metaheuristic approach. The basic idea of this approach is to obtain a good estimation of the Pareto optimal front for the bi-objective problem. At this aim, first the total setup number of the production system is minimized, then a different procedure is employed to spread the setups over departments keeping constant the total number of setups. Different procedures to guide the algorithms toward the discovering of a greater part of the Pareto optimal front are implemented. The proposed approach returns a set of non-dominated points achieving a high probability of covering almost all the Pareto optimal front in an acceptable computation time.

The paper is organized as follows. In Section 2, literature results and applications are discussed. In Section 3, the industrial context is described, a formal description of the problem and a geometrical characterization of the feasible solution set are given. Moreover, we also show that these geometrical properties are also useful to solve a class of single objective problems, in which the setup costs in the two departments are general increasing functions of the number of setups. In Section 4, three metaheuristic algorithms are presented, and in Section 5 a large sample of experiments are reported, showing the effectiveness of the proposed approaches. Finally, in Section 6, conclusions are drawn.

Section snippets

Literature and applications

Minimizing the impact of setups (i.e., changeovers) has been widely described as a main component of modern production management strategies (Voß and Woodruff, 2003). Pursuing high changeover performances is a way to enable agile and responsive manufacturing processes by improving line productivity and reducing downtime losses (McIntosh et al., 2001). This aspect of the production management, involving both organizational and economic points of view, has received an increasing attention also in

Problem description and formulation

This paper addresses a problem arising in the coordination between two consecutive production departments of an industrial system (Agnetis et al., 2001), in which a large number of different slabs of wood are cut, painted and assembled to build kitchen furniture. Due to the lack of interstage buffering, departments must process the batches in the same order. The two departments are the cutting and the painting departments and batches are characterized only by shapes and colors. In the cutting

Algorithms

In this section we describe three metaheuristic algorithms developed to tackle the problem. A metaheuristic is an iterative solution procedure, combining subordinate heuristic tools into a more sophisticated framework (Glover and Kochenberger, 2003, Hoos and Stützle, 2004). All the developed algorithms are based on the same basic subordinate procedures, namely a constructive heuristic, some improving procedures and an update routine.

These subordinate procedures are used by some Master procedure

Computational experiments

In this section we describe the experiments carried out to evaluate the behavior of the three proposed algorithms.

The algorithms have been tested on one set of 32 real-life instances (GSET) and on 460 randomly generated problems (Agnetis et al., 2001). The 32 real-life instances consist of unbalanced bipartite graphs G=(V1,V2,E) where |V1|=32 and |V2|=14. In these instances |E| ranges from 150 to about 300. The other sets of randomly generated instances consist of connected balanced bipartite

Conclusions and future research

In this paper a two objective setup coordination problem arising in a two-stage serial manufacturing system is addressed. The problem consists in finding a common sequence of batches to be produced such that the number of setup paid on each department is minimized. In particular the case in which all the setups are identical has been considered. For this problem a geometrical characterization of the Pareto optimal front is given and it is used to develop effective algorithms. Three

Acknowledgements

The authors thank the anonymous referees and editors for the constructive comments and suggestions that have helped to improve the presentation quality of the paper.

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