Integrated job shop scheduling and layout planning: a ... - Springer Link

Evolving Systems (2014) 5:121–132 DOI 10.1007/s12530-013-9092-7

ORIGINAL PAPER

Integrated job shop scheduling and layout planning: a hybrid evolutionary method for optimizing multiple objectives Kazi Shah Nawaz Ripon • Jim Torresen

Received: 15 February 2013 / Accepted: 18 June 2013 / Published online: 10 July 2013 Ó Springer-Verlag Berlin Heidelberg 2013

Abstract The facility layout planning (FLP) and the job shop scheduling problem (JSSP) are two major design issues that impact on the efficiency and productivity of manufacturing systems. The interactions between these two combinatorial optimization problems are widely known. Although, a great deal of research has been focused on solving these problems, relatively few techniques have been developed for solving them as an inter-dependent problem, none of which consider multiple objectives to better reflect practical manufacturing scenarios. Also, traditional approaches do not consider the transportation delay between two consecutive operations while solving JSSPs. Focusing on the autonomy of the manufacturing environment, this paper presents a multi-objective evolutionary method for solving JSSP that considers transportation delays and FLP as an integrated problem, which presents the final solutions as a Pareto-optimal set. In this research, a hybrid genetic algorithm by incorporating variable neighborhood search is applied to simultaneously optimize makespan and mean flow time for JSSPs, as well as total material handling cost and closeness rating scores for FLPs. This is an extension to the authors’ previous work.

K. S. N. Ripon (&) Computer Science and Engineering Discipline, Khulna University, Khulna, Bangladesh e-mail: [email protected] J. Torresen Department of Informatics, University of Oslo, Oslo, Norway e-mail: [email protected]

Keywords Job shop scheduling problem (JSSP) Facility layout planning (FLP) Variable neighborhood search (VNS) Transportation delay

1 Introduction The facility layout planning (FLP) is to find the most efficient one-to-one mapping between facilities and locations on the factory floor in order to optimize one or more manufacturing objectives. A facility in this context is a physical entity in the manufacturing system used for facilitating the processing of a particular task, and can include a machine tool, a department, a work center, a manufacturing cell, or a warehouse. FLPs are known to be computationally difficult and are generally NP-hard (Drira et al. 2007). Layout decisions are one of the key facts determining the long-run efficiency of manufacturing systems. Layout planning in a manufacturing company is an important economical consideration. A proper layout will help any company improve its business performance and can reduce up to 50 % of total operating expenses (Tompkins 2003). Scheduling exists almost everywhere in practical manufacturing situations. Various classes of scheduling problems have been investigated over the years, and many different methods have been developed for solving them. The shop scheduling is one of the most challenging scheduling problems (Ripon 2007). It can be classified into four main categories: (i) single-machine scheduling, (ii) flow-shop scheduling, (iii) job-shop scheduling, and (iv) open-shop scheduling. This work focuses on solving the job-shop scheduling integrated with the FLP, since this type of scheduling is widely found in the industry and is often considered to be representative of many general

123

122

scheduling problems in practice (Ripon et al. 2007; Xia and Wu 2005). The job shop scheduling problem (JSSP) is the determination of the sequencing of jobs on several machines following a specified processing sequence for each job such that one or more performance measures are optimized subject to some constraints. The JSSP has been considered as the worst of the worst among combinatorial problems (Garey et al. 1976). Similar to the FLP, the JSSP has great importance to manufacturing industries with an aim to minimize the production cost (Ripon et al. 2011). JSSPs and FLPs appear frequently not only in manufacturing industries, but also in engineering design contexts, including automobile, computer, semiconductor, chemical, printing, pharmaceutical, and construction industries. Recognizing their importance, researchers and operations managers, in their search for fast and optimal solutions to these problems, have used a wide variety of approaches. Not surprisingly, these approaches have been formulated by a diverse spectrum of researchers ranging from management scientists to production workers. A comprehensive survey of the current research work on JSSPs and FLPs can be found in Drira et al. (2007); Ławrynowic (2011); Herrmann (2006); Hart et al. (2005); Singh and Sharma (2006). Even though manufacturing companies spend a significant amount of time and money solving JSSPs and FLPs, they are typically performed independently and sequentially, where scheduling is executed after layouts for the facilities (where the machines will be placed) are generated. Such decomposition of these integrated problems requires prior domain knowledge, and the final solution is sensitive to the solution of the previous stage. Therefore, it is possible that the layouts generated may not be optimal from the scheduling point of view, or vice versa. By targeting the autonomy and global optimization of a manufacturing environment, the adaptation of the new production process has brought an urgent need to study and develop integrated FLP and JSSP approaches so that the placement of facilities (where machines will be placed) and the job shop operations assigned to these facilities can be synchronized as much as possible. This is because; requests of job orders deeply affect the transportation sequence of materials among the facilities in any manufacturing plant. Therefore, the coordination of JSSPs and FLPs must be considered in order to achieve global optimization for the entire production process. Also, in practical scheduling, different job orders require different sequence of operations (Yang et al. 2011). As a result, the choice of layout for facilities and the scheduling of jobs significantly impact the performance of each other (Wang et al. 2010). The importance of an integrated JSSP and FLP involves reducing costs, improving system performance, and responding quickly to customer demands to stay alive in the

123

Evolving Systems (2014) 5:121–132

intense competition of global market, thus justifying a costly long-term investment (Ripon et al. 2012a, b). However, to the best of the authors’ knowledge, FLPs and JSSPs are solved independently by researchers. It is only recently that some integrated approaches have been proposed for solving these problems (Yang et al. 2011; Wang et al. 2010; Pirayesh and Poormoaied 2012; Wang 2011; Chen and Lau 2011). Still these approaches are not practical, because they are implemented as schedule dependent layout planning approaches and ignored the inter-dependency between JSSPs and FLPs. Also, the majority of studies on JSSPs assume that transportation delays among machines are negligible, which does not reflect the practical scenarios considering the integrated problems of JSSPs and FLPs. Almost every manufacturing system involves simultaneous optimization of several objectives. It is also common that conflicts exist among the objectives. Some performance measures used frequently in JSSPs include makespan, mean flow time, and mean tardiness. Similarly, minimization of the total material handling costs, the closeness rating, hazardous movement, safety, and similar considerations are important criteria in FLPs. A single absolute optimal solution is absent for such problems. This is because, a solution that is optimal with respect to a certain criterion might be a poor candidate for where another is paramount. Therefore, the designer must instead select a solution that offers the most profitable trade-off between objectives. It is only recently that some attempts have been made for the multiobjective JSSPs and FLPs (Garen 2004; Sarker et al. 2007; Singh and Singh 2010). However, they are not suitable for complex multi-objective manufacturing optimization problems. These approaches usually either optimize a single objective and treat other objectives as constraints or combines multiple objectives into a single objective function using a weighted linear combination of all objectives, and then a single-objective optimization algorithm is used to find a single solution at a time. However, relative preferences require prior domain knowledge and the solution quality is sensitive to the relative preferences used. An efficient way to handle the problem of multiple objectives is to introduce the concept of Pareto-optimization (Deb 2001; Nuń˜ez et al. 2011). The outcome of Pareto-optimization is a set of solutions, popularly known as the Pareto-optimal set (Nuń˜ez et al. 2010), in which every element is a solution for which no other solution is better with respect to all objectives. Among these solutions, the designer is free to select any solution that offers the most profitable trade-off among the objectives based on the current requirements. Literature review represents that, up to now, no research paper deals with the Pareto-optimality for solving the integrated problems of JSSPs and FLPs. Ripon et al. (2012a, b) first proposed Pareto-optimality based evolutionary methods for solving multi-objective


FLPs and JSSPs as integrated one. This work is an extension to the these research by incorporating more manufacturing objectives and local search method. The FLP and the JSSP are both computationally difficult tasks. For the standard JSSP of n-jobs and m-machines, the search space will be (n!)m. To solve an FLP with p-facilities, the number of layouts that has to be considered is p!. Within the context of an integrated JSSP and FLP, the size of the search space is (n!)mp! For solving such combinatorial optimization problems, optimal algorithms require high computational efforts and extensive memory capabilities, even when the problem size is small. Researchers have thus relied on heuristic and meta-heuristic approaches to search through the huge spaces that are typical of practical production systems. Among these approaches, the genetic algorithm (GA) (Holland 1975) has found a wide application in research intended to solve the combinatorial optimization problems due to its ability to generate feasible solutions in a minimum amount of time (Aytug et al. 2003; Corte´s et al. 2010; Drira et al. 2007; Yang et al. 2011). Although the advantages and good performance of GAs in numerous optimization problems have been demonstrated in the literature, GAs have a major limitation when applied to optimization problems with complex search spaces and constraints. GAs can do global search in the entire search space, but there is no way for exploring the search space within the convergence area generated by the GA loop. A very successful way to remove this limitation is to hybridize it with local search. In this work, the variable neighborhood search (VNS) (Hansen and Mladenovic´ 2001; Mladenovic´ and Hansen 1997) is used as a local search. The VNS is a relatively recent meta-heuristic which is based on systematic change of neighborhood within a possibly local search. This paper presents an integrated JSSP and FLP method based on a hybrid multi-objective GA by incorporating the VNS within the GA loop. The proposed method presents the final solutions as a set of Paretooptimal solutions by simultaneous optimization of multiple objectives. The solution would answer two questions simultaneously: (i) the schedule of each job considering transportation delays, and (ii) the layout of facilities considering the scheduling of jobs among the facilities. Here, the aim is to simultaneous optimization of the makespan and the mean flow time for JSSPs, as well as the total material handling (MH) costs and the closeness rating (CR) scores for FLPs. The paper is organized in the following way. Section 2 discusses background relevant to this work. Section 3 outlines the implementation of the proposed approach. Section 4 presents experimental setup, results and observations. Finally, Section 5 provides a conclusion of the paper, and proposes directions for possible future works.

123

2 Background As stated earlier, there are basically two manufacturing optimization problems that have to consider for the proposed method: 1. 2.

Layout for the machines (facilities) which is dependent on the corresponding schedule. Schedules for the jobs which are dependent on the corresponding layout for the machines (facilities) considering the transportation delays among machines for transporting materials.

2.1 The facility layout problem Facilities usually represent the largest and most expensive assets of the organization and are of crucial importance to the organization. The FLP can be defined as the physical arrangement of a number of interacting facilities on the factory floor of a manufacturing system such that one or more performance measures are optimized subject to some constraints. Traditionally, the FLP has been presented as a quadratic assignment problem (QAP), which assigns p facilities to p equal area locations with the constraint that each facility is restricted to one location . The output of the FLP is a block layout, which specifies the relative location of each facility. Figure 1 presents example of a layout consisting of nine facilities. In this figure, facilities A, B, C, D, E, F, G, H, and I are assigned to locations (within circle) 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. The lines in this figure indicate the flow of materials between facilities to produce a product. In this work, two objectives are optimized for the FLP: the material handling (MH) cost, and the closeness rating (CR) scores. The MH cost is considered as the most common objective in FLPs. It can be defined as the sum of the distances between all facilities multiplied by the corresponding flows. This objective is subject to minimization. The material flow is expressed in the format of a from–to chart. Figure 2 presents a from–to chart for a 6facility layout.

Fig. 1 A 3 9 3 FLP

123

124

Fig. 2 From–to chart expressing material flows


(a)

Fig. 3 Chart for closeness rating scores

The CR scores is used as the other objective which aims to maximize the overall subjective closeness rating scores between various facilities. The closeness rating score is a numerical value that indicates the desirability of locating any two facilities close together. These scores are also expressed in a chart shown in Fig. 3.

(b) Fig. 4 A JSSP instance and corresponding schedule

2.2 The job shop scheduling problem The efficient scheduling of shared resources is the essence of success for any manufacturing system. The JSSP, a popular model in scheduling theory, is often formulated as follows. Given that a finite set {Jj}1 B j B n of n independent jobs have to be processed on a finite set {Mk}1 B k B m of m machines. Each job Jj has a specified sequence of operations (technological sequence of Jj) that have to be processed on m machines. Operation Ojk for job Jj requires the exclusive use of machine Mk for an uninterrupted duration tjk, its processing time. Each operation, which has started, runs to completion and can be processed by only one machine at a time. Each machine performs operations one after another. The target is to find the processing sequence of jobs (schedule) so that one or more performance measure(s) can be optimized. Figure 4a presents a 6 9 6 JSSP instance with (machine, processing time) pairs. A possible schedule for this JSSP is presented in Fig. 4b. As described earlier, traditional approaches for JSSPs mostly assume that transportation delays among consecutive

123

(a)

(b)

Fig. 5 Two different layouts

machines are negligible. However, in a schedule for any particular job, a time delay between two successive operations is necessary for transporting materials from one machine to another, especially if the machines are not adjacent. This is of more importance in the case of an integrated JSSP and FLP, in which the placement of machines depend on the corresponding schedule. This can be described by an arbitrary integrated example of a 6 9 6 JSSP (Fig. 4a) and the corresponding example of a 2 9 3 FLP (Fig. 5a). In this JSSP, the first two consecutive operations of job-1 require the transportation of materials from machine-3 to machine-1. However, the layout presented in Fig. 5a shows that the facilities (C and A), where these machines are located (positions 1 and 6), are far apart. Therefore, it is natural that there must be


some transportation delays between two consecutive operations, at least if they are processed by two machines which are not adjacent. Furthermore, for layouts with more facilities like the 3 9 5 one presented in Fig. 5b, the transportation delay is a key factor affecting the performance of JSSPs a lot. Consequently, it affects the performance of the total manufacturing systems. It is necessary mentioning that much of the research published on FLPs is done on the static FLP (SFLP), in which the relevant parameters are assumed to be invariant over time (Arabani and Farahani 2012; McKendall and Shang 2006). In contrast to those assumptions, the parameters are subject to change in many practical situations. Global economic competition is currently undergoing drastic growth leading to shorter production cycle times and greater volatility in product variety and design. Today, most manufacturing facilities have to operate in a dynamic and market-driven environment in which production rates and production mixes are continuously adapted. This requires the efficient operation of layouts and their ability to quickly respond to such changes. It is, therefore, often necessary to analyze and redesign the current layout. Similar to FLPs, in real manufacturing systems, scheduling is performed on a shorter cycle (e.g. weekly) based on the pending orders and/or current users’ requirements. Since developing a system for solving FLPs and JSSPs as an integrated problem is a relatively newer concept, the focus of this paper is to develop a unified approach for solving the integrated problem of JSSP that considers transportation delays and FLP. Therefore, this work ignores the dynamic nature of both JSSPs and FLPs. 2.3 The variable neighborhood search GAs have been proven to be more efficient and robust than the other conventional methodologies in treating a complex search space (Deb 2001; Yun 2006). They have been known to offer significant advantages against conventional methods in developing near-optimal solutions by using simultaneously and inherently parallel search principles and heuristics. Consequently, GAs have been successful in obtaining near-optimal solutions to many different combinatorial optimization problems. Generally speaking, the GA outperforms other heuristic and meta-heuristic methods due to its capability to generate feasible solutions in a minimum amount of time, and seems to have become quite popular in solving manufacturing optimization problems like FLPs and JSSPs (Drira et al. 2007; Hu and Wang 2004). GAs have also been shown to be effective in solving multi-objective optimization problems and in producing quite good results when applied individually. However, GAs have inherent difficulties in converging to the global

125

optimum with an adequate precision in complex and large search space. In certain cases, it performs too slowly to be practical. This is because of GA’s fundamental characteristics—not using a priori knowledge and inability to explore the search space within the convergence area generated by the GA loop.

Local search methods are improvement heuristics that examine a set of points in the neighborhood of the current solution and replace it if a better neighbor exists (da Silva et al. 2010). Hybridization with local search can improve the situations mentioned above, in which GAs globally explore the domain and find a good set of initial estimates, while local search further refines these solutions in order to locate the nearest, best solution. The VNS is an explorative local search method whose basic idea is systematic change of neighborhood within a possible local search. In contrast other meta-heuristics based on local search methods, which use one constant type of neighborhood structure; the VNS switches neighborhoods of growing size with shaking strategies (Hansen and Mladenovic´ 2003), and jumps from the current solution to a new one if and only if there is an improvement. In this way, it keeps favorable characteristics of the incumbent solution and obtains promising neighboring solutions. By allowing the use of different neighborhood search methods, it can easily escape from local optima and move towards global optimum (Ripon et al. 2013). The steps of basic VNS are presented in Algorithm 1, where Nk represents the kth neighborhood structure ðk ¼ 1; . . .; kmax Þ; S represents the set of all feasible solutions, and Nk(s) represents the set of all solutions in the kth neighborhood of the solution s.

123

126

3 Multi-objective GA-based solution approach This section explains the major steps towards the multiobjective GA-based solution approach. The GA (Holland 1975), a particular class of evolutionary algorithms, is a search algorithm for global optimization in a complex search space. It starts with a population of randomly generated candidate solutions (chromosomes) and uses probabilistic rules to evolve a population from one generation to the next by using several techniques inspired by evolutionary biology such as selection, mutation, crossover, and inheritance. In this approach, the non-dominated sorting genetic algorithm-2 (NSGA-2) proposed by Deb et al. (2002) is used as the multi-objective GA.


into a feasible schedule, but two or more different individuals may be decoded into an identical schedule. The advantage of this representation is that it requires a very simple schedule builder because all generated schedules are legal. For the second (FLP) part, a form of direct representation is applied. The chromosome of this part is represented as a string of integers of length p, where p is the number of facilities. The integers denote the facilities and their positions in the string denote the positions of the facilities in the layout.

3.1 Chromosome representation In the proposed approach, chromosomes are composed of two parts. The first part presents the chromosome for JSSPs, and the second part is for FLPs. Figure 6 depicts a chromosome representation for a 3-job, 5-machine, and 5-facility problem (the technological sequence of the JSSP is shown arbitrarily). It is very important mentioning that, for obvious reason, the number of facilities (where the machines will be placed) will be equal to the number of machines. For JSSPs, an indirect representation incorporated with a schedule builder is applied. This representation is known as permutation with repetition (Bierwirth 1995). The genes for this portion are represented as a string of integers of length m 9 n, where each job integer (n) is repeated m (machines) times. In Fig. 6, for example, job-1 is repeated 5 times (M1, M2, M3, M4, M5). By scanning the permutation from left to right, the kth occurrence of a job number refers to the kth operation in the technological sequence of this job. For such indirect representation for the JSSP, a schedule builder (presented in Sect. 3.2) is required to decode the chromosome into a valid schedule. In this representation, it is possible to avoid the schedule operations whose technological predecessors have not been scheduled yet. Therefore, any individual can be decoded

Fig. 6 Chromosome representation for a integrated problem of 3 9 5 JSSP and 5-facility FLP

123

3.2 Schedule builder In addition to decode an indirect representation for the JSSP into a schedule, a schedule builder also performs the evaluation procedure and should be chosen with respect to the performance measure of optimization. In this work, a variant of Giffler and Thompson algorithm (Varela et al. 2005) with a slight modification is employed in order to fit with the chromosome and to produce active schedules only. A schedule is called active when no permissible left shift can be applied to that schedule. Permissible left shift is the reassigning of an operation to the left without delaying other jobs to reduce the makespan of any schedule. Active schedules are good in average and at the same time an optimal schedule is always active; so the search space can be safely limited to the set of all active schedules. Interested readers may refer to (Ripon et al. 2007) for the details. Here, we modified the Giffler and Thompson algorithm in order to taking into account the transportation delays considering the positions of facilities in the layout constructed from the same chromosome.


127

If the consecutive operations are to be processed by the facilities which are not adjacent, transportation delays (TD) are added before the starting of the next operation. This modified algorithm is presented in Algorithm 2, where S is the schedule being constructed. The set A is used to hold the set of schedulable operations, where an operations o is said to be schedulable if it has not been scheduled yet. 3.3 Formulation of the objective functions In this work, four objectives are simultaneously optimized—two for JSSPs and FLPs each. It is worth mentioning that the objectives for the JSSP and the FLP are calculated only considering the genes of the respective portion of the chromosome (as shown in Fig. 6). In the proposed method, however, objectives of each problem are subject to the formulation of its counterpart. In JSSPs, minimization of the makespan (maximum completion time of all jobs) is usually considered as the main optimization criterion (Ripon et al. 2011; Hart et al. 2005). The mean flow time (average flow time for all jobs), as the second objective, continues to be very important in JSSPs since it assists to select the appropriate one when many approaches proposed in the literature have reached the same makespan for many instances. Both of these objectives are subject to minimization. For FLPs, we use the total MH cost and the CR scores as objectives. Here the optimization goals are to minimize the first objective, while to maximize the later one. These objectives can be expressed by the following mathematical models: Makespan ¼ max½Ci 1 Mean flow time ¼ n Total MH costs ¼

n X

ð2Þ

Ci

i¼1

p X p X p X p X

fik djl Xij Xkl

ð3Þ

p X p X p X p X

Wijkl Xij Xkl

ð4Þ

i¼1 j¼1 k¼1 l¼1

subject to p X

Xij ¼ 1;

j ¼ 1; 2; . . .; p

ð5Þ

Xij ¼ 1;

i ¼ 1; 2; . . .; p

ð6Þ

i¼1 p X j¼1

Wijkl ¼

rik ; 0;

ð8Þ ð9Þ

where, Ci is the completion time of job i; n is the number of jobs; i, k are facilities; j, l are locations in the layout; fik is the material flow from facility i to k; djl is the distance from location j to l; p is the number of facilities in the layout, and rik is the closeness ranking value when facility i and k are neighbors with common boundary. Constraints 5 and 6 ensure that each location is assigned to exactly one facility and each facility is assigned to only one location, respectively. The subjective closeness ratings used in this work are: A (absolutely necessary) = 6, E (essentially important) = 5, I (important) = 4, O (ordinary) = 3, U (un-important) = 2, and Z (undesirable) = 1. Unlike the traditional FLP, the flow matrix (fik) is not predetermined for the specific FLP. Rather, it is calculated based on the technological sequence of the specific JSSP which will be assigned to this FLP. On the other hand, the completion time for job Ci is calculated by incorporating the transportation delay between two distant facilities considering the complete solution for the integrated problem. As a result, the proposed model can consider the interdependency between these two problems. 3.4 Implementation of the variable neighborhood search

ð1Þ

i¼1 j¼1 k¼1 l¼1

CR Scores ¼

providing that 1; if facility i is assigned to location j Xij ¼ 0; otherwise 1; if facility k is assigned to location l Xkl ¼ 0; otherwise

if locations j and l are neighbors otherwise

ð7Þ

To implement the variable neighborhood search (VNS), two different types of neighborhood structure, each comprising of two different orders, are applied. The structures are based on insertion neighborhood. These two types are divided based on the number of chromosome segment (JSSP and FLP) taking part in constructing the neighborhood. In this work, the number of segments are decided randomly. If it is one, the segment is chosen at random. Then, a single gene is randomly removed from its position and is inserted elsewhere within the same segment. All genes within these positions are moved one position forward or backward to fill up the gaps. If the number of segment is two, the same process is repeated for both segments. For the other two neighborhoods, the same process (single segment or double segments) is repeated, but changing the number of genes. Instead of one gene, two genes are removed from their positions and inserted elsewhere within the same segment. Therefore, the VNS explores neighborhood of growing size.

123

128


4 Computational results 4.1 Test problems

The extended 1-opt local search (Merz and Freisleben 2002) is used in the local search step of the VNS algorithm (Algorithm 1) by incorporating the domination strategy (Deb et al. 2002). The incorporation of domination strategy is necessary because the proposed approach deals with multiple objectives. This implementation of local search is to replace the current solution with its neighbor that dominates the current solution (if any exists). To save computation time and effort, this algorithm stops searching the neighborhood as soon as it finds a solution which dominates the current one. The general outline of the extended 1-opt local search is given in Algorithm 3, where fit is the objective of a chromosome. The subscripts (1 and 2) used in fit indicate a chromosome before and after the local search. Whereas, the superscripts (1–4) used in fit indicate the objective functions of a particular chromosome.

There are no benchmark datasets published for the combined areas of the multi-objective FLP and the multiobjective JSSP considering the transportation delay, even without transportation delay, as of now. Ripon et al. (2012a) proposed a multi-objective integrated approach for JSSPs and FLPs. To the best of the authors’ knowledge, it is the only available benchmark data sets for the combined areas of multi-objective JSSPs that consider transportation delays and FLPs. In this work, the results are compared with those results. However, Ripon et al. (2012a) used a different strategy for incorporating transportation delays within the framework of JSSPs. To match the number of machines with the number of facilities, the benchmark data sets are composed of the existing data sets (mt06, abz7, tai02, tai10, la38, la39, la40) for JSSPs, and (nug6, nug15) for FLPs. Similar to Ripon et al. (2012a), in this work, the transportation delay is also set to 1 unit whenever necessary. This is due to the lack of practical data. 4.2 Test setup The experiments are conducted using a population of 200 chromosomes and 400 generations. The probabilities of crossover and mutation are [0.7, 0.8, 0.9] and [0.1, 0.2, 0.3], respectively. We use traditional tournament selection with tournament size of 2. Each problem is tested for 30 times with different seeds and different (random) combinations of crossover and mutation rates. Then each of the final generations is combined and a non-dominated sorting is performed to produce the final non-dominated solutions. 4.3 Experimental analysis

3.5 Genetic operations To apply crossover operation, the crossover points for the two parent chromosomes are chosen randomly with the restriction that both points should be on the same portion. Based on the crossover points, two types of crossover operation are applied: (i) the improved precedence preservation crossover (IPPX) proposed by Ripon et al. (2011) for the JSSP portion, and (ii) the crossover operation proposed by Suresh et al. (1995) for the FLP portion. For mutation, swap mutation is used with the same restriction of selecting two genes randomly from the same portion of a chromosome. If the genes are from the FLP part, traditional swap mutation is used; while in the case of the JSSP portion, swap mutation is applied with additional restriction of choosing two non-identical genes.

123

Table 1 shows the comparison of the best and average values (in parentheses) obtained by the proposed method and previous approach (Ripon et al. 2012a) in the context of all four objectives. As mentioned earlier, Ripon et al. (2012a) used a different strategy for incorporating transportation delays within JSSPs, and, therefore, it is not reasonable to compare with this results. Also, this approach optimize only three objectives. However, these are mentioned as references. As shown in the table, in most cases, the results obtained by the proposed approach are better than or on par with the previous method for all the objectives. In fact, the proposed approach clearly outperforms the previous approach considering all objectives. Among the 7 JSSP–FLP combinations, it achieves better makespan, MH costs, and CR

176 (160.5)

168 (158.45) 583 (704.05)

583 (705.25) 983 (1,007.5)

1,068 (1,118.5) 1,238 (1,356.75)

1,249 (1,291.4) 170 (156.75)

168 (156.20) 584 (706.2)

583 (707.5) NA

NA 1,238 (1,381.7)

1,250 (1,326.8) 15

15 nug15

nug15

15 la40

15

15 la39

15

170 (156.75) 582 (692.5) 971 (1,024.25) 1,206 (1,256.15) 166 (154.85) 586 (704.3) NA 1,209 (1,285.1) 15 nug15 15 la38

15

170 (158.5) 184 (178.025) 580 (676.45) 580 (686.75) 529 (592.25) 586 (612.35) 1,260 (1,303.2) 680 (702.75) 166 (156.40) 184 (174.65) 580 (691.5) 580 (690.25) NA NA 1,260 (1,318.2) 681 (716.2) 15 15 nug15 nug15 15 20 tai10 abz7

15 15

48 (42.4)

168 (160.05) 583 (686.15)

45 (40.1) 44 (46.35)

524 (584.25) 1,259 (1,319.625)

58 (61.9) 46 (40.6)

168 (156.25) 583 (702.05)

46 (49.2) NA

NA 1,263 (1,327.6)

58 (62.6) 6

15 nug15

nug6 6

15

6

15 tai02

MH cost MF time F FLP M J JSSP

Table 1 Comparison with exiting multi-objective approach

129

mt6

Makespan Makespan

CR score

Proposed approach Previous approach

MF time

MH cost

CR score


scores in 4, 3, and 4 cases, respectively. In addition, the previous approach never finds a better value for any of these three objectives. For the lack of existing results, it is not possible to present any comparison for mean flow time. However, it is worthy mentioning that the overall performance of the proposed method is very promising considering all the objectives simultaneously. Most importantly, average values for all objectives considerably improve. In Ripon et al. (2012a), the average values were relatively unstable. However, the introduction of local search in form of VNS makes the averages more stable, which definitely justify the application of VNS. This can be further justified by Fig. 7, where the convergence behavior of the proposed and previous methods over generations for all four objectives in case of la38 is depicted. These figures also justify that the proposed method successfully optimizes all the objectives with generations. From the figures, it can be found that from first generations to last generations, the proposed and previous methods are able to optimize makespan (minimize), mean flow time (minimize), MH cost (minimize) and CR score (maximize) simultaneously. However, the incorporation of VNS reduces the gaps between the best and average values more than that of the competing method for all the objectives. The best and average values obtained by the approaches as mentioned in Table 1 also justify this. Assessing the quality of an EA-based model commonly implies experimental comparison between the given model and existing evolutionary- or traditional algorithm-based model (Eiben and Smith 2007). Due to the stochastic nature of EAs, multiple runs on the same problem are necessary to get a good estimation of performance (Eiben and Smit 2011). Also, because of the stochastic nature of EAs, the performance measures should be statistical in nature. In order to analyze the performance of the proposed approach, four statistical measures are used in this work. These are: (i) Mean Square Error (MSE), (ii) Root Mean Square Error (RMSE), (iii) Mean Absolute Error (MAE), and (iv) Mean Absolute Percent Error (MAPE). All of these are frequently used measures of the difference between values predicted by a model and the values actually obtained by any previous model. In addition to this, in conjunction with the averages, these are effective measures to describe the spread/distribution of data. Table 2 highlights the values of these measures obtained by the proposed approach and the previous approach for all the objectives. It is necessary mentioning that an algorithm having a smaller value is better in terms of all the four measures. The values of the metrics as shown in this table indicate that the proposed approach obtained smaller values for all the measures considering all the objectives, and the difference is very significant. Only

123

130


(a)

(b)

(c)

(d)

Fig. 7 Optimization of objectives over generations

Table 2 Statistical performance measures MSE

RMSE

MAE

MAPE

Previous

262.5587

16.20366

1,347.843

0.002388401

Proposed

122.4298

11.0648

583.9721

0.001673664

Previous

NA

NA

NA

NA

Proposed

71.58266

8.460654

393.261

0.002125543

Previous

415.9922

20.39589

2,513.405

0.005362813

Proposed

365.8526

19.12727

2,211.458

0.005376972

3.92965 3.831941

1.982334 1.957534

26.13645 3.89133

0.002776002 0.002639647

Makespan

MF time

MH cost

CR score Previous Proposed

123

in a single case of MH cost (considering MAPE), the proposed approach finds larger value than that of the previous one. However, the difference is very marginal (0.005362813 and 0.005376972 in the case of previous and proposed approach, respectively). To summarize the result, the proposed hybrid evolutionary approach incorporating the VNS for solving the integrated problems of multi-objective FLPs and JSSPs that consider transportation delays is capable of producing near-optimal and non-dominated solutions, which are also the best-known results in many cases. Accordingly, it can provide a wide range of alternative trade-off choices for the designers. Therefore, the designers have the flexibility in choosing the final solution via simultaneously considering all the objectives based on the current requirements.


5 Conclusion and future works Aiming for the autonomy of the entire manufacturing system has brought an urgent need to study and develop integrated FLP and JSSP approaches so that the layout for facilities and the job operations assigned to these facilities can be synchronized as much as possible. However, in traditional manufacturing plants, layout planning and job scheduling are performed independently. Then again, transportation delay between two consecutive operations is neglected while solving JSSPs. This paper results in a hybrid multiobjective GA for solving JSSPs that consider transportation delays and FLPs as an integrated problem, which presents the final solutions as Pareto-optimal set by considering multiple objectives simultaneously. Experimental results validated the proposed approach as an efficient integrated framework capable of producing a set of trade-off solutions. The results also demonstrate the success of the VNS as a local search in improving the best and average objective values, and the optimization behavior of the proposed method. Accordingly, the proposed method can significantly affect the productivity of a manufacturing system. A natural direction for future work could be to estimate what impact the developed methods could have on actual manufacturing systems. However, due to the lack of practical data, it is not possible to asses the performance of the proposed method on actual manufacturing systems. More objectives related to manufacturing systems can also be utilized. In future, the authors hope to collect real-world data from practical manufacturing industries to obtain a measure of the performance of the developed approaches and also to identify other objectives. Also, in future, the authors hope to extend the proposed system by considering the dynamic nature of FLPs and JSSPs to better reflect today’s dynamic manufacturing scenarios.

References Arabani AB, Farahani RZ (2012) Facility location dynamics: an overview of classifications and applications. Comput Ind Eng 62(1):408–420 Aytug H, Khouja M, Vergara FE (2003) Use of genetic algorithms to solve production and operations management problems: a review. Int J Prod Res 41(17):3955–4009 Bierwirth C (1995) A generalized permutation approach to job shop scheduling with genetic algorithms. OR Spektrum 17:87–92 Chen HX, Lau HC (2011) A math-heuristic approach for integrated resource scheduling in a maritime logistics facility. In: 2011 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), pp 195–199 Corte´s CE, Saéz D, Milla F, Nuń˜ez A, Riquelme M (2010) Hybrid predictive control for real-time optimization of public transport systems’ operations based on evolutionary multi-objective optimization. Transp Res Part C: Emerg Technol 18(5):757–769

131 Deb K (2001) Multi-objective optimization using evolutionary algorithms, 1st edn. Wiley, Chichester Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197 Drira A, Pierreval H, Hajri-Gabouj S (2007) Facility layout problems: a survey. Annu Rev Control 31(2):255–267 Eiben AE, Smit SK (2011) Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm Evol Comput 1(1): 19–31 Eiben AE, Smith JE (2007) Introduction to evolutionary computing, 2nd edn. Springer, Berlin Garen J (2004) A genetic algorithm for tackling multiobjective jobshop scheduling problems. In: Gandibleux X, Sevaux M, So¨rensen K, T’kindt V (eds) Metaheuristics for multiobjective optimisation, Lecture Notes in Economics and Mathematical Systems, vol 535. Springer, Berlin, pp 201–219 Garey MR, Johnson DS, Sethi R (1976) The complexity of flowshop and jobshop scheduling. Math Oper Res 1(2):117–129 Hansen P, Mladenovic´ N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130(3):449–467 Hansen P, Mladenovic´ N (2003) Variable neighborhood search. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics, International Series in Operations Research & Management Science, vol 57. Springer, New York, pp 145–184 Hart E, Ross P, Corne D (2005) Evolutionary scheduling: a review. Genetic Program Evol Mach 6(2):191–220 Herrmann J (2006) Handbook of production scheduling. Springer, New York Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor Hu MH, Wang MJ (2004) Using genetic algorithms on facilities layout problems. Int J Adv Manuf Technol 23(3–4):301–310 Lawrynowic A (2011) A survey of evolutionary algorithms for production and logistics optimization. Res Logist Prod 1(2): 57–91 McKendall AR Jr, Shang J (2006) Hybrid ant systems for the dynamic facility layout problem. Comput Oper Res 33(3):790–803 Merz P, Freisleben B (2002) Greedy and local search heuristics for unconstrained binary quadratic programming. J Heuristics 8:197–213 Mladenovic´ N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24(11):1097–1100 Nuń˜ez A, De Schutter B, Saéz D, Corte´s C (2010) Hierarchical multiobjective model predictive control applied to a dynamic pickup and delivery problem. In: Proceedings of the 13th International IEEE Conference on Intelligent Transportation Systems (ITSC 2010), Madeira Island, Portugal, pp 1553–1558 Nuń˜ez A, Corte´s C, Saéz D, Gendreau M, De Schutter B (2011) Multiobjective model predictive control applied to a dial-a-ride system. In: Proceedings of the 90th Annual Meeting of the Transportation Research Board, Washington, DC, Paper 11-1942 Pirayesh M, Poormoaied S (2012) Location and job shop scheduling problem in fuzzy envirenment. In: The 5th International Conference of the Iranian Society of Operations Research Ripon KSN (2007) Hybrid evolutionary approach for multi-objective job-shop scheduling problem. Malays J Comput Sci 20(2): 183–198 Ripon KSN, Tsang CH, Kwong S (2007) An evolutionary approach for solving the multi-objective job-shop scheduling problem. In: Dahal K, Tan K, Cowling P (eds) Evolutionary scheduling, studies in computational intelligence, vol 49. Springer, Berlin, pp 165–195 Ripon KSN, Siddique N, Torresen J (2011) Improved precedence preservation crossover for multi-objective job shop scheduling problem. Evol Syst 2(2):119–129

123

132 Ripon KSN, Glette K, Hovin M, Torresen J (2012a) Job shop scheduling with transportation delays and layout planning in manufacturing systems: a multi-objective evolutionary approach. In: Kamel M, Karray F, Hagras H (eds) AIS’12. Lecture Notes in Computer Science, vol 7326. Springer, New York, pp 209–219 Ripon KSN, Glette K, Hovin M, Torresen J (2012b) A multi-objective evolutionary algorithm for solving integrated scheduling and layout planning problems in manufacturing systems. In: 2012 IEEE Conference on Evolving and Adaptive Intelligent Systems (EAIS), pp 157–163 Ripon KSN, Glette K, Khan KN, Hovin M, Torresen J (2013) Adaptive variable neighborhood search for solving multi-objective facility layout problems with unequal area facilities. Swarm Evol Comput 8(1):1–12 Sarker R, Ray T, da Fonseca J (2007) An evolutionary algorithm for machine layout and job assignment problems. In: 2007 IEEE Congress on Evolutionary Computation (CEC 2007), pp 3991–3997 da Silva F, Sańchez Pe´rez J, Go´mez Pulido J, Vega Rodrı´guez M (2010) AlineaGA—a genetic algorithm with local search optimization for multiple sequence alignment. Appl Intell 32(2): 164–172 Singh S, Sharma R (2006) A review of different approaches to the facility layout problems. Int J Adv Manuf Technol 30(5–6): 425–433 Singh S, Singh V (2010) An improved heuristic approach for multiobjective facility layout problem. Int J Prod Res 48(4):1171–1194

123

Evolving Systems (2014) 5:121–132 Suresh G, Vinod VV, Sahu S (1995) A genetic algorithm for facility layout. Int J Prod Res 33(12):3411–3423 Tompkins JA (2003) Facilities planning, 2nd edn. Wiley, New York Varela R, Serrano D, Sierra M (2005) New codification schemas for ´ lvarez J (eds) scheduling with genetic algorithms. In: Mira J, A Artificial intelligence and knowledge engineering applications: a bioinspired approach. Lecture Notes in Computer Science, vol 3562. Springer, Berlin, pp 11–20 Wang L (2011) Combining facility layout redesign and dynamic routing for job-shop assembly operations. In: 2011 IEEE International Symposium on Assembly and Manufacturing (ISAM), pp 1–6 Wang L, Keshavarzmanesh S, Feng HY (2010) A hybrid approach for dynamic assembly shop floor layout. In: 2010 IEEE Conference on Automation Science and Engineering (CASE), pp 604–609 Xia W, Wu Z (2005) An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems. Comput Ind Eng 48(2):409–425 Yang CL, Chuang SP, Hsu TS (2011) A genetic algorithm for dynamic facility planning in job shop manufacturing. Int J Adv Manuf Technol 52(1–4):303–309 Yun Y (2006) Hybrid genetic algorithm with adaptive local search scheme. Comput Ind Eng 51(1):128–141