Discrete Dynamics in Nature and Society

Volume 2018, Article ID 1529058, 8 pages

https://doi.org/10.1155/2018/1529058

## An Improved Genetic Algorithm Based Robust Approach for Stochastic Dynamic Facility Layout Problem

School of Management, Shanghai University, Shanghai 200444, China

Correspondence should be addressed to Beixin Xia; nc.ude.uhs@aixxb

Received 31 August 2018; Accepted 25 November 2018; Published 5 December 2018

Guest Editor: Xinchang Wang

Copyright © 2018 Yunfang Peng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper deals with stochastic dynamic facility layout problem under demand uncertainty in terms of material flow between facilities. A robust approach suggests a robust layout in each period as the most frequent one falling within a prespecified percentage of the optimal solution for multiple scenarios. Mont Carlo simulation method is used to randomly generate different scenarios. A mathematical model is established to describe the dynamic facility layout problem with the consideration of transport device assignment. As a solution procedure for the proposed model, an improved adaptive genetic algorithm with population initialization strategy is developed to reduce the search space and improve the solving efficiency. Different sized instances are compared with Particle Swarm Optimization (PSO) algorithm to verify the effectiveness of the proposed genetic algorithm. The experiments calculating the cost deviation ratio under different fluctuation level show the good performance of the robust layout compared to the expected layout.

#### 1. Introduction

Nowadays, the increasingly fierce market competition and the growing variable demands of customers have gradually made the production mode shift from high volume and repetitiveness to high mix and low volume. How to meet the variant production requirements is thought to be an important objective for new intelligent manufacturing system, which is an advanced manufacturing mode of next generation. Designing agile facilities makes much sense to satisfy these requirements [1]. Dynamic changes, such as fluctuations in product quantity, varieties in product mix, introduction of new products, and discontinuation of existing products, are frequently taking place in high-mix and low-volume production environment. As a result of these changes, the previous layout becomes less efficient, which makes material handling cost increased. The uncertainty of demand has brought great challenges to design a suitable facility layout. Therefore, it is of great theoretical and practical significance to study the facility layout problem under dynamic environment [2].

The research on facility layout problem (FLP) started in the 1950s. Koopmans and Beckmann [3] initially defined the facility layout problem as the assignment of facilities to discrete locations with the objective of minimizing the material handling cost. Static facility layout is obtained according to the deterministic material flow when the demand is constant. But when the demand changes frequently with time, static layout becomes no more suitable for various periods in the planning horizon. Dynamic facility layout problem (DFLP) divides the planning horizon into several discrete time periods, with different product demand. Designing flexible layout and designing robust layout are two approaches to deal with DFLP [4]. Flexible layout optimization is to design an optimal layout for each period in the multiperiod planning horizon so that the total material handling and rearrangement cost is minimized. The facility layout is changed according to the production demand in different periods. On the other hand, the robust approach is to design a fixed robust layout to minimize the total material handling cost over the entire time planning horizon [5]. Although the robust layout is not an optimal layout for a particular time period, its performance is good in each period. In a traditional DFLP, the demand in each period is determined by demand forecasting. But, in reality, the product demand in one period is difficult to forecast accurately. Therefore, it would be more valuable to study DFLP, assuming the product demand is stochastic in each period. Considering uncertainty of the product demand in each period leads to stochastic dynamic facility layout problem (SDFLP) [6].

#### 2. Literature Review

The approaches for the DFLP can be classified into four categories: exact methods, heuristics, metaheuristics, and hybrid approaches [1, 4]. Rosenblatt [7] who is the pioneer in DFLP presented a dynamic programming (DP) formulation. Based on this formulation, both optimal and heuristic procedures are developed. Lacksonen and Enscore [8] extended five algorithms to solve the DFLP, which is modeled as a modified Quadratic Assignment Problem (QAP) formulation. And the cutting plane algorithm was illustrated to be the best for all the test problems. To avoid the computational complexity of the DP and QAP formulations, Urban [9] proposed a new heuristic algorithm based on the steepest-decent pairwise-interchange procedure, which performs well in most of situations. Recently, more specifically metaheuristic and hybrid approaches, such as genetic algorithm (GA), tabu search (TS), and simulated annealing (SA), have been widely applied for DFLP. Kaku and Mazzola [10] defined a TS heuristic utilizing a dynamic tabu list for dynamic plant layout problem. Madhusudanan et al. [5] applied a robust layout to minimize the total material handling cost over all periods. They proposed a mathematical model for robust approach and designed a SA algorithm to solve the model. Tayal and Singh [11] presented mathematical formulation for multiobjective stochastic dynamic facility layout problem and solved it by SA and chaotic simulated annealing (CSA) metaheuristics. The experiment results observed that CSA performs better than SA. GA has been proven to be effective to generate suboptimal solutions for large-scale dynamic facility layout problems. Fazlelahi et al. [12] devised a customized permutation-based robust genetic algorithm in dynamic manufacturing environments, which is expected to be generating a unique robust layout for all the manufacturing periods.

Kulturel-Konak surveyed recent developments in designing robust and flexible facilities layout under uncertainty [1]. Webster and Tyberghein [13] measured the flexibility of a layout as the ability to react to disturbances caused by future change. They analyzed the annual material handling costs to measure the flexibility. Gupta [14] solved the FLP by Monte Carlo simulation to randomly generate the flow between all pairs of departments. Chan and Malmborg [15] also used Monte Carlo simulation to empirically search for robust solutions for dynamic line layout problem. Rosenblatt and Lee [16] solved the single period plant layout problem under stochastic demand by a robustness approach. They defined the robustness of a layout as the frequency it falls within a prespecified percentage of the optimal solution for various sets of scenarios. The robustness approach searches for a reliable layout for all scenarios but not the optimal layout for any given scenario. Besides the scenario-based robust optimization to deal with uncertainty, some other methods such as stochastic programming or fuzzy programming are widely used. Stochastic programming employs probabilistic models and describes the uncertainty by probability distributions. Moslemipour and Lee [6] considered the randomly changing product demands as independent normally distributed random variables with known probability density function. SA metaheuristic algorithm was utilized to solve the mathematical model. Fuzzy programming models uncertain parameters with fuzzy numbers and establishes constraints using fuzzy sets and membership functions. Considering the uncertainty of material flows, Cheng et al. [17] introduced fuzzy numbers to represent the material flows between department pairs. Then, GA was applied to solve this hard fuzzy combinatorial problem. Kaveh et al. [18] modeled the DFLP as fuzzy programming and solved the models by a hybrid intelligent algorithm including GA, simulated annealing, and fuzzy simulation.

Although previous studies have significantly improved FLP with uncertainty, most of articles assumed that the demand is in exact probability distribution or is defined by fuzzy numbers. In fact, the information about the uncertainty is sometimes lacking and its behavior is difficult to predict. Therefore, a scenario-based method is applied in this paper to describe the demand uncertainty. Designing flexible layout and designing robust layout are two approaches to cope with dynamic layout problem. In this article, these two approaches are combined. In each period, a robust layout inspired from Rosenblatt and Lee [16] for DFLP considering the assignment of transport devices under uncertain demands is present. The robust layout is the most frequent layout falling within a prespecified percentage of the optimal solution for different sets of scenarios generated by Mont Carlo simulation. To improve the search speed of finding the robust layout, an improved adaptive genetic algorithm with population initialization strategy is proposed to reduce the search space and improve the efficiency of solving the model.

The rest of this paper is organized as follows. In the next section, the dynamic facility layout problem that considers the assignment of transport devices is modelled. Then, a robust approach based on Monte Carlo simulation is proposed to deal with material flow uncertainty in Section 3. After that, an improved genetic algorithm is developed to solve the mathematical model. Some numerical results are compared and the advantages of the robust layout are illustrated in Section 5. Finally, the conclusions are given.

#### 3. Dynamic Facility Layout Problem

DFLP considers material flow over multiple time periods. The material flow between facilities changes over time. But traditional dynamic layout optimization is studied under the condition that the demand in each period is constant; it cannot effectively solve the problem with demand fluctuation. Therefore, on the basis of proposing an improved adaptive genetic algorithm, Monte Carlo simulation method is used to describe the effect of demand fluctuation on the material flow. In our research, the assignment of transport devices (such as conveyor, AGV, and tow train) is an important decision because of different unit material handling cost for each transport device. Although we consider the fluctuation of material flow in each period, the problem becomes a determined dynamic facility problem when one scenario is generated.

The mathematical model for DFLP is discussed as follows and Table 1 gives the notations used.