An appropriate facility layout is required to reduce total manufacturing cost, especially in uncertain environments. The design of a desirable facility layout isessential when the rearrangement of the facilities is expensive. Using RoutingFlexibility (RF) as a principle of the Flexible Manufacturing System (FMS) canlead to the fulfillment of this need. This paper propounds two new mathematical models for the Dynamic Facility Layout Problem (DFLP) with stochasticapproaches. The RF is considered when the demands of the independent partsfollow Exponential and Normal distributions in which their parameters randomlyalter from period to period. The primary nonlinear models are first linearized by the proposed innovative technique. Then, the performance of the proposed models andthe linearization technique is assessed by solving two test problems. Next, the RFeffect on the manufacturing system is analyzed. The obtained results verify thevalidity and applicability of the proposed models. It is also shown that the suggestedlinearization technique is an efficient technique with 99% accuracy, even ifconvexity conditions are not met.

This paper aims at proposing a novel quadratic assignment-based mathematical model for designing an optimal facility layout in each period of the stochastic dynamic facility layout problem (SDFLP). Considering routing flexibility is the main assumption of this problem so that parts can pass through multiple routes. It is also assumed that product demands are independent, normally distributed random variables with known expected value and variance changing from period to period at random. In addition, to solve the proposed model, a new hybrid meta-heuristic algorithm is developed by combining simulated annealing (SA) and the CRAFT approaches. Finally, the proposed model and the hybrid algorithm are verified and validated using design of experiment, real case study and sensitivity analysis methods as well as solving some numerical examples. The results show that the hybrid algorithm has an outstanding performance from both solution quality and computational time perspectives. Moreover, the proposed model can be used to design the layout of facilities in both of the stochastic and deterministic environments of traditional and modern manufacturing systems.

A facility layout problem is concerned with determining the best position of departments, cells, or machines on the plant. An efficient layout contributes to the overall efficiency of operations. It’s been proved that, when system characteristics change, it can cause a significant increase in material handling cost. Consequently, the efficiency of the current layout decreases or is lost and it does necessitate rearrangement. On the other hand, the rearrangement of the workstations may burden a lot of expenses on the system. The problem that considers balance between material handling cost and the rearrangement cost is known as the Dynamic Facility Layout Problem (DFLP). The objective of a DFLP is to find the best layout for the company facilities in each period of planning horizon considering the rearrangement costs. Due to the complex structure of the problem, there are few researches in the literature which tried to find near optimum solutions for DFLP with budget constraint. In this paper, a new heuristic approach has been developed by combining Genetic Algorithm (GA) and Parallel Simulated Annealing Algorithm (PSAA) which is the main contribution of the current study. The results of applying the proposed algorithm were tested over a wide range of test problems taken from the literature. The results show efficiency of the hybrid algorithm GA- to solve the Dynamic Facility Layout Problem with Budget Constraint (DFLPBC).