Robust inter and intra-cell layouts design model dealing with stochastic dynamic problems

In this paper, a novel quadratic assignment-based mathematical model is developed for concurrent design of robust inter and intra-cell layouts in dynamic stochastic environments of manufacturing systems. In the proposed model, in addition to considering time value of money, the product demands are presumed to be dependent normally distributed random variables with known expectation, variance, and covariance that change from period to period at random. This model is verified and validated by solving a number of different-sized test problems and a real world problem as well as doing sensitivity analysis by using the analysis of variance (ANOVA) technique.The validation process will be ended by investigating the effect of considering dependent product demands and time value of money (interest rate) on the total cost. Dynamic programming and simulated annealing algorithms programmed in Matlab are used to solve the problems. Some conclusions can be summarised as follows: (i) the simulated annealing algorithm has a performance as good as the dynamic programming algorithm from solution quality point of view; (ii) the simulated annealing is a robust algorithm; (iii) different values of the input parameters lead to design of different facility layouts; (iv) total cost of inter and intra-cell layouts is affected by the interest rate and the percentile level; and (v) the proposed model can be used in both of the stochastic and deterministic environments.