Non-linear Programming Method for Buffer Allocation in Unreliable Production Lines

Abstract : This paper proposes a new algorithm based on a non-linear programming approach to deal with the buffer allocation problem in the case of unreliable production lines. Processing, failure and repair times are assumed to be random variables exponentially distributed. The proposed approach can be used to solve the different versions of the buffer allocation problem: primal, dual and generalized. This method is based on the modeling and the analysis of the serial production line using an equivalent machines method. The idea is to model the different possible states of each buffer using dedicated birth-death Markov processes to calculate the blockage and starvation probabilities of each machine. Then, each original machine is replaced by an equivalent one taking into account these probabilities. A comparative study based on different test instances issued from the literature is presented and discussed. The obtained results show the effectiveness and the accuracy of the proposed approach.