Determining the optimum production quantity in three-echelon production system with stochastic demand

This paper considers a three-echelon integrated production inventory model consisting of a central warehouse and a manufacturer including two independent departments as processing and assembly stages. To assemble the finished product, materials are carried to the assembly stage through two different flow channels. One group requires preprocessing in the processing stage, and the other one directly arrives from an outside supplier. Storing inventories either in a warehouse (as finished products) or in the stages (as work-in-process) and shipping them between the stages incur inventory costs that must be balanced to achieve minimum joint total cost. The central warehouse faces stochastic demand, which is assumed to be a generally distributed demand. It is controlled by continuous review (R,Q) policy. Additionally, warehouse ordering cost can be reduced through further investment. To analyze, we formulate a nonlinear cost function to aggregate all the costs. After, a simulated annealing algorithm has been suggested to solve the problem. Numerical experiments are presented to evaluate the performance and effectiveness of the proposed algorithm. Also, we use the branch and bound technique and a nonlinear optimization technique—generalized reduced gradient—for solving this problem. The experimental results show a fine performance of the proposed algorithm in comparison with two other methods.