Modelling and optimising the multi-item stochastic joint replenishment problem with uncertain lead-time and controllable major ordering cost

In this paper, we extend the existing stochastic joint replenishment model to a more realistic condition by considering uncertainties in lead-time and effective investment to reduce the major ordering cost. The aim is to determine the optimal strict cyclic replenishment policy and the optimal major ordering cost simultaneously to minimise the total cost. The objective cost function is approximated by expressing one element of the cost function as a Taylor series expansion. A bounds-based heuristic algorithm is then developed to solve the proposed model. The performance of the algorithm and the quality of the approximation are examined by computational experiments. The results of the models without considering uncertainty and ordering cost reduction are presented to illustrate the effectiveness of the proposed model. Experimentation and analysis of results demonstrate that the standard deviation of lead-time has a significant effect on the system. [Received: 21 December, 2016; Revised: 29 July 2017; Revised: 29 December 2017; Revised: 30 September 2018; Revised: 17 November 2018; Accepted: 26 January 2019]