Pricing and determining the optimal policy in multi-stage production systems with stochastic lead time, variable demand, partial backordering and failure rate

This paper considers multi-period serial production systems with Periodic order quantity (POQ) policy, lead-time uncertainties and demand dependent to the price. It is assumed that actual lead-time for each stage is probabilistic with known distribution and ordering system is multi period. During the production at each stage, the items may be produced in a longer time than it was schedule, causing a delay in production at this stage and this may result in backorders of the finished product. It is assumed in this case that a fixed percentage of the shortage is backlogged and other sales are lost. The objective of this paper is to find the pricing of unit product, planned lead-time and periodicity with quantity (POQ) policy in order to maximize the total system profit.