Single-period inventory model for one-level assembly system with stochastic lead times and demand

Replenishment planning of an assembly system with one type of finished product assembled from diverse external suppliers to satisfy finished product demand. It is supposed that the component lead times and finished product demand are random discrete variables. The assembly company must determine what are the best quantities of components and when is the right time to order. The objective is to minimise the total cost which is composed of holding component costs, tardiness penalties, lost sales and surplus item costs for finished products. A single-period analytical model is proposed. Several properties of the objective function are proven. They are used to develop a Branch and Bound algorithm. Numerical tests for the algorithm are presented. Five heuristics based on Newsvendor model for lead time and demand are proposed and compared with the Branch and Bound algorithm. These tests show that the suggested Branch and Bound algorithm can solve large size problems within a short time. The proposed heuristics but one are not competitive with the Branch and Bound algorithm. The truncated version of Branch and Bound gives better results. The model suggested is better adapted to actual contract assembler environments, more realistic and can better approximate real-life industrial situations. The proposed exact algorithm provides optimal solutions for all discrete distributions of probabilities of lead times and demand. A new general approach to design such discrete optimisation algorithms is presented.