A single-vendor single-buyer production-inventory model with controllable lead time and service level constraint for decaying items

Abstract

This paper presents a production-inventory model in a single-vendor single-buyer system for decaying items which deplete with constant decay rate. It is assumed that the lead time demand follows a normal distribution and shortages are backordered. Also, buyer's lead time can be reduced at an added cost. A model has been formulated to find the optimal order quantity, lead time and the number of shipments from the vendor to the buyer during one production cycle while minimising the total expected cost per unit time of the vendor-buyer integrated system. It is often difficult to estimate the stock-out cost in inventory systems. Therefore, instead of having a stock-out term in the objective function, a service level constraint is included in the model. Due to mathematical complexities involved, it is difficult to establish the solutions analytically. An iterative procedure is developed to find the optimal solution using LINGO 10, and a numerical example is given to illustrate the results of the proposed model. Furthermore, the effects of key parameters are also studied to provide the insight into the structure of the solution. In addition, the savings of buyer and vendor are investigated from implementation of joint optimisation model over the model in which they minimise their own cost independently.