Optimal policies for vendor-buyer inventory system involving defective items with variable lead time and service level constraint

This paper investigates a single-vendor-single-buyer production inventory model involving defective items in both an individual and joint management system with service level constraint. In the system under study, the vendor produces a product in a batch with finite production rate and transfers the lot in equal size to the buyer facing stochastic demand, which is assumed to be normally distributed. The lead time can be reduced by added crashing cost. Moreover, the backorder rate is dependent on the length of lead time through the amount of shortages and the lead time and ordering cost reduction are interacted. A model has been formulated to minimise the joint total expected cost and individual total expected cost by simultaneously optimising order quantity, lead time, and the number of lots delivered from the vendor to the buyer for joint and individual management system respectively. For each model, an effective iterative procedure is developed to identify the optimal solutions. Numerical examples are provided to illustrate the algorithmic procedure and the effects of key parameters are studied for both systems.

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