Complete search procedure for replenishment and collection policies in a product life cycle for a retailer

In this paper, assuming the retailer is responsible for used-product collection, we investigate replenishment and collection policies by considering a general, time-varying, continuous, and deterministic demand function for a product life cycle. The objection is to optimally determine the number of inventory replenishments, the inventory replenishment time points, and the return rates of used-product in the product life cycle by minimising the total relevant cost of the inventory replenishment and used-product collection system. A complete search procedure is developed to find the optimal solution by employing the properties derived in this paper and the well-known Nelder-Mead algorithm. Also, numerical examples are carried out to illustrate the features of the proposed problem discussed in this paper.