An optimal policy for recovery and procurement under multiple setups

This paper attempts to find the economic ordering quantity (EOQ) and economic procurement quantity (EPQ) for a system in which the demand can be satisfied by a combination of newly purchased products and recovered, used products. Used products are collected from customers and then they undergo recovery processes. These recovered products are regarded as perfectly new ones. The model developed here considers a realistic case where there can be multiple setups for both recoveries and procurements. We study cases where production/procurement rate is finite and infinite. We obtain the EOQ for newly procured products and the optimal inventory level of recoverable items to start the recovery process simultaneously. The total cost equation is found to be the function of the inventory level of recoverable items to start recovery and the ratio of orders for newly procured items to setups. Then, a search procedure to find the optimal control parameters is presented. The models have been validated with illustrating numerical examples and sensitivity analysis.