Optimizing a Joint Economic Lot Sizing Problem with Price-Sensitive Demand

This paper considers the problem of a vendor-buyer integrated production-inventory model. The vendor manufactures the item at a finite rate and delivers the final goods at a lot-for-lot shipment policy to the buyer. We relax the assumption of uniform demand in the hitherto existing joint economic lot sizing models and analyze the problem where the end customer demand is price-sensitive. The relation between demand and price is considered to be linear. The model proposed, based on the integrated expected total relevant profits of both buyer and vendor, finds out the optimal values of order quantity and mark-up percentage, using an analytical approach. Some numerical examples are also used to analyze the effect of the price-sensitivity of demand on the improvements in joint total profit over individually derived policies.