Synchronizing the Market Entry, Production, and Pricing Strategies for Co-Products

We model a situation in which the manufacturer generates two co-products in a single process with fixed ratio. The overall production quantity is based on the prime (high profit margin) product. However, the sales of the by-product would alleviate the average production cost and generate more profit. Prior to the selling season, he determines the two strategies: 1. the production quantity for the co-products; 2. the number of alternative markets to enter for the by-product. After that, he allocates the by-product in each market. During the season when both demands are realized, he supplies the demand of the prime product with the on-hand inventory, enduring possible overage and underage cost while he would sell the by-product in each market with a market clearing price. Our paper aims to analyze the optimal strategies in such an environment. We find the production quantity and the optimal market number are uniquely determined. Finally, we demonstrate the effects of various parameters on these strategies.