Research on Processing Game Problem of Fixed-Proportions Co-products Under Correlated Demand

We study the game of co-product processing between two manufacturers under the condition of fixed-proportions. Each manufacturer processes one raw material to simultaneously produce a fixed proportion of multiple linked products. There is an alternative competition between the similar products of different manufacturers. When a similar products of the manufacturer is out of stock, some unsatisfied customers will buy the similar products of another manufacturer. They maximize their personal profit and loss by choosing the amount of processing. In this paper, firstly, a single period processing game model is established when the total demand and market share are random, and it proves that the equilibrium processing quantity and the equilibrium profit and loss value will increase with the substitution rate of each co-products. Secondly, further considering the problem of multi-period processing game, the equilibrium processing strategy is given and found that the equilibrium processing volume of manufacturers will decrease with the increase of the initial inventory of themselves and competitors. Finally, simulation examples are used to analyze the influence of competition and its strength and output ratio on the co-products system.