随机产出环境下联产品的产量及价格策略研究

基于制造商生产主产品的过程中会随机产出两类存在替代关系的副产品的联产品系统,采用清仓定价模型,研究了不同需求函数(线性需求和指数需求)下,制造商对于主产品和副产品的最优产量与定价策略。通过两阶段优化模型的建立和求解,确定了主产品的最优产量和价格。借助数值分析,归纳出产品替代度和产出波动性对最优产量和利润的影响。研究结果表明,随着产品替代度的增加,制造商的产量上升;随着波动性的增加,制造商的产量下降。最后,将模型扩展到市场非出清的情况,并得出制造商的最优生产决策。

The Joint Pricing and Quantity Decisions for a Co-product System Under Supply Uncertainty

This article investigates the manufacturer's optimal pricing and quantity strategies in a co-product system assuming a clearance pricing policy in the by-product markets. This system includes one prime product and two by-products. By a two-stage optimization model, we obtain the optimal pricing and quantities under different demand functions (i.e., linear demand and exponential demand). Through numerical examinations, we explore the effects of different parameters (substitutability, standard deviation) on the manufacturer's quantity and profit. The results show that the substitutability has a positive effect on the quantity of the prime product. But standard deviation has negative effects on this quantity. The reason is that the manufacturer will produce more products to satisfy the demand of by-product market when the substitutability of by-products becomes larger which means the products become similar. But standard deviation and coefficient of correlation have negative effects on this quantity .The intuition of this result is that the manufacturer will decrease the production of primary product to reduce risk when the risk of obtain profits from by-product increases owing to the increasing of the volatility of random yield. Finally, we extend our basic model by considering that the byproduct market is not clear and derive the manufacturer's optimal production decision.