部分延迟订购的易变质品联合定价与生产策略

构建了一个需求同时依赖于销售价格和库存水平,生产率和变质率均为常数,允许缺货且缺货量部分延迟订购的易变质品联合定价与生产控制模型。首先证明了在销售价格给定的情况下,系统的总利润函数是关于生产计划的严格凹函数,平均利润函数是严格的伪凹函数,即存在唯一的最优解,并给出其充分条件。接着给出问题的一个数值求解算法。最后通过算例,展示了模型及相关算法的应用,并对相关参数进行了灵敏度分析,结果显示:当产品的生产成本、缺货成本和机会成本增加时,系统的平均利润将下降;生产成本和延迟订购阻力系数对最优定价和生产策略以及平均利润的影响较大。

Joint Pricing and Production Policy for Deterioration Items with Partial Backlogging

In this paper, we develop a joint pricing and production model for deterioration items in which we assume that the demand rate is dependent both on the selling price and the inventory level, the production rate and the deterioration rate are known and constant and the unmet demand is partial backlogged in the shortage period. We first prove that for any given selling price, the total profit function is strictly concave, and the average profit function is strictly pseudo-concave, that is, there exists the unique and optimal solution to the problem, and the sufficient condition is also presented. Then an algorithm is proposed to obtain the optimal solution of the problem. At last, we give a numerical example to illustrate the application of the model and algorithm proposed, and then we also conduct the sensitivity analysis on the parameters. The results show that when the production cost, the shortage cost and the opportunity cost of items increase, the average profit of system will decrease. The optimal pricing-production policy and the average profit are highly sensitive to the production cost and the backordering resistance.