Joint replenishment and pricing of a single product under exchange rate uncertainty

Abstract

Purchasing cost uncertainty in the future subject to exchange rate fluctuation is modeled as a markov chain transition matrix, and it is combined with supply chain profit maximization problem. This problem is modeled as a multi-period stochastic inventory control problem on USD/TRY dataset. Replenishment problem is considered under the myopic and dynamic inventory policies. Excess demand is lost, and salvage cost is zero. The procedures to compute order up to inventory levels of both inventory policies are determined. It is verified that (1-P) value, which is an indicator of myopic solution effectiveness, shows the closeness of the dynamic and myopic inventory policies. Average profit is computed with a simulation which includes multi-period purchasing and selling steps. Demand is taken as a random variable with gamma distribution, since it can take only positive values. Price dependent demand is also evaluated. Moreover, the effect of variance in demand on both of order up to inventory level and average profit is analyzed. It is seen that the variance in demand increases the volatility in order up to inventory levels with respect to purchasing costs, and average profits. Optimal inventory level and pricing are also assessed together after replenishment problem is evaluated. Two different pricing systems are used, namely best constant pricing and best pricing. Best constant pricing represents that price is announced before purchasing cost is determined and it cannot be changed period by period. Best pricing represents that price can be updated with respect to purchasing cost in each period. A procedure to find out optimal order up to inventory level and best price combination is formed to handle exchange rate uncertainty. It is observed that purchasing cost volatility promotes the best pricing to maximize profit.