Ordering policies under currency risk sharing agreements: a Markov chain approach

If an exporter or a wholesaler sells goods at a fixed price to be paid in the currency of the seller’s country, then the purchase price of the importer depends upon the prevailing exchange rate of their respective currencies. Ideally, in a floating exchange rate system, the purchase price has to change according to shifts in the exchange rate. In such a scenario the entire exchange rate risk is borne by the importer/buyer. However, in international trade, it is customary for the parties to enter into a risk-sharing agreement, under which the buyer does not pay the seller on the basis of the prevailing exchange rate, but pays a mutually agreed upon price that falls within a range of fluctuating exchange rates. In this manner, the profit or loss due to fluctuations in the exchange rate would be shared by both the parties. These stochastic variations in purchase prices are modeled through a Markov chain. In this article, the resulting purchase and inventory problem is analyzed by identifying a regenerative cycle. An optimal selling price that maximizes the expected profit per unit time is also discussed. Further, optimal ordering policies under no stock-out conditions are derived with an optimal uniform demand corresponding to the optimal selling price. Through sensitivity analyses, differences in profit function with respect to carrying cost fraction, setup costs, and purchase prices are also shown. An investigation into the possible loss if this model solution is not implemented is also made through numerical illustrations. A discussion of a special case of two-purchase price scenario gives additional insight into the problem.