An optimal inventory policy when purchase price follows geometric Brownian motion process

In a supply chain management, whenever a retailer purchases goods from a foreign supplier, even though the purchase price remains constant in supplier currency, due to the fluctuation of the exchange rate, the purchase price of the retailer fluctuates. Since the foreign exchange rate keeps changing continuously, the purchase price of the retailer also changes continuously. This not only impacts on total purchase cost but also affects the total holding cost in a price-dependent holding cost inventory model. This article considers an optimal inventory policy for the continuously changing purchase price due to the fluctuation of the exchange rate. The finite horizon inventory model with constant demand and price dependent holding cost is considered. The exchange rate process is modelled by the geometric Brownian motion. The real exchange rate data of INR versus USD is used to estimate the model parameters. The impact of continuously changing purchase price because of the fluctuating exchange rate is identified by comparing the optimal expected cost for the constant and fluctuating purchase price. An alternate stochastic process, namely, the Gaussian process is also examined to model the exchange rate and model solutions are compared with that of solutions obtained by the geometric Brownian motion. The difference in optimal expected cost between the model with the constant purchase price and our model is found for different parametric values through sensitivity analysis. It is found that for larger demands, the difference in the optimal expected cost of the constant and varying price models is more. Coefficient of variations of the total cost for Gaussian process and GBM process are compared and found that GBM performs better than Gaussian process.