Determining Optimal Price and Order Quantity Under the Uncertainty in Demand and Supplier’s Wholesale Price

Introduction

In recent years, manufacturers in the high-tech durable product industry (e.g., personal computers, digital music devices, plasma and LCD TVs) have experienced some emerging changes in the environment. Due to the rapid advancements in technology, the life cycle of high-tech durable products tends to be shorter and the obsolescence rate of these products gets faster, similar to fashion items. In order to respond properly to the shifting markets, manufacturers have to continuously bring innovative product ideas into the markets and make an effort to quickly employ the newly available technology for reducing operational costs. The recent advent of Internet technology, for example, helps find cost-effective suppliers on a global basis, which enables manufacturers to offer better prices to their customers. This means that the customers in this particular market segment become increasingly sensitive to price and the competition of high-tech durable products at the retail level has become more complex and tougher than ever before.

One of the important factors that determine a manufacturer’s competitiveness in the high-tech durable product industry is product availability at a reasonable price. However, it is difficult for manufacturers to decide the most profitable levels of production and pricing because of the uncertainty associated with the supplier’s wholesale price as well as product demand. Suppliers may have to change their unit wholesale price to be profitable as the factors in the external environment change. A supplier’s unit wholesale price at time, for instance, can be affected by uncertain factors, such as the exchange rate at the time when the manufacturer buys the materials, the volatility of sourcing prices from foreign suppliers, the price changes of raw commodities, and fluctuation in manufacturer’s demand. This also leads to manufacturers’ retail price adjustments because the changes in the supplier’s wholesale price affect the production costs. Therefore, without building a close long-term strategic partnership with key suppliers, manufacturers can hardly satisfy an ever-changing marketplace and create values for customers.

In this paper, we are concerned with the two major types of uncertainty that are associated with product demand and in supplier’s wholesale price. After we investigate how such uncertainties can disrupt the activities of a manufacturer and a supplier, we attempt to develop an optimization model that describes how the manufacturer should reflect the uncertainty issues in their pricing and order quantity policy to achieve a desirable profit. In the modeling process, three important managerial problems are discussed: 1) the effect of coordination between a manufacturer and its supplier in dealing with uncertainties on product demand and supplier’s wholesale price; 2) strategies for mitigating both errors in demand forecasting and supply risk; 3) modeling frameworks to determine the optimal solution for price and order quantity based on the varying levels of coordination in the given time. To identify best operational decisions under market uncertainty, we use the stochastic optimal control theory.

The remainder of this paper is organized as follows: Section 2 contains a brief literature review. Section 3 studies decision-making problems and demonstrates the models for optimal stocking and pricing policies. The numerical examples that support the model and the analytical discussions are presented in Section 4. Finally, Section 5 summarizes conclusions reached.