Pricing, production, scheduling, and delivery-time competition

This paper studies competition between firms that produce goods or services for customers sensitive to delay time. Firms compete by setting prices and production rates for each type of customer and by choosing scheduling policies. The existence of a competitive equilibrium is proved. The competitive equilibrium is well defined whether or not a firm can differentiate between customers based upon physical characteristics because each customer has incentive to truthfully reveal its delay cost. Further insights are derived in two special cases. A unique equilibrium exists for each of the cases. In the first case, firms are differentiated by cost, mean processing time, and processing time variability, but customers are homogeneous. The conclusions include that a faster, lower variability and lower cost firm always has a larger market share, higher capacity utilization, and higher profits. However, this firm may have higher prices and faster delivery time, or lower prices and longer delivery time. In the second case, firms are differentiated by cost and mean processing time, but customers are differentiated by demand function and delay sensitivity. The results include that customers with higher waiting costs pay higher full prices, and that each firm charges a higher price and delivers faster to more impatient customers. Competing firms that jointly serve several types of customers tend to match prices and delivery times.