Capacity optimization and competition with cyclical and lead-time-dependent demands

Capacity acquisition is often capital- and time-consuming for a business, and capacity investment is often partially or fully irreversible and difficult to change in the short term. Moreover, capacity determines the action space for service/production scheduling and lead-time quotation decisions. The quoted lead-time affects the customer’s perceived service quality. Thus, capacity acquisition level and lead-time quotation affect a firm’s revenue/profit directly or indirectly. In this paper, we investigate a joint optimization problem of capacity acquisition, delivery lead-time quotation and service-production scheduling with cyclical and lead-time-dependent demands. We first explore the structural properties of the optimal schedule given any capacity and lead-time. Then, the piecewise concave relationship between the delay penalty cost and the capacity acquisition level is found. Thereby, an efficient and effective polynomial time algorithm is provided to determine the optimal capacity acquisition level, delivery lead-time quotation and service/production schedule simultaneously. Furthermore, a capacity competition game among multiple firms is addressed. The numerical studies show that capacity equilibrium often exists and converges to a unique solution.