A Coordinated Production Planning Model with Capacity Expansion and Inventory Management

Motivated by a problem faced by a large manufacturer of a consumer product, we explore the interaction between production planning and capacity acquisition decisions in environments with demand growth. We study a firm producing multiple items in a multiperiod environment where demand for items is known but varies over time with a long-term growth and possible short-term fluctuations. The production equipment is characterized by significant changeover time between the production of different items. While demand growth is gradual, capacity additions are discrete. Therefore, periods immediately following a machine purchase are characterized by excess machine capacity. We develop a mathematical programming model and an effective solution approach to determine the optimal capacity acquisition, production and inventory decisions over time. Through a computational study, we show the effectiveness of the solution approach in terms of solution quality and investigate the impact of product variety, cost of capital, and other important parameters on the capacity and inventory decisions. The computational results bring out some key insights---increasing product variety may not result in excessive inventory and even a substantial increase in set-up times or holding costs may not increase the total cost over the horizon in a significant manner due to the ability to acquire additional capacity. We also provide solutions and insights to the real problem that motivated this work.