An Integrated Two-Stage Inventory and Workforce Planning Model with Variable Production Rates

This paper addresses the economic lot-sizing and manpower planning in a two-stage manufacturing system. We refer to the first and second stages as the vendor and the manufacturer, respectively. Both the vendor and the manufacturer can operate at different production rates by varying the levels of their manpower. In Economics and Econometrics, the rate of production is usually modelled using the production function, a model which links company productivity to the level of existing resources, such as labour and capital. Namely, we utilize the Cobb-Douglas production function to represent the relationship between the production inputs (labour and capital) and the productivity. The impact of manpower planning decisions on the proposed supply chain system is studied. An efficient solution technique is proposed; then, sensitivity analysis and fractional factorial design were conducted to assess the performance of the proposed model. Our results suggest that the variable production rates may lead to substantial savings to the supply chain, especially in the case of low-profit margins. Furthermore, considering the vendor as a leader and the manufacturer as a follower in a Stackelberg sequential game, we present two contracts to share the resulting savings between the vendor and the manufacturer.