Planning Production and Workforce in a Discrete-Time Financial Model Using Scenarios Modeling

Production planning interacts with a number of functional aspects within the entire system of a company. Two of those aspects involve workforce and financial planning, which are usually conflicting, in the sense that more workforce increases the financial costs but it may also increase production capability. In effect, there should exist an adequate balance on the production levels such that the cash-flows can generate the highest profits. This suggests that these three elements of the system (production, workforce and cash-flows) are tightly connected, and that they should be planned together in a single framework. This paper explores this interaction using a mixed integer linear programming formulation for a general outline of this three elements system. The model includes sequences of overlapping work-shifts and sequences of overlapping short-term loans. We discuss a number of scenarios concerning some of the uncertain parameters involved in the process, assuming that they do not follow any known distribution function, so handling uncertainty using a scenarios modeling methodology. Contrarily to usual lot-sizing problems, we consider demand as an upper limit for setting the production. So, we want to plan production and workforce in order to assist the cash-flows along the planning horizon, to the best convenience of the financial profits. We discuss a small fictitious example using a single-product with a homogeneous type of workers in the process. We then indicate a number of generalizations, including some real-world applications.