Aggregate Production Planning

Aggregate Production Planning (APP) is the medium-term OR/MS problem a manufacturer faces of jointly setting, across a multi-product, multi-period horizon (typically 3-18 months), the production rate, end-of-period inventory level, regular workforce, hiring and firing actions, overtime, subcontracting and backlog. The objective is total cost minimum — regular labour + overtime premium + hire + fire + inventory holding + backlog penalty + subcontract — or least cost subject to a fill-rate constraint. The canonical formulation is the HMMS model by Holt, Modigliani, Muth and Simon (1960): a single LP/QP with quadratic (smooth) penalties on workforce change and production-rate change captures these decisions as continuous variables. A linear-cost alternative is the transportation-tableau LP (Bowman 1956). For multi-product and Labour Law constraints, MIP is used. Nam and Logendran (1992) surveyed models and methodologies; Mula et al. (2006) reviewed production planning under uncertainty. APP is the layer above Wagner-Whitin lot sizing (problem 16, 'should I produce this month, and how much?' for a single product): APP first sets the monthly production rate and the workforce-overtime-subcontract mix at product-family level, then lot sizing breaks the monthly quantity into weekly batch sizes.