Linear programming models with planned lead times for supply chain operations planning

This paper contributes to the development of models for capacity constrained Supply Chain Operations Planning (SCOP). We focus on production environments with arbitrary supply chain structures. The demand for the end items is assumed to be exogenously determined. We solve the SCOP problem with Linear Programming models using planned lead times with multi-period capacity consumption. Using planned lead times increases the reliability of the communication between SCOP and Scheduling with regard to the feasibility of the planning. Planned lead times also reduce the nervousness in the system. We model capacity constraints on the quantity of items that can be assembled within a time interval. In particular, items can be assigned to multiple resources. We discuss two LP approaches which plan the production of items so that a sum of inventory costs and costs due to backordering is minimized.