Full paper
Full paper

A New Positive Dynamic Model Of Capacity Planning With Logical And Binary Set-Up Constraints

L. Caccetta
L.R. Foulds
V.G. Rumchev


One of the most important concepts in production planning is that of the establishment of an overall or aggregate production plan. In this paper we consider this problem for a manufacturing plant. Our aim is to meet the pre-specified demand taking into account decisions concerning when and how many to hire and fire, how much inventory to hold, when to use overtime and undertime, as well as product families and set-up times. We develop a new dynamic model of this issue. The model turns out to be a discrete-time positive system with side linear, and logical and binary set-up constraints. Some interesting new characterizations of production systems important for the objectives of planning and control appear in the model. On the basis of the model we formulate and discuss a discrete-time positive system optimal control problem for capacity planning and provide a number of interesting insights into capacity planning and at the same time address some open problems.