This work is concerned with multi-level, multi-stage capacity-constrained production-inventory problems. The aim is to provide a contribution to a theoretical background for Material Requirements Planning (MRP) using the Laplace Transform approach and Input-Output Analysis.
In an extensive literature survey, we summarise the work on the capacitated lot-sizing problem (CLSP) within both the deterministic and the stochastic environments. Certain aspects related to model formulation are highlighted. It was found that methods for solving this class of problems have been concentrating on heuristics and mathematical programming.
Unlike classic methods, this thesis formulates models for capacityconstrained production-inventory systems using the Laplace transform and input-output analysis. As a first step to incorporate capacity limitations into previous theory, we introduce alternative formulations of extensions to MRP theory in order to incorporate capacity constraints. We focus our attention on the way in which the fundamental balance equations for inventory and backlogs need to be modified.
Then we develop a stochastic model, in which external demand for end items is assumed to be unknown. Unlike the classic total cost objective function, the Net Present Value is used as the objective function. As an intermediate result, the backlog function for a discrete time demand process is derived. Besides, an extension of the model is presented in which both capacity and demand are considered along a continuous time scale, without time buckets.
Numerical examples are provided to explain the theory both in the deterministic and in the stochastic situations.
Linköping: Linköpings universitet , 2001. , 81 p.