Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction

Abstract

This paper introduces a line of research on capacity-constrained multi-stage production scheduling problems. The first section introduces the problem area as it arises from a failure of MRP systems. Then a review of the literature and an analysis of the type of problems that exist are presented in §2. Section 3 outlines linear and mixed integer-linear programming formulations. These formulations compute the required production lead times according to the demands on available capacity, thereby reducing in-process inventory compared to the usual practice in MRP. A discussion of how to use the LP version is included. However, the size of the problems in practice implies that more efficient solution techniques must be found. The final topic of this paper, Product Structure Compression, is introduced as a method to reduce the size of the problem without losing optimality.inventory/production: material requirements planning, programming: large-scale systems, programming: integer, applications

An agile operations management system for green factory

“…In addition, studies have been performed on aggregation planning for planning production, [13][14][15][16] and on resource planning and process scheduling, for a long time. [17][18][19][20][21] These have been continuously conducted with regard to planning and optimization from the aspect of handling materials.…”

Setting safety stocks in multi-stage inventory systems under rolling horizon mathematical programming models

“…Capacity constraints are modelled explicitly as aggregate constraints. The principles are based on research stemming from advanced MRP modelling (Billington et al 1983) or from multi-period lot sizing problems (Tempelmeier and Derstroff 1996;Stadtler 2003). The principles have been implemented in commercial software, mostly using CPLEX solving logic (See also Stadtler and Kilger 2005).…”

The Capacity Aspect of Inventories

“…The determination of a production plan can be simplified considerably by assuming that the demand can be forecasted accurately. Such an approach has for example been used by Billington, McClain and Thomas [11], Bitran and Hax [13], Gabbay [22], and Hax and Meal [28]. Because of its simplicity, this approach is often used in practical situations, compare e.g.…”

“…As a rule such developments are characterized by (1) decomposition of the large system into smaller subsystems which are later composed or coordinated to r'econstruct the original system, or by (2) aggregation of the variables in the lat"ge system thereby reducing its dimensionality. The ultimate gain from these methods is not only to obtain a computer solution in a reasonable time (or at all) but also to aid in the conceptualization and understanding of lat"ge-scale interactions • 11 We will show, in Sectien 3.4, that a sensible form of aggregation in the model actually conforma to restricting the class of strategies in the Markov deelsion problem to capacity-oriented strategies. Analogously a sensible form of decomposition in the model conforma to restricting the class of possible strategies to product-oriented strategies (see Section 3.5).…”