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A stochastic model of multi-level/multi-stage capacity-constrained production–inventory systems
Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
2003 (English)In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 81-82, 483-494 p.Article in journal (Refereed) Published
Abstract [en]

A great deal of research has been done on capacity-constrained production–inventory systems, most of which concerns deterministic demand situations and single-product systems. In this paper we present a model of a multi-level capacity-constrained system when external demand is stochastic. Unlike the traditional total cost objective, adopted in the vast majority of capacity-constrained production–inventory models, the (expected) Net Present Value is here used as the objective function. Dynamic programming is chosen as the solution procedure. Numerical examples are given to explain the model and to illustrate features when changing available capacity.

The Laplace transform together with input–output analysis are employed as tools to construct the model. This approach has been used in previous research to formulate a theoretical base for Material Requirements Planning (MRP) systems.

The paper provides a further argument for the use of transforms in combination with matrix representations of product structures and capacity requirements, and it extends previous theory in the direction of capacity considerations combined with uncertainty in external demand. Dynamic programming is also shown to be a practical method for the multi-stage optimisation involved.

The numerical examples further illustrate, for instance, the natural propensity for subordinate items to be lot sized in a more lumpy way than their parents, and also how the marginal benefit of capacity increments follows the law of diminishing returns. Also comparisons are made with solutions from the deterministic equivalence model, using average demand as a proxy.

Place, publisher, year, edition, pages
2003. Vol. 81-82, 483-494 p.
Keyword [en]
Capacity constraints, Input-output analysis, Laplace transform, Material requirements planning, Stochastic demand
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-46750DOI: 10.1016/S0925-5273(02)00358-4OAI: oai:DiVA.org:liu-46750DiVA: diva2:267646
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
In thesis
1. Capacity-constrained production-inventory systems: modelling and analysis in both a traditional and an e-business context
Open this publication in new window or tab >>Capacity-constrained production-inventory systems: modelling and analysis in both a traditional and an e-business context
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis addresses issues in production-inventory systems in both a traditional and an e-business context, with an emphasis on capacity considerations. The general aim of the thesis is to model capacity-constrained production-inventory systems and thereby provide theoretical frameworks for control as well as design of these systems.

The research has been conducted in two different contexts. In the traditional context, an extensive survey of the literature on capacity-constrained production-inventory systems is first presented. Production-inventory systems with capacity limitations are then modelled using the Laplace transform and input-output analysis for deterministic and stochastic demand situations, respectively. In the formulation of the model for the deterministic demand situations, the focus is on the way in which the fundamental balance equations for inventory and backlogs need to be modified. In the formulation for stochastic demand situations, the model extends previous theory in the direction of capacity considerations combined with uncertainty in external demand. The results of the modelling and analysis in the traditional context contribute to the development of a theoretical background for production-inventory system control applying the Laplace transform approach and input-output analysis.

In the e-business context, those aspects which are affected by e-business based customer ordering systems, and hence influence production-inventory systems, are studied. A mathematical model based on the assumption of a simple e-business model of direct sales channels is presented. Since e-business significantly facilitates customisation, models of two different production systems which consider customisation are provided. The production-inventory systems are then developed into an extended system where customers are included. For this system, a multiple objective formulation is obtained, in view of the importance of customers. The results of the modelling and analysis in the ebusiness context contribute insights and perspectives on ways to design and control ebusiness influenced production - inventory systems.

Place, publisher, year, edition, pages
Linköping, Sweden: Linköpings universitet, 2004. 34 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 889Dissertation from the Swedish Research School of Management and Information Technology (MIT). Dissertation, 2
National Category
Computer Science
Identifiers
urn:nbn:se:liu:diva-23761 (URN)3275 (Local ID)91-8529-508-6 (ISBN)3275 (Archive number)3275 (OAI)
Public defence
2004-11-05, Visionen, Hus B, Campus Valla, Linköping, 10:15 (Swedish)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2012-12-13Bibliographically approved

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Grubbström, Robert W.Wang, Zhiping

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