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  • 1.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Huynh, Thuy
    Linköping University, Department of Production Economics. Linköping University, The Institute of Technology.
    Analysis of standard ordering policies within the framework of MRP theory2006In: International Journal of Production Research, ISSN 0020-7543, E-ISSN 1366-588X, Vol. 44, no 18-19, p. 3759-3773Article in journal (Refereed)
    Abstract [en]

    A number of different standard ordering policies are presented within the methodology of Material Requirements Planning (MRP), such as Lot-For-Lot (L4L), Fixed Order Quantity (FOQ), Fixed Period Requirements (FPR), etc. In MRP theory the time development of the production-inventory system is determined by a set of fundamental equations for available inventory, total inventory and backlogs using Input-Output Analysis for capturing the Bill of Materials and Laplace transforms for describing the advanced timing requirements. This paper aims at formally introducing standard ordering policies into the fundamental equations of MRP Theory in order to analyse the possibility to obtain closed-form expressions for the time development of the system, when such rules are applied.

  • 2.
    Grubbström, Robert W.
    et al.
    Linköping University, Department of Management and Engineering, Production Economics. Linköping University, The Institute of Technology.
    Huynh, Thuy
    Linköping University, The Institute of Technology. Linköping University, Department of Production Economics.
    Multi-level, multi-stage capacity-constrained production-inventory systems in discrete time with non-zero lead times using MRP theory2006In: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 101, no 1 SPEC. ISS., p. 53-62Article in journal (Refereed)
    Abstract [en]

    A substantial amount of research has been carried out on capacity-constrained production-inventory systems. This has mostly dealt with models assuming deterministic demand and single-item systems. In previous work, one of the authors together with a co-researcher designed a basic theoretical model for systems with multiple items and stochastic external demand. These developments were presented within a discrete time framework. Lead times were assumed to be given constants and the net present value principle was applied. Although the theory developed concerned situations in which the lead times could be any non-zero constants, in order to design an analytical solution procedure, the assumption was made that lead times were zero, in order to be able to apply dynamic programming. Cumulative production and cumulative demand were taken as state variables. In this paper, we remain in the discrete time framework and develop a methodology for the case that lead times are non-zero, whereas demand is deterministic. Our emphasis is on the design of the state space, the properties of which depend on the product structures (the input matrix), the distribution of lead times among the production processes (the lead time matrix), and on the historical sequences of the production vectors. Once an efficient state space is designed, dynamic programming may be applied as a solution method. The net present value principle is again applied. © 2005 Elsevier B.V. All rights reserved.

  • 3.
    Huynh, Thi Thu Thuy
    Linköping University, Department of Management and Engineering. Linköping University, The Institute of Technology.
    Capacity Constraints in Multi-Stage Production-Inventory Systems: Applying Material Requirments Planning Theory2006Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, capacity-constrained aspects of multi-level, multi-stage productionplanning are investigated. The aim has been to extend Material Requirements Planning Theory (MRP Theory) to cover more general problems dealing with capacity constraints, in particular when non-zero lead times are present and the processes take place in continuous time.

    MRP Theory deals with multi-level production systems with multiple items taking place either within a discrete or continuous time framework. External demand is considered either deterministic or stochastic. Lead times are assumed to be given constants, and the Net Present Value Principle has been applied as the objective function. The Bill-of-Materials, capturing component as well as capacity requirements, in volume as well as in advanced timing due to lead times, has been described using a generalised input matrix involving Laplace transforms or z transforms.

    In order to be able to apply Dynamic Programming as a solution method, the system state has been defined and designed in terms of a matrix, in which historical values of cumulative production and cumulative demand are given state variables. A high power computer has been used to calculate solutions to numerical examples.

    Moreover, this thesis examines the fundamental equations of MRP Theory in order to analyse the possibility to obtain closed-form expressions for the time development of the system, when standard ordering rules of MRP are applied.

    In addition, capacity-constrained production planning problems and procedures in a paper mill have been surveyed and are presented in the form of a case study.

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