A probabilistic bi-level linear multi-objective programming problem to supply chain planning

Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible...

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Vydáno v:Applied mathematics and computation Ročník 188; číslo 1; s. 786 - 800
Hlavní autoři: Roghanian, E., Sadjadi, S.J., Aryanezhad, M.B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Elsevier Inc 01.05.2007
Elsevier
Témata:
Bi-level programming
Exact sciences and technology
Fuzzy decision-approach
Mathematical analysis
Mathematics
Multi-level multi-objective decision-making
Multi-objective decision-making
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Sciences and techniques of general use
Stochastic programming
Supply chain management
Supply chain management
Multi-level multi-objective decision-making
Bi-level programming
Multi-objective decision-making
Fuzzy decision-approach
Stochastic programming
Decision making
Optimization method
Linear programming
Probability distribution
Scheduling
Nonlinear problems
Non linear programming
Extremum problem
Numerical analysis
Applied mathematics
Distribution function
Probabilistic model
Fuzzy decision- approach
Random variable
Programming theory
Mathematical programming
ISSN:0096-3003, 1873-5649
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Shrnutí:Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels. In most of the real life problems in mathematical programming, the parameters are considered as random variables. The branch of mathematical programming which deals with the theory and methods for the solution of conditional extremum problems under incomplete information about the random parameters is called “stochastic programming”. Supply chain planning problems are concerned with synchronizing and optimizing multiple activities involved in the enterprise, from the start of the process, such as procurement of the raw materials, through a series of process operations, to the end, such as distribution of the final product to customers. Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a multi-level decision network structure can be mathematically represented by using “multi-level programming” principles. In this paper, we consider a “probabilistic bi-level linear multi-objective programming problem” and its application in enterprise-wide supply chain planning problem where (1) market demand, (2) production capacity of each plant and (3) resource available to all plants for each product are random variables and the constraints may consist of joint probability distributions or not. This probabilistic model is first converted into an equivalent deterministic model in each level, to which fuzzy programming technique is applied to solve the multi-objective nonlinear programming problem to obtain a compromise solution.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2006.10.032