A stochastic production planning problem with nonlinear cost

Most production planning models are deterministic and often assume a linear relation between production volume and production cost. In this paper, we investigate a production planning problem in a steel production process considering the energy consumption cost which is a nonlinear function of the p...

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Bibliographic Details
Published in:Computers & operations research Vol. 39; no. 9; pp. 1977 - 1987
Main Authors: Tang, Lixin, Che, Ping, Liu, Jiyin
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.09.2012
Elsevier
Pergamon Press Inc
Subjects:
Algorithms
Applied sciences
Demand
Energy consumption
Exact sciences and technology
Heuristic
Integer programming
Inventory
Inventory control, production control. Distribution
Linear programming
Marketing
Mathematical analysis
Mathematical models
Mathematical programming
Mathematics
MINLP
Nonlinearity
Operational research and scientific management
Operational research. Management science
Probability and statistics
Production planning
Sampling theory, sample surveys
Scenario-based approach
Sciences and techniques of general use
Statistics
Steel production
Stepwise Lagrangian relaxation
Stochastic models
Stochastic production planning
Stochasticity
Studies
Variable splitting
MINLP
Stepwise Lagrangian relaxation
Stochastic production planning
Variable splitting
Scenario-based approach
Inventory
Energy consumption
Non linear programming
Production function
Polynomial method
Linear model
Optimization
Lagrange multiplier
Uncertain system
Production planning
Relaxation method
Production process
Script
Quantity production
Linear programming
Mixed integer programming
Stochastic programming
Polynomial time
Production management
Supply demand balance
Deterministic model
Non linear model
Heuristic method
Production cost
Approximation error
Mixed problem
Piecewise linearization
Piecewise-linear techniques
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:Most production planning models are deterministic and often assume a linear relation between production volume and production cost. In this paper, we investigate a production planning problem in a steel production process considering the energy consumption cost which is a nonlinear function of the production quantity. Due to the uncertain environment, the production demands are stochastic. Taking a scenario-based approach to express the stochastic demands according to the knowledge of planners on the demand distributions, we formulate the stochastic production planning problem as a mixed integer nonlinear programming (MINLP) model. Approximated with the piecewise linear functions, the MINLP model is transformed into a mixed integer linear programming model. The approximation error can be improved by adjusting the linearization ranges repeatedly. Based on the piecewise linearization, a stepwise Lagrangian relaxation (SLR) heuristic for the problem is proposed where variable splitting is introduced during Lagrangian relaxation (LR). After decomposition, one subproblem is solved by linear programming and the other is solved by an effective polynomial time algorithm. The SLR heuristic is tested on a large set of problem instances and the results show that the algorithm generates solutions very close to optimums in an acceptable time. The impact of demand uncertainty on the solution is studied by a computational discussion on scenario generation.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2011.09.007