A stochastic production planning problem with nonlinear cost

Authors:
Lixin Tang;Ping Che;Jiyin Liu
Affiliations:
Liaoning Key Laboratory of Manufacturing System and Logistics, The Logistics Institute, Northeastern University, 110004 Shenyang, China;Liaoning Key Laboratory of Manufacturing System and Logistics, The Logistics Institute, Northeastern University, 110004 Shenyang, China and The Department of Mathematics, Northeastern University, ...;Liaoning Key Laboratory of Manufacturing System and Logistics, The Logistics Institute, Northeastern University, 110004 Shenyang, China and Business School, Loughborough University, Leicestershire ...
Venue:
Computers and Operations Research
Year:
2012

Citing 7
Cited 1

Determining lot sizes and resource requirements: A review

Operations Research
Scenarios and policy aggregation in optimization under uncertainty

Mathematics of Operations Research
A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times

Management Science
A scenario-based stochastic programming approach for technology and capacity planning

Computers and Operations Research
Lagrangian Solution Techniques and Bounds for Loosely Coupled Mixed-Integer Stochastic Programs

Operations Research
Dual decomposition in stochastic integer programming

Operations Research Letters
Dynamic lot sizing with random demand and non-stationary costs

Operations Research Letters

Fast assessment of production makespan using aggregate technical data

Computers in Industry

Quantified Score

Hi-index	0.01

Visualization

Abstract

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.