Deterministic Approximations to Stochastic Production Problems

Gabriel R. Bitran · Horácio Hideki Yanasse

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Supply Chain and Inventory Management Management and Optimization Techniques Scheduling and Optimization Algorithms

Abstract

In this paper we consider deterministic approximations to a nonsequential stochastic production problem with setup costs. We show that, for the most commonly used probability distributions of the demands, the relative error bounds tend to be very small. We also consider a sequential stochastic problem, without setup costs, and discuss its relationship to the nonsequential case. Throughout the paper, we present limited computational results and indicate topics for further research.

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References

1966Nonlinear and Dynamic Programming 1969Production-Inventory Systems: Planning and Control 1960Inequalities for Stochastic Linear Programming Problems

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1993Production planning via scenario modelling 2012Flexible long-term capacity planning in closed-loop supply chains with remanufacturing 2007An Efficient Trajectory Method for Probabilistic Production-Inventory-Distribution Problems 2006On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints 1992Deterministic Approximations to Co-Production Problems with Service Constraints and Random Yields 1995Multistage stochastic programs: The state-of-the-art and selected bibliography 2002A stochastic model of multi-level/multi-stage capacity-constrained production–inventory systems 2016Scenario-based model predictive control for multi-echelon supply chain management

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