Dynamic capacitated lot sizing with random demand and dynamic safety stocks

Authors:
Stefan Helber;Florian Sahling;Katja Schimmelpfeng
Affiliations:
Department of Production Management, Leibniz University, Hannover, Germany;Department of Production Management, Leibniz University, Hannover, Germany;Chair of Accounting and Control, Brandenburg University of Technology, Cottbus, Germany
Venue:
OR Spectrum
Year:
2013

Citing 8
Cited 0

Strategies for the probabilistic lot-sizing problem with service-level constraints

Management Science
A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem

Mathematical Programming: Series A and B
Production Planning by Mixed Integer Programming (Springer Series in Operations Research and Financial Engineering)

Production Planning by Mixed Integer Programming (Springer Series in Operations Research and Financial Engineering)
Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic

Computers and Operations Research
The multi-item capacitated lot-sizing problem with safety stocks and demand shortage costs

Computers and Operations Research
The impact of sampling methods on bias and variance in stochastic linear programs

Computational Optimization and Applications
Lot-sizing on a tree

Operations Research Letters
A simple heuristic for the multi item single level capacitated lotsizing problem

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a stochastic version of the single-level, multi-product dynamic lot-sizing problem subject to a capacity constraint. A production schedule has to be determined for random demand so that expected costs are minimized and a constraint based on a new backlog-oriented 驴-service-level measure is met. This leads to a non-linear model that is approximated by two different linear models. In the first approximation, a scenario approach based on the random samples is used. In the second approximation model, the expected values of physical inventory and backlog as functions of the cumulated production are approximated by piecewise linear functions. Both models can be solved to determine efficient, robust and stable production schedules in the presence of uncertain and dynamic demand. They lead to dynamic safety stocks that are endogenously coordinated with the production quantities. A numerical analysis based on a set of (artificial) problem instances is used to evaluate the relative performance of the two different approximation approaches. We furthermore show under which conditions precise demand forecasts are particularly useful from a production---scheduling perspective.