Stochastic lot-sizing with backlogging: computational complexity analysis

Authors:
Yongpei Guan
Affiliations:
Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA 32611
Venue:
Journal of Global Optimization
Year:
2011

Citing 14
Cited 1

A simple forward algorithm to solve general dynamic lot sizing models with n periods in 0(n log n) or 0(n) time

Management Science
Economic lot sizing: an O(n log n) algorithm that runs in linear time in the Wagner-Whitin case

Operations Research - Supplement
Improved algorithms for economic lot size problems

Operations Research
An O(T3) algorithm for the economic lot-sizing problem with constant capacities

Management Science
A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times

Management Science
Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs

Management Science
A Dynamic Lot-Sizing Model with Demand Time Windows

Management Science
bc -- prod: A Specialized Branch-and-Cut System for Lot-Sizing Problems

Management Science
Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows

Operations Research
An Approximation Scheme for Stochastic Integer Programs Arising in Capacity Expansion

Operations Research
A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems

Management Science
The Value of Multistage Stochastic Programming in Capacity Planning Under Uncertainty

Operations Research
An O(n2) algorithm for lot sizing with inventory bounds and fixed costs

Operations Research Letters
On stochastic lot-sizing problems with random lead times

Operations Research Letters

Solving the stochastic dynamic lot-sizing problem through nature-inspired heuristics

Computers and Operations Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

For a multi-stage stochastic programming problem, one approach is to explore a scenario tree based formulation for the problem and solve the formulation efficiently. There has been significant research progress on how to generate scenario trees in the literature. However, there is limited work on analyzing the computational complexity of the scenario-tree based formulation that considers the number of tree nodes as the input size. In this paper, we use stochastic lot-sizing problems as examples to study the computational complexity issues for the scenario-tree based formulations. We develop production path properties and a general dynamic programming framework based on these properties. The dynamic programming framework allows us to show that the optimal value function is piecewise linear and continuous, which enables us to develop polynomial time algorithms for several different problems, including those with backlogging and varying capacities under certain conditions. As special cases, we develop polynomial time algorithms that run in $${\mathcal{O}(n^2)}$$ and $${\mathcal{O}(n^2T\,{\rm log}\,n)}$$ times, respectively for stochastic uncapacitated and constant capacitated lot-sizing problems with backlogging, regardless of the scenario tree structure.