Paper Info
Title
An Efficient Trajectory Method for Probabilistic Production-Inventory-Distribution Problems
Abstract
We consider a supply chain operating in an uncertain environment: The customers' demand is characterized by a discrete probability distribution. A probabilistic programming approach is adopted for constructing an inventory-production-distribution plan over a multiperiod planning horizon. The plan does not allow the backlogging of the unsatisfied demand, and minimizes the costs of the supply chain while enabling it to reach a prescribed nonstockout service level. It is a strategic plan that hedges against undesirable outcomes, and that can be adjusted to account for possible favorable realizations of uncertain quantities. A modular, integrated, and computationally tractable method is proposed for the solution of the associated stochastic mixed-integer optimization problems containing joint probabilistic constraints with dependent right-hand side variables. The concept of p-efficiency is used to construct a finite number of demand trajectories, which in turn are employed to solve problems with joint probabilistic constraints. We complement this idea by designing a preordered set-based preprocessing algorithm that selects a subset of promising p-efficient demand trajectories. Finally, to solve the resulting disjunctive mixed-integer programming problem, we implement a special column-generation algorithm that limits the risk of congestion in the resources of the supply chain. The methodology is validated on an industrial problem faced by a large chemical supply chain and turns out to be very efficient: it finds a solution with a minimal integrality gap and provides substantial cost savings.
Year
DOI
Venue
2007
10.1287/opre.1060.0356
Operations Research
Keywords
Field
DocType
strategic plan,p-efficient demand trajectory,probabilistic programming approach,large chemical supply chain,joint probabilistic constraint,efficient trajectory method,supply chain,demand trajectory,probabilistic production-inventory-distribution problems,inventory-production-distribution plan,unsatisfied demand,supply chain operating,probability distribution,scheduling,integer,programming,product distribution,transportation,service level,optimization problem,stochastic,column generation
Column generation,Mathematical optimization,Service level,Time horizon,Integer programming,Supply chain,Probabilistic logic,Optimization problem,Stochastic programming,Mathematics,Operations management
Journal
Volume
Issue
ISSN
55
2
0030-364X
Citations 
PageRank 
References 
32
1.68
23
Authors
2
Name
Order
Citations
PageRank
Miguel A. Lejeune125321.95
Andrzej Ruszczyński279884.38