Journal ArticleDOI
Generalized Dynamic Programming for Stochastic Combinatorial Optimization
Reads0
Chats0
TLDR
A generalization of DP is developed that guarantees optimality even in the absence of monotonicity, and is illustrated on a version of the stochastic traveling salesman problem for which a previously proposed DP algorithm E. Kao is potentially suboptimal due to the violation ofmonotonicity.Abstract:
In stochastic versions of combinatorial optimization problems, the objective is to maximize or minimize a function of random variables. For many problems of this type, conventionally applied dynamic programming DP may fail to generate an optimal solution due to the potential violation of the monotonicity assumption of DP. We develop a generalization of DP that guarantees optimality even in the absence of monotonicity. We illustrate the methodology on a version of the stochastic traveling salesman problem for which a previously proposed DP algorithm E. Kao is potentially suboptimal due to the violation of monotonicity M. Sniedovich. Using Generalized DP, we are able to modify the algorithm to guarantee optimality.read more
Citations
More filters
Journal ArticleDOI
Stochastic vehicle routing.
TL;DR: The main problems of stochastic vehicle routing are described within a broad classification scheme and the most important contributions are summarized in table form.
Journal ArticleDOI
The Vehicle Routing Problem with Stochastic Travel Times
TL;DR: Three mathematical programming models are presented: a chance constrained model, a three-index simple recourse model and a two-index recourse model that indicate that moderate size problems can be solved to optimality.
Journal ArticleDOI
Stochastic Vehicle Routing with Random Travel Times
Astrid S. Kenyon,David P. Morton +1 more
TL;DR: This work considers stochastic vehicle routing problems on a network with random travel and service times and provides bounds on optimal objective function values and conditions under which reductions to simpler models can be made.
Book ChapterDOI
Chapter 6 Vehicle Routing
TL;DR: This chapter presents a comprehensive overview of the available exact and heuristic algorithms for the VRP, most of which have been adapted to solve other variants.
Journal ArticleDOI
Planning and Scheduling under Uncertainty: A Review Across Multiple Sectors
TL;DR: This paper provides an overview of the key contributions within the planning and scheduling communities with specific emphasis on uncertainty analysis, and is the first work which attempts to provide a comprehensive description of two-stage stochastic programming and parametric programming.
References
More filters
Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Dynamic Programming
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Journal ArticleDOI
A Dynamic Programming Approach to Sequencing Problems
Michael Held,Richard M. Karp +1 more
TL;DR: In this paper, a dynamic programming approach to the solution of three sequencing problems, namely, a scheduling problem involving arbitrary cost functions, the traveling-salesman problem, and an assembly line balancing problem, is presented.
Journal ArticleDOI
Optimal, rules for ordering uncertain prospects+
TL;DR: In this article, the Third Order Stochastic Dominance (TSD) rule is shown to be the optimal rule when comparing uncertain prospects with equal means, and in the general case of unequal means, no known selection rule uses both necessary and sufficient conditions for dominance.