Stochastic Shortest Path Problems with Piecewise-Linear Concave Utility Functions

Murthy, Ishwar; Sarkar, Sumit

doi:10.1287/mnsc.44.11.s125

Cited by 48 publications

(23 citation statements)

References 10 publications

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“…In many cases, costs represent time and the objective is to minimize expected tardiness, the probability of tardiness or to find a minimum-cost route that meets an acceptable tardiness service level (Jula et al 2006, Kenyon and Morton 2003, Laporte et al 1992. Our approach to model uncertain arc costs is similar to many stochastic shortest path problems, e.g., Bertsekas and Tsitsiklis (1991), Murthy and Sarkar (1998), Patek and Bertsekas (1999), Polychronopoulos and Tsitsiklis (1996), Provan (2003), and sometimes appears in real-time shortest path applications (Kim et al 2005a, b;Thomas and White 2007).…”

Section: Literature Reviewmentioning

confidence: 99%

A Dynamic Traveling Salesman Problem with Stochastic Arc Costs

Toriello

Haskell

Poremba

2014

Operations Research

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We propose a dynamic traveling salesman problem (TSP) with stochastic arc costs motivated by applications, such as dynamic vehicle routing, in which the cost of a decision is known only probabilistically beforehand but is revealed dynamically before the decision is executed. We formulate this as a dynamic program (DP) and compare it to static counterparts to demonstrate the advantage of the dynamic paradigm over an a priori approach. We then apply approximate linear programming (ALP) to overcome the DP's curse of dimensionality, obtain a semi-infinite linear programming lower bound, and discuss its tractability. We also analyze a rollout version of the price-directed policy implied by our ALP and derive worst-case guarantees for its performance. Our computational study demonstrates the quality of a heuristically modified rollout policy using a computationally effective a posteriori bound.Subject classifications: traveling salesman problem; stochastic vehicle routing; approximate dynamic program; semi-infinite linear program.

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Section: Literature Reviewmentioning

confidence: 99%

A Dynamic Traveling Salesman Problem with Stochastic Arc Costs

Toriello

Haskell

Poremba

2014

Operations Research

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“…However, this approach does not address stochastic edge lengths and time-dependent availability of edges to model delays and missings of follow-up transports. Stochastic shortest path problems are also widely studied [4,15]. However, research on stochastic problems that also considers multiple criteria is rare [16].…”

Section: Literature Reviewmentioning

confidence: 99%

Multicriteria decentralized decision making in logistic chains: a dynamic programming approach for collaborative forwarding of air cargo freight

Berger

Schröder

2011

Logist. Res.

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Forwarding air freight cargo globally from the shipper’s door to the door of the consignee is a complex logistic process and involves freight handling by several collaborating logistics companies. The door to door process is currently standardized by the International Air Transport Association with the industry initiative Cargo 2000. Many individuals with their own perspectives along the logistic chain decide how freight is transported and handled but have only limited insights how their decisions influence the follow-up decisions and the final on time delivery. A central planning authority can not be realized due to the heterogeneity of decision makers, the individual interests of the logistics companies, and their global operations. We argue that it is possible to overcome the deficient situation of complex transportation chains like in the air cargo industry by using optimization methods for decentralized decision making. This paper proposes a dynamic programming approach, which enables the decision makers in the decentralized situation to align their decisions better with the decisions of the involved partners. The approach guarantees that sensitive information of the logistics companies is kept local and only the most necessary information is shared along the logistic chain for a better planning. The transportation is planned with regard to multiple criteria, like the expected transportation costs and the probability to deliver the freight on time. We further show that our decentralized and multicriteria approach leads to better results compared to a local strategy that only exploits each decision maker’s own perspective. Our approach is decentralized by nature and needs lean information exchange. Furthermore, it is as strong as a centralized approach that gathers all distributed information but that authorizes the logistic service providers to decide individually

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“…The solution method presented here for PS-1 is a modification of the stochastic shortest-path algorithm (Murthy and Sarkar 1998) to suit the special structure of PS-1. Lemmas 1, 2, and 3 present some results about the nature of the function g p p that will be used in our algorithm to solve PS-1.…”

Section: The Static Model For Single-job Assignmentmentioning

confidence: 99%

“…The approach is based on a well-known labeling procedure (see Murthy and Sarkar 1998) that uses the pruning rules described earlier. The procedure starts at node 1 and proceeds towards node n, processing nodes sequentially.…”

Section: Algorithmic Approach For the Static Modelmentioning

confidence: 99%

Sequential Grid Computing: Models and Computational Experiments

Ransbotham

Murthy

Mitra

et al. 2011

INFORMS Journal on Computing

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T hrough recent technical advances, multiple resources can be connected to provide a computing grid for processing computationally intensive applications. We build on an approach, termed sequential grid computing, that takes advantage of idle processing power by routing jobs that require lengthy processing through a sequence of processors. We present two models that solve the static and dynamic versions of the sequential grid scheduling problem for a single job. In the static and dynamic versions, the model maximizes a reward function tied to the probability of completion within service-level agreement parameters. In the dynamic version, the static model is modified to accommodate real-time deviations from the plan. We then extend the static model to accommodate multiple jobs. Extensive computational experiments highlight situations (a) where the models provide improvements over scheduling the job on a single processor and (b) where certain factors affect the quality of solutions obtained.

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Stochastic Shortest Path Problems with Piecewise-Linear Concave Utility Functions

Cited by 48 publications

References 10 publications

A Dynamic Traveling Salesman Problem with Stochastic Arc Costs

A Dynamic Traveling Salesman Problem with Stochastic Arc Costs

Multicriteria decentralized decision making in logistic chains: a dynamic programming approach for collaborative forwarding of air cargo freight

Sequential Grid Computing: Models and Computational Experiments

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