Decomposing inventory routing problems with approximate value functions

Toriello, Alejandro; Nemhauser, George L.; Savelsbergh, Martin

doi:10.1002/nav.20433

Cited by 27 publications

(14 citation statements)

References 29 publications

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“…11.4), Godfrey and Powell (2002a, b), Toriello et al (2010); the text Powell (2010) includes many such applications and surveys general ADP methodology. There are also many ADP methodologies in addition to ALP for approximating value functions, such as approximate policy iteration (Bertsekas 2012), approximate value iteration (Powell 2010), approximate bilinear programming (Petrik 2010, Petrik andZilberstein 2011), as well as various statistical methods, e.g., parametric and nonparametric regression (Hastie et al 2009, Powell 2010.…”

Section: Literature Reviewmentioning

confidence: 98%

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: 98%

A Dynamic Traveling Salesman Problem with Stochastic Arc Costs

Toriello

Haskell

Poremba

2014

Operations Research

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“…The IRPs with finite planning periods are addressed by Nananukul (2009a, 2009b), Kang and Kim (2010), Toriello, Nemhauser, and Savelsbergh (2011), Solyali and Süral (2011), etc., where both exact and heuristic algorithms are presented.…”

Section: Literature Reviewmentioning

confidence: 99%

An inventory–routing problem with the objective of travel time minimization

Чэн

Sivakumar

et al. 2014

European Journal of Operational Research

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a b s t r a c tIn this paper, we consider an inventory-routing problem (IRP) in a large petroleum and petrochemical enterprise group. Compared to many other IRPs, the problem in this paper includes some special aspects due to the operational constraints, such as hours-of-service regulations of the company and the industry. Also, in some cases, it is more important to avoid stock out for any station, rather than purely focusing on transportation cost minimization. The objective is to minimize the maximum of the route travel time, which is not addressed in the literature so far. We present a tabu search algorithm to tackle the problem, which builds in an efficient and effective procedure to improve the search quality in each iteration. Moreover, lower bounds of reasonable sized problems, which are intractable in the formulated mathematical model by existing optimization software, are obtained via Lagrangian relaxation technique. Computational results indicate that the lower bounds are tight and the tabu search is capable of providing near optimal, close-to-lower-bound solutions in a computational time effective manner.

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“…The time dimension presents an opportunity for decomposition, as the master problem with multiple time periods can be broken down into single-period sub-problems. This approach was adopted by Toriello, Nemhauser, and Savelsbergh (2010) in combination with dynamic programming.…”

Section: Inventory Routing Problemsmentioning

confidence: 99%

A multi-day activity-based inventory routing model with space–time–needs constraints

Chow

Nurumbetova

2014

Transportmetrica A: Transport Science

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We extend activity routing problems to consider 'needs' satisfaction over multiple days using an inventory routing problem concept. The resulting inventory-based selective household activity routing problem allows activity type choice, duration choice, activity destination choice, departure time, and scheduling of activities, all within space-time-needs constraints. A Lagrangian relaxation-based algorithm is proposed to solve the model for multiple days. A computational study is conducted. The model can measure several effects: heterogeneity in impacts of travel time changes on different days; the use of dual price as a threshold when needs play a role in the utility maximisation objectives; the possibility for activity participation consolidation due to increased travel time; and non-uniform impacts of travel time increase on utilities across a heterogeneous population. Comparison of the algorithm's performance against a commercial package showed average objective values that differed by only 1.8% or less.

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Decomposing inventory routing problems with approximate value functions

Cited by 27 publications

References 29 publications

A Dynamic Traveling Salesman Problem with Stochastic Arc Costs

A Dynamic Traveling Salesman Problem with Stochastic Arc Costs

An inventory–routing problem with the objective of travel time minimization

A multi-day activity-based inventory routing model with space–time–needs constraints

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