## A price-directed approach to stochastic inventory/routing (2002)

Venue: | Operations Research |

Citations: | 32 - 2 self |

### BibTeX

@ARTICLE{Adelman02aprice-directed,

author = {Daniel Adelman},

title = {A price-directed approach to stochastic inventory/routing},

journal = {Operations Research},

year = {2002},

volume = {52},

pages = {2004}

}

### Years of Citing Articles

### OpenURL

### Abstract

informs ® doi 10.1287/opre.1040.0114 © 2004 INFORMS We consider a new approach to stochastic inventory/routing that approximates the future costs of current actions using optimal dual prices of a linear program. We obtain two such linear programs by formulating the control problem as a Markov decision process and then replacing the optimal value function with the sum of single-customer inventory value functions. The resulting approximation yields statewise lower bounds on optimal infinite-horizon discounted costs. We present a linear program that takes into account inventory dynamics and economics in allocating transportation costs for stochastic inventory routing. On test instances we find that these allocations do not introduce any error in the value function approximations relative to the best approximations that can be achieved without them. Also, unlike other approaches, we do not restrict the set of allowable vehicle itineraries in any way. Instead, we develop an efficient algorithm to both generate and eliminate itineraries during solution of the linear programs and control policy. In simulation experiments, the price-directed policy outperforms other policies from the literature. Subject classifications: dynamic programming/optimal control, discounted infinite-horizon: separable functional

### Citations

1267 |
Markov decision processes: discrete stochastic dynamic programming
- Puterman
- 1994
(Show Context)
Citation Context ...licy �. 2.3. Optimality Equations Because we assume all costs are bounded and both state and action spaces are finite, there exists an optimal policy that is Markovian, stationary, and deterministic (=-=Puterman 1994-=-). Markovian means that �n�a � hn� = �n�a � sn�; i.e., the action only depends on the current state, not the prior history. Stationary means that �n�a � sn� = ��a� sn�; i.e., the policy is the same fo... |

153 | The linear programming approach to approximate dynamic programming - Farias, Roy - 2003 |

123 | The Traveling-Salesman problem and minimum spanning trees - Held, Karp - 1971 |

102 | Generalized polynomial approximations in Markovian decision processes - Schweitzer, Seidmann - 1985 |

49 | ªAn analysis of bid-price controls for network revenue management,º - Talluri, Ryzin - 1996 |

32 |
A combined vehicle routing and inventory allocation problem, Management Science 32
- Federgruen, Zipkin
- 1984
(Show Context)
Citation Context ... Operations Research 52(4), pp. 499–514, © 2004 INFORMS 511 7.1. Policy Performance We compared our price-directed policy against the direct shipment policy (Kleywegt et al. 2002), the myopic policy (=-=Federgruen and Zipkin 1984-=-), and the procedure given by Minkoff (1993). 7.1.1. Experimental Design. We simulated the policies on 24 different problem instances. Each of 15 different items had �S i = 10, a holding cost of hi = ... |

29 |
Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer
- Bell, Dalberto, et al.
- 1983
(Show Context)
Citation Context ... product from a central depot to geographically dispersed customers with limited storage and stochastic demand. Such problems are common in industrial gas distribution, in firms such as Air Products (=-=Bell et al. 1983-=-) and Praxair. On a daily basis, a dispatcher assigns each vehicle an itinerary that specifies which customers to visit, the route to use, and the delivery quantity for each customer. The objective is... |

23 | The Stochastic Inventory Routing Problem with Direct Deliveries
- Kleywegt, Nori, et al.
- 2002
(Show Context)
Citation Context ...d Approach to Stochastic Inventory/Routing Operations Research 52(4), pp. 499–514, © 2004 INFORMS 511 7.1. Policy Performance We compared our price-directed policy against the direct shipment policy (=-=Kleywegt et al. 2002-=-), the myopic policy (Federgruen and Zipkin 1984), and the procedure given by Minkoff (1993). 7.1.1. Experimental Design. We simulated the policies on 24 different problem instances. Each of 15 differ... |

19 |
An adaptive, distribution-free approximation for the newsvendor problem with censored demands, with applications to inventory and distribution problems
- Godfrey, Powell
- 2001
(Show Context)
Citation Context ...te dynamic programming. Attention has focused on developing rigorous simulation-based methods for adaptively computing value function approximations. Powell and co-authors (Powell and Topaloglu 2002, =-=Godfrey and Powell 2001-=-) use gradient information from optimization subproblems solved through simulated time, and frequently employ the separable approximation (1), although in contexts different from ours. The neurodynami... |

19 | Dynamic programming approximations for a stochastic inventory routing problem. Transportation Sci - Kleywegt, Nori, et al. - 2004 |

19 | A Markov decision model and decomposition heuristic for dynamic vehicle dispatching - Minkoff - 1993 |

18 | The inventory routing problem - Campbell, Clarke, et al. - 1998 |

16 | Price-directed replenishment of subsets: Methodology and its application to inventory routing - Adelman |

16 | Stochastic inventory routing: Route design with stockouts and route failures - Trudeau, Dror - 1992 |

13 | Stochastic programming in transportation and logistics,” in Stochastic Programming
- Powell, Topaloglu
- 2003
(Show Context)
Citation Context ...owing interest in approximate dynamic programming. Attention has focused on developing rigorous simulation-based methods for adaptively computing value function approximations. Powell and co-authors (=-=Powell and Topaloglu 2002-=-, Godfrey and Powell 2001) use gradient information from optimization subproblems solved through simulated time, and frequently employ the separable approximation (1), although in contexts different f... |

12 |
Heavy traffic analysis of the dynamic stochastic inventory-routing problem
- Reinman, Rubio, et al.
- 1999
(Show Context)
Citation Context ...n costs over an infinite horizon. Despite the practical significance of this class of problems, it remains notoriously intractable and “a concomitant mathematical theory ���has not been forthcoming” (=-=Reiman et al. 1999-=-, p. 362). The structure of an optimal policy is not known even for the single-customer version of our problem (Gallego and Scheller-Wolf 2000, Zipkin 2000). Federgruen and Zipkin (1984) consider heur... |

9 | 2001. “Deliveries in an Inventory/Routing Problem Using Stochastic Dynamic Programming”. Transportation Science 35(2):192–213 - Berman, Larson |

8 | On the nucleolus of the basic vehicle routing game - Lundgren, Jornsten, et al. - 1992 |

5 |
Price-Directed Control of Remnant Inventory Systems
- Adelman, Nemhauser
- 1999
(Show Context)
Citation Context ...us-time, deterministic version of our problem with only fixed replenishment costs. Heuristic operating policies based on prices also have been considered in the contexts of remnant inventory systems (=-=Adelman and Nemhauser 1999-=-), revenue management (Talluri and van Ryzin 1998), and vehicle dispatching (Gans and van Ryzin 1999), although the connection with dynamic programming is not exploited as rigorously as is done here. ... |

4 | Inventory routing: Reduction from an annual to a short-period problem - Dror, Ball - 1987 |

4 | Capacitated inventory problems with fixed order costs: Some optimal policy structure
- Gallego, Scheller-Wolf
- 2000
(Show Context)
Citation Context ... and “a concomitant mathematical theory ���has not been forthcoming” (Reiman et al. 1999, p. 362). The structure of an optimal policy is not known even for the single-customer version of our problem (=-=Gallego and Scheller-Wolf 2000-=-, Zipkin 2000). Federgruen and Zipkin (1984) consider heuristics for implementing the myopic policy, which minimizes the expected costs incurred only in the current period. Except for relatively tiny ... |

3 | Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance And Practical Insights - Gans, Ryzin - 1999 |

2 | Internal transfer pricing for a decentralized operation with a shared supplier. Working paper, Graduate - Adelman - 2003 |