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A pricedirected approach to stochastic inventory/routing
 Operations Research
, 2002
"... 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 decisi ..."
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Cited by 42 (2 self)
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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 singlecustomer inventory value functions. The resulting approximation yields statewise lower bounds on optimal infinitehorizon 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 pricedirected policy outperforms other policies from the literature. Subject classifications: dynamic programming/optimal control, discounted infinitehorizon: separable functional
Dynamic programming approximations for a stochastic inventory routing problem
 Transportation Science
, 2004
"... This work is motivated by the need to solve the inventory routing problem when implementing a business practice called vendor managed inventory replenishment (VMI). With VMI, vendors monitor their customers ’ inventories, and decide when and how much inventory should be replenished at each customer. ..."
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Cited by 29 (3 self)
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This work is motivated by the need to solve the inventory routing problem when implementing a business practice called vendor managed inventory replenishment (VMI). With VMI, vendors monitor their customers ’ inventories, and decide when and how much inventory should be replenished at each customer. The inventory routing problem attempts to coordinate inventory replenishment and transportation in such a way that the cost is minimized over the long run. We formulate a Markov decision process model of the stochastic inventory routing problem, and propose approximation methods to find good solutions with reasonable computational effort. We indicate how the proposed approach can be used for other Markov decision processes involving the control of multiple resources. ∗ Supported by the National Science Foundation under grant DMI9875400.
Pricedirected replenishment of subsets: Methodology and its application to inventory routing
 Manufacturing & Service Operations Management
, 2003
"... The idea of pricedirected control is to use an operating policy that exploits optimal dual prices from a mathematical programming relaxation of the underlying control problem. We apply it to the problem of replenishing inventory to subsets of products/locations, such as in the distribution of indus ..."
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Cited by 23 (5 self)
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The idea of pricedirected control is to use an operating policy that exploits optimal dual prices from a mathematical programming relaxation of the underlying control problem. We apply it to the problem of replenishing inventory to subsets of products/locations, such as in the distribution of industrial gases, so as to minimize longrun time average replenishment costs.Given a marginal value for each product/location, whenever there is a stockout the dispatcher compares the total value of each feasible replenishment with its cost, and chooses one that maximizes the surplus.We derive this operating policy using a linear functional approximation to the optimal value function of a semiMarkov decision process on continuous spaces.This approximation also leads to a math program whose optimal dual prices yield values and whose optimal objective value gives a lower bound on system performance.We use duality theory to show that optimal prices satisfy several structural properties and can be interpreted as estimates of lowest achievable marginal costs.On realworld instances, the pricedirected policy achieves superior, near optimal performance as compared with other approaches.
Tzur: Period Vehicle Routing Problem with Service Choice 454 Transportation Science 40(4
, 1998
"... Abstract The period vehicle routing problem (PVRP) is a variation of the classic vehicle routing problem in which delivery routes are constructed for a period of time (for example, multiple days). In this paper, we consider a variation of the PVRP in which service frequency is a decision of the mod ..."
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Cited by 18 (2 self)
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Abstract The period vehicle routing problem (PVRP) is a variation of the classic vehicle routing problem in which delivery routes are constructed for a period of time (for example, multiple days). In this paper, we consider a variation of the PVRP in which service frequency is a decision of the model. We refer to this problem as the PVRP with service choice (PVRPSC). We explore modeling issues that arise when service choice is introduced and suggest efficient solution methods. Contributions are made both in modeling this new variation of the PVRP and in introducing an exact solution method for the PVRPSC. In addition, we propose a heuristic variation of the exact method to be used for larger problem instances. Computational tests show that adding service choice can improve system efficiency and customer service. We also present general insights on the impact of node distribution on the value of service choice.
INTEGRATED SUPPLY CHAIN DESIGN MODELS: A SURVEY AND FUTURE RESEARCH DIRECTIONS
, 2007
"... Optimization models, especially nonlinear optimization models, have been widely used to solve integrated supply chain design problems. In integrated supply chain design, the decision maker needs to take into consideration inventory costs and distribution costs when the number and locations of the f ..."
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Cited by 15 (2 self)
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Optimization models, especially nonlinear optimization models, have been widely used to solve integrated supply chain design problems. In integrated supply chain design, the decision maker needs to take into consideration inventory costs and distribution costs when the number and locations of the facilities are determined. The objective is to minimize the total cost that includes location costs and inventory costs at the facilities, and distribution costs in the supply chain. We provide a survey of recent developments in this research area.
Mechanism design for optimal consensus problems
 In Proc. 45th IEEE Conf. on Decision and Control
, 2006
"... Abstract — We consider stationary consensus protocols for networks of dynamic agents with fixed and switching topologies. At each time instant, each agent knows only its and its neighbors ’ state, but must reach consensus on a group decision value that is function of all the agents ’ initial state.W ..."
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Cited by 12 (1 self)
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Abstract — We consider stationary consensus protocols for networks of dynamic agents with fixed and switching topologies. At each time instant, each agent knows only its and its neighbors ’ state, but must reach consensus on a group decision value that is function of all the agents ’ initial state.We show that our protocol design is the solution of individual optimizations performed by the agents. This notion suggests a game theoretic interpretation of consensus problems as mechanism design problems. Under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives. We prove that such objectives can be chosen so that rational agents have a unique optimal protocol, and asymptotically reach consensus on a desired group decision value. I.
Delivery cost approximations for inventory routing problems in a rolling horizon framework
 Transportation Science
, 2002
"... The inventory routing problem considered in this paper is concerned with the repeated distribution of a commodity, such as heating oil, over a long period of time to a large number of customers. The problem involves a central depot as well as various satellite facilities which the drivers can visit ..."
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Cited by 10 (0 self)
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The inventory routing problem considered in this paper is concerned with the repeated distribution of a commodity, such as heating oil, over a long period of time to a large number of customers. The problem involves a central depot as well as various satellite facilities which the drivers can visit during their shift to refill their vehicles. The customers maintain a local inventory of the commodity. Their consumption varies daily and cannot be predicted deterministically. In case of a stockout, a direct delivery is made and a penalty cost is incurred. In this paper we present incremental cost approximations to be used in a rolling horizon framework for the problem of minimizing the total expected annual delivery costs.
Inventory Routing with Continuous Moves
"... The typical inventory routing problem deals with the repeated distribution of a single product from a single facility with an unlimited supply to a set of customers that can all be reached with outandback trips. Unfortunately, this is not always the reality. We introduce the inventory routing prob ..."
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Cited by 7 (1 self)
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The typical inventory routing problem deals with the repeated distribution of a single product from a single facility with an unlimited supply to a set of customers that can all be reached with outandback trips. Unfortunately, this is not always the reality. We introduce the inventory routing problem with continuous moves to study two important reallife complexities: limited product availabilities at facilities and customers that cannot be served using outandback tours. We need to design delivery tours spanning several days, covering huge geographic areas, and involving product pickups at different facilities. We develop an innovative randomized greedy algorithm, which includes linear programming based postprocessing technology, and we demonstrate its effectiveness in an extensive computational study. 1
Approximate dynamic programming methods for an inventory allocation problem under uncertainty
, 2006
"... We propose two approximate dynamic programming methods to optimize the distribution operations of a company manufacturing a certain product at multiple production plants and shipping it to different customer locations for sale. We begin by formulating the problem as a dynamic program. Our first appr ..."
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Cited by 5 (1 self)
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We propose two approximate dynamic programming methods to optimize the distribution operations of a company manufacturing a certain product at multiple production plants and shipping it to different customer locations for sale. We begin by formulating the problem as a dynamic program. Our first approximate dynamic programming method uses a linear approximation of the value function and computes the parameters of this approximation by using the linear programming representation of the dynamic program. Our second method relaxes the constraints that link the decisions for different production plants. Consequently, the dynamic program decomposes by the production plants. Computational experiments show that the proposed methods are computationally attractive, and in particular, the second method performs significantly better than standard benchmarks.