Shipping Multiple Items by Capacitated Vehicles: An Optimal Dynamic Programming Approach

Anily, Shoshana; Tzur, Michal

doi:10.1287/trsc.1030.0080

Cited by 50 publications

(35 citation statements)

References 10 publications

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“…Anily and Tzur [1] have considered a closely related inventory model. In particular, in their model there are n requests, not necessarily unit size, and the capacities are uniform (i.e., c(t) = C, for each t = 1, .…”

Section: Previous Resultsmentioning

confidence: 99%

Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs

Even

Levi

Rawitz

et al. 2008

ACM Trans. Algorithms

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In the rectangle stabbing problem we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. In this paper we study the capacitated version of this problem in which the input includes an integral capacity for each line. The capacity of a line bounds the number of rectangles that the line can cover. We consider two versions of this problem. In the first, one is allowed to use only a single copy of each line (hard capacities), and in the second, one is allowed to use multiple copies of every line, but the multiplicities are counted in the size (or weight) of the solution (soft capacities).We present an exact polynomial-time algorithm for the weighted one dimensional case with hard capacities that can be extended to the one dimensional weighted case with soft capacities. This algorithm is also extended to solve a certain capacitated multi-item lot sizing inventory problem with joint set-up costs. For the case of d-dimensional rectangle stabbing with soft capacities, we present a 3d-approximation algorithm for the unweighted case. For d-dimensional rectangle stabbing problem with hard capacities, we present a bi-criteria algorithm that computes 4d-approximate solutions that use at most two copies of every line. Finally, we present hardness results for rectangle stabbing when the dimension is part of the input and for a twodimensional weighted version with hard capacities.

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Section: Previous Resultsmentioning

confidence: 99%

Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs

Even

Levi

Rawitz

et al. 2008

ACM Trans. Algorithms

View full text Add to dashboard Cite

show abstract

“…Jaruphongsa et al (2005) analyzed a dynamic lot-sizing model in which replenishment orders may be delivered by multiple shipment modes with different lead times and cost functions. Anily and Tzur (2005) considered a dynamic model of shipping multiple items by capacitated vehicles. They presented an algorithm based on a dynamic programming approach.…”

Section: Introductionmentioning

confidence: 99%

Meta-Heuristic Algorithms for a Multi-Product Dynamic Lot-Sizing Problem with a Freight Container Cost

Kim¹,

Lee

2012

Industrial Engineering and Management Systems

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Lot sizing and shipment scheduling are two interrelated decisions made by a manufacturing plant and a third-party logistics distribution center. This paper analyzes a dynamic inbound ordering problem and shipment problem with a freight container cost, in which the order size of multiple products and single container type are simultaneously considered. In the problem, each ordered product placed in a period is immediately shipped by some freight containers in the period, and the total freight cost is proportional to the number of containers employed. It is assumed that the load size of each product is equal and backlogging is not allowed. The objective of this study is to simultaneously determine the lot-sizes and the shipment schedule that minimize the total costs, which consist of production cost, inventory holding cost, and freight cost. Because the problem is NP-hard, we propose three meta-heuristic algorithms: a simulated annealing algorithm, a genetic algorithm, and a new population-based evolutionary meta-heuristic called selfevolution algorithm. The performance of the meta-heuristic algorithms is compared with a local search heuristic proposed by the previous paper in terms of the average deviation from the optimal solution in small size problems and the average deviation from the best one among the replications of the meta-heuristic algorithms in large size problems.

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“…They develop a O(T 3 log T ) algorithm by extending a dynamic lot-sizing model in which orders must be an integer number of batches. Anily and Tzur [3,4] consider multiple products to be delivered from warehouse to retailer in capacitated vehicles, each incurring a fixed cost per trip, and propose both a dynamic programming algorithm [3] and a search algorithm [4] to solve the problem optimally.…”

Section: Introductionmentioning

confidence: 99%

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

Jin¹,

Muriel

2009

Naval Research Logistics

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Abstract:We consider a multi-stage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Fixed costs are incurred for each truck dispatched and all trucks have the same capacity limit. Costs are stationary, or more generally monotone as in Lippman (Management Sci 16, 1969, 118-138). Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system-wide inventory and transportation costs without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T 2 ) algorithm for the single-stage dynamic lot sizing problem; (2) an O(T 3 ) algorithm for the case of a single-warehouse single-retailer system; and (3) a nested shortest-path algorithm for the single-warehouse multi-retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single-stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems. Finally, we show that the decentralized solution is asymptotically optimal.

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Shipping Multiple Items by Capacitated Vehicles: An Optimal Dynamic Programming Approach

Cited by 50 publications

References 10 publications

Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs

Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs

Meta-Heuristic Algorithms for a Multi-Product Dynamic Lot-Sizing Problem with a Freight Container Cost

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

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