Economic lot sizing: an O(n log n) algorithm that runs in linear time in the Wagner-Whitin case
Operations Research - Supplement
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A faster strongly polynomial minimum cost flow algorithm
Operations Research
Efficient minimum cost matching and transportation using the quadrangle inequality
Journal of Algorithms
Capacity Acquisition, Subcontracting, and Lot Sizing
Management Science
An O(T log T) Algorithm for the Dynamic Lot Size Problem with Limited Storage and Linear Costs
Computational Optimization and Applications
Solving Real-Life Locomotive-Scheduling Problems
Transportation Science
The Locomotive Routing Problem
Transportation Science
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The objective of the classical minimum cost flow problem is to send units of a good that reside at one or more points in a network (sources or supply nodes) with arc capacities to one or more other points in the network (sinks or demand nodes), incurring minimum cost. We develop fast algorithms for previously unstudied specially structured minimum cost flow problems that have applications in many areas, such as locomotive and airline scheduling, repositioning of empty rail freight cars, highway and river transportation, congestion pricing, shop loading, and production planning. First, we consider the case where the n1 supply and n2 demand nodes lie on a circle (or line) (n = n1 + n2) and flow is allowed only in one direction; our algorithm solves this problem in O(n) time. Next, we consider a constrained version of this problem and show that it can be solved in O(n log n2) time. Finally, we consider the version where the nodes lie on a circle (or line), flow is allowed in both directions, and the costs of flow between two nodes in the clockwise and the counterclockwise direction are different; our algorithm solves this problem in O(n log n) time. Our algorithms are based on the successive shortest-path algorithm for the minimum cost flow problem. We exploit the special structure of the problem and use advanced data structures, when required, to achieve short run times.