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Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming
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DOI：10.1287/trsc.1120.0431.png)
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This paper considers a minimum-cost network flow problem in a bipartite graph with a single sink. The transportation costs exhibit a staircase cost structure because such types of transportation cost functions are often found in practice. We present a dynamic programming algorithm for solving this so-called single-sink, fixed-charge, multiple-choice transportation problem exactly. The method exploits heuristics and lower bounds to peg binary variables, improve bounds on flow variables, and reduce the state-space variable. In this way, the dynamic programming method is able to solve large instances with up to 10,000 nodes and 10 different transportation modes in a few seconds, much less time than required by a widely used mixed-integer programming solver and other methods proposed in the literature for this problem.
Keyword:
supplier selection
network flow
piecewise linear cost
dynamic programming
mixed-integer programming
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