Paper Info
Title
The maximum flow problem with minimum lot sizes
Abstract
In many transportation systems, the shipment quantities are subject to minimum lot sizes in addition to regular capacity constraints. That is, either the quantity must be zero, or it must be between the two bounds. In this work, we consider a directed graph, where a minimum lot size and a flow capacity are defined for each arc, and study the problem of maximizing the flow from a given source to a given terminal. We prove that the problem is NP-hard. Based on a straightforward mixed integer programming formulation, we develop a Lagrangean relaxation technique, and demonstrate how this can provide strong bounds on the maximum flow. For fast computation of near-optimal solutions, we develop a heuristic that departs from the zero solution and gradually augments the set of flow-carrying (open) arcs. The set of open arcs does not necessarily constitute a feasible solution. We point out how feasibility can be checked quickly by solving regular maximum flow problems in an extended network, and how the solutions to these subproblems can be productive in augmenting the set of open arcs. Finally, we present results from preliminary computational experiments with the construction heuristic.
Year
DOI
Venue
2011
10.1007/978-3-642-24264-9_13
ICCL
Keywords
Field
DocType
maximum flow,flow capacity,regular maximum flow problem,zero solution,construction heuristic,open arc,minimum lot size,near-optimal solution,feasible solution,regular capacity constraint
Flow network,Mathematical optimization,Heuristic,Computer science,Directed graph,Relaxation technique,Integer programming,Maximum flow problem,Minimum-cost flow problem,Computation
Conference
Volume
ISSN
Citations 
6971
0302-9743
4
PageRank 
References 
Authors
0.54
4
3
Name
Order
Citations
PageRank
Dag Haugland115115.18
Mujahed Eleyat272.98
Magnus Lie Hetland3738.04