Heuristics for unequal weight delivery problems with a fixed error guarantee

Authors:
Kemal Altinkemer;Bezalel Gavish
Affiliations:
Krannert Graduate School of Management, Purdue University, West Lafayette, IN 47907, USA;William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY 14627, USA
Venue:
Operations Research Letters
Year:
1987

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Abstract

This paper presents heuristics that are based on optimal partitioning of a travelling salesman tour, for solving the unequal weight delivery problem. The worst case error performance is given as a bound on the worst case ratio of the cost of the heuristic solution to the cost of the optimal solution. A fully polynomial procedure which consists of applying the optimal partitioning to a travelling salesman tour generated by Christofides' heuristic has a worst case error bound of 3.5-3/Q where Q is the capacity limit of the vehicles. When optimal partitioning is applied to an optimal travelling salesman tour, the worst case error bound becomes 3-2/Q.