Abstract
Abstract An employee transporting problem is described and a set partitioning model is developed. An investigation of the model leads to a knapsack problem as a surrogate problem. Finding a partition corresponding to the knapsack problem provides a solution to the problem. An exact algorithm is proposed to obtain a partition (subset-vehicle combination) corresponding to the knapsack solution. It requires testing and matching too many alternatives to obtain a partition. The sweep algorithm is implemented in obtaining a partition (subset-vehicle combination) in an efficient manner. Illustrations are provided to show how the algorithms obtain solutions.
Highlights
A number of employees will be picked up from various places within a city and brought to the plant
All the arguments up to now apply well to the case of bounded integer knapsack problem. In this form, the employee transporting problem is reduced to the common sense problem of determining the number of vehicles of each capacity to transport all the passengers at a minimum cost provided that the distance of any route to a subset of destinations does not exceed a predetermined limit without any consideration of routing and vehicle-subset assignments
The capacities of the vehicles vary in size. It is a heterogenous fleet problem. These facts make the employee transporting problem belong to a different class of problems than the heterogeneous vehicle routing problem (HVRP) in the literature
Summary
A number of employees will be picked up from various places (bus-stops) within a city and brought to the plant. The knapsack problem with the righthand side s(A) ≤ r < b can have a solution in Y (r), but there cannot be any corresponding vehicle-subset assignments and/or partitions available satisfying the distance (time) constraint. All the arguments up to now apply well to the case of bounded integer knapsack problem In this form, the employee transporting problem is reduced to the common sense problem of determining the number of vehicles of each capacity to transport all the passengers at a minimum cost provided that the distance (time) of any route to a subset of destinations does not exceed a predetermined limit without any consideration of routing and vehicle-subset assignments. As an indication of the efficiency of the sweep algorithm, one should point out that a small laptop computer (netbook) with a processor chip of 1.60 GHz solves the last problem in 1.73 s of CPU time
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