Transactions of the Society of Instrument and Control Engineers
Online ISSN : 1883-8189
Print ISSN : 0453-4654
ISSN-L : 0453-4654
Characterization of Infeasible Solutions in a Bag-Packing Problem for Achieving Desired Weight
Yoshihiro MURAKAMIJyunichi KURATAHironobu UCHIYAMATakafumi UENO
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2002 Volume 38 Issue 9 Pages 784-791

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Abstract

In a bag-packing problem, it is important to determine how many items are to be put in a bag in order to make the pack weigh the given desired weight. In some cases, even though all the possible solutions to the problem are enumerated, it may be that none of them achieves a weight satisfactorily close enough to the desired standard. If a constraint is imposed that the sum weight of a pack should not exceed the acceptable maximum weight, such insufficient solution proposals turn out to be infeasible ones. In order to characterize such Infeasible solution proposals, the bag-packing problem is formulated into an integer programming.
In the formulated model, the bag-packing problem is regarded as one of constraint satisfaction problem (CSP). Firstly, two objective constraints are taken into consideration, i) the sum weight of a pack should not be less than the desired weight, and ii) it also should not exceed the acceptable maximum weight. Secondly, to make the searching for a suitable candidate solution more effective, a certain constraint is imposed which may strictly limit the search space. An algorithm is developed that can enumerate candidate solutions for the imposed constraints. This algorithm is so developed as to make it possible to simulate the bag-packing operation.
In the bag-packing simulation, such desperate situations are made clear in which there is no feasible solution. There are two of such cases: i) a case in which even searching is not necessary because it is obvious that there is no solution at all, and ii) a case in which, after examining all the candidate solutions, it is concluded that there is no feasible one. Concerning the former case, several numerical simulations are done by varying the values of several parameters to characterize the infeasible solutions. In the process of pairing the constituent items for a pack, the number of generating an infeasible solution may be reduced by evading the former case.

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