Unbounded knapsack problem with controllable rates: the case of a random demand for items

This paper focuses on a dynamic, continuous-time control generalization of the unbounded knapsack problem. This generalization implies that putting items in a knapsack takes time and has a due date. Specifically, the problem is characterized by a limited production horizon and a number of item types...

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Bibliographic Details
Published inThe Journal of the Operational Research Society Vol. 54; no. 6; pp. 594 - 604
Main Author Kogan, K
Format Journal Article
LanguageEnglish
Published London Taylor & Francis 01.06.2003
Palgrave Macmillan Press
Palgrave Macmillan UK
Palgrave
Taylor & Francis Ltd
Subjects
Algorithms
Applied sciences
Business and Management
Carrying costs
computational analysis
control
Costs
Estimate reliability
Exact sciences and technology
Fines & penalties
Inventory
Knapsack problem
Linear equations
Management
Mathematical models
Minimization of cost
Objective functions
Operational research and scientific management
Operational research. Management science
Operations research
Operations Research/Decision Theory
Optimal solutions
optimization
Production capacity
Production functions
Random variables
Scheduling
Scheduling, sequencing
Surplus
Theoretical Paper
Theoretical Papers
Time
scheduling
control
computational analysis
optimization
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Summary:This paper focuses on a dynamic, continuous-time control generalization of the unbounded knapsack problem. This generalization implies that putting items in a knapsack takes time and has a due date. Specifically, the problem is characterized by a limited production horizon and a number of item types. Given an unbounded number of copies of each type of item, the items can be put into a knapsack at a controllable production rate subject to the available capacity. The demand for items is not known until the end of the production horizon. The objective is to collect items of each type in order to minimize shortage and surplus costs with respect to the demand. We prove that this continuous-time problem can be reduced to a number of discrete-time problems. As a result, solvable cases are found and a polynomial-time algorithm is suggested to approximate the optimal solution with any desired precision.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0160-5682
1476-9360
DOI:10.1057/palgrave.jors.2601554