Jacko, Peter and Niño-Mora, José (2007) Time-constrained restless bandits and the knapsack problem for perishable items (Extended Abstract). Electronic Notes in Discrete Mathematics, 28. pp. 145-152. ISSN 1571-0653
Abstract
Motivated by a food promotion problem, we introduce the Knapsack Problem for Perishable Items (KPPI) to address a dynamic problem of optimally filling a knapsack with items that disappear randomly. The KPPI naturally bridges the gap and elucidates the relation between the PSPACE-hard restless bandit problem and the NP-hard knapsack problem. Our main result is a problem decomposition method resulting in an approximate transformation of the KPPI into an associated 0-1 knapsack problem. The approach is based on calculating explicitly the marginal productivity indices in a generic finite-horizon restless bandit subproblem.