TECHNICAL NOTE---The Adaptive Knapsack Problem with Stochastic Rewards

Authors:
Taylan İlhan;Seyed M. R. Iravani;Mark S. Daskin
Affiliations:
Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208;Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208;Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109
Venue:
Operations Research
Year:
2011

Citing 10
Cited 0

Dynamic programming: deterministic and stochastic models

Dynamic programming: deterministic and stochastic models
Risk criteria in a stochastic knapsack problem

Operations Research
Allocating bandwidth for bursty connections

STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On a stochastic knapsack problem and generalizations

Advances in computational and stochastic optimization, logic programming, and heuristic search
Rollout Algorithms for Stochastic Scheduling Problems

Journal of Heuristics
Finite Horizon Stochastic Knapsacks with Applications to Yield Management

Operations Research
The Dynamic and Stochastic Knapsack Problem with Random Sized Items

Operations Research
Stochastic Load Balancing and Related Problems

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity

FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Risk-aware limited lookahead control for dynamic resource provisioning in enterprise computing systems

Cluster Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a set of items with associated deterministic weights and random rewards, the adaptive stochastic knapsack problem (adaptive SKP) maximizes the probability of reaching a predetermined target reward level when items are inserted sequentially into a capacitated knapsack before the reward of each item is realized. This model arises in resource allocation problems that permit or require sequential allocation decisions in a probabilistic setting. One particular application is in obsolescence inventory management. In this paper, the adaptive SKP is formulated as a dynamic programming (DP) problem for discrete random rewards. The paper also presents a heuristic that mixes adaptive and static policies to overcome the “curse of dimensionality” in the DP. The proposed heuristic is extended to problems with normally distributed random rewards. The heuristic can solve large problems quickly, and its solution always outperforms a static policy. The numerical study indicates that a near-optimal solution can be obtained by using an algorithm with limited look-ahead capabilities.