Approximation Schemes for Multiperiod Binary Knapsack Problems

  title={Approximation Schemes for Multiperiod Binary Knapsack Problems},
  author={Zuguang Gao and J. Birge and Varun Gupta},
An instance of the multiperiod binary knapsack problem (MPBKP) is given by a horizon length T , a nondecreasing vector of knapsack sizes (c1, . . . , cT ) where ct denotes the cumulative size for periods 1, . . . , t, and a list of n items. Each item is a triple (r, q, d) where r denotes the reward or value of the item, q its size, and d denotes its time index (or, deadline). The goal is to choose, for each deadline t, which items to include to maximize the total reward, subject to the… Expand
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Technical Note - The Multiperiod Knapsack Problem
  • B. Faaland
  • Mathematics, Computer Science
  • Oper. Res.
  • 1981
A branch and bound algorithm exploits the special structure of the multiperiod knapsack problem by calculating bounds by the direct solution of linear programs with m constraints in 0(m) operations. Expand
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