Exact algorithms for the 0–1 Time-Bomb Knapsack Problem

We consider a stochastic version of the 0–1 Knapsack Problem in which, addition to profit and weight, each item is associated with probability exploding destroying all contents knapsack. The objective maximise expected selected items. resulting problem, denoted as Time-Bomb (01-TB-KP), has applications logistics cloud computing scheduling. introduce nonlinear mathematical formulation study its computational complexity, propose techniques derive upper lower bounds using convex optimisation integer linear programming. present three exact approaches based on enumeration, branch bound, dynamic programming, computationally evaluate their performance large set benchmark instances. analysis shows that proposed methods outperform direct application solvers model, provide high quality solutions limited amount time.