The stochastic linear continuous type knapsack problem: A generalized P model

Abstract

This paper considers a stochastic version of the linear continuous type knapsack problem in which the cost coefficients are random variables. The problem is to find an optimal solution and an optimal probability level of the chance constraint. This problem P 0 is first transformed into a deterministic equivalent problem P. Then a subproblem with a positive parameter is introduced and a close relation between P and its subproblem is shown. Further, an auxiliary problem of the subproblem is introduced and a direct relation between P and the auxiliary problem is derived through a relation connecting the subproblem and its auxiliary problem. Fully utilizing these relations, an efficient algorithm is proposed that finds an optimal solution of P in at most O( n 4) computational time where n is the number of decision variables. Finally, further research problems are discussed.