The optimal solution value of the multiknapsack problem as a function of the knapsack capacities is studied under the assumption that the profit and weight coefficients are generated by an appropriate random mechanism. A strong asymptotic characterization is obtained, that yiclds a closed form expression for certain special cases.

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Mathematical programming
Erasmus School of Economics

Meanti, M., Rinnooy Kan, A., Stougie, L., & Vercellis, C. (1990). A probabilistic analysis of the multiknapsack value function. Mathematical programming, 46(1-3), 237–247. doi:10.1007/BF01585741