Continuous maximin knapsack problems with GLB constraints
Mathematical Programming: Series A and B
Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
A max-min allocation problem: its solutions and applications
Operations Research
Minimax resource allocation with tree structured substitutable resources
Operations Research
Solving knapsack sharing problems with general tradeoff functions
Mathematical Programming: Series A and B
Optimal storage allocation for serial files
Communications of the ACM
Resource allocation among competing activities: a lexicographic minimax approach
Operations Research Letters
An algorithm for separable non-linear minimax problems
Operations Research Letters
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We consider a nonlinear minimax allocation problem with multiple knapsack-type resource constraints. Each term in the objective function is a nonlinear, strictly decreasing and continuous function of a single variable. All variables are continuous and nonnegative. A previous algorithm for such problems repeatedly solves relaxed problems without the nonnegativity constraints. That algorithm is particularly efficient for certain nonlinear functions for which there are closed-form solutions for the relaxed problems; for other functions, however, the algorithm must employ search methods. We present a new algorithm that uses at each iteration simple-to-compute algebraic expressions to check optimality conditions, instead of solving the relaxed minimax problems. The new algorithm is therefore significantly more efficient for more general nonlinear functions.