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This article deals with a single-machine resource allocation scheduling problem with deteriorating jobs. Under a group technology environment, the actual processing times of jobs are a convex resource allocation function of their starting time and the amount of resource allocation. The objective is to minimize the weighted sum of makespan and resource allocation cost. For two special cases, it is proved that the problem can be solved in polynomial time. For the general case of the problem, heuristic and branch-and-bound procedures are developed to solve the problem. Computational experiments are also performed to examine the effectiveness and the efficiency of the algorithms. [ABSTRACT FROM AUTHOR]