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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]

This article deals with an integrated optimization problem of production scheduling and common due-window assignment on a single machine. The objective is to minimize the total cost, which is a weighted sum function of earliness and tardiness, due-window starting time, and due-window size, where the weights only depend on their position in a sequence (i.e. position-dependent weights). A polynomial time solution algorithm is provided for the corresponding problem. The problem can also be extended to slack due-windows assignment and general position-dependent processing times. It is proved that both these extensions remain polynomially solvable. [ABSTRACT FROM AUTHOR]