Note on Single-machine due-window assignment and scheduling with resource allocation, aging effect, and a deteriorating rate-modifying activity

Ji et al. Computers & Industrial Engineering 66 (2013) 952-961 studied the single-machine common due-window problem considering convex resource allocation and aging effect with a deteriorating rate-modifying activity. The objective is to minimize the total cost which is a function of earliness, tardiness, window location, window size and resource consumption. An algorithm of time complexity O ( n 2 logn ) , where n is the number of jobs, was given to solve a special case while the job-dependent aging factor is a constant for all jobs. In this paper we firstly point out an error in this algorithm. Secondly we show this algorithm remains valid when all the modifying rates are 1.