Abstract: In sharing economics era, it arises a new manufacturing mode where one manufacturer may temporarily rent social processing resources or machines, if necessary, to complete its customer orders and pay a reasonable rental fee. This work investigates an online scheduling problem where one manufacturer owning two parallel identical machines may lease a number of external machines to satisfy its jobs via a manufacturing resource sharing platform. The objective is to minimize the sum of the total completion time of jobs and the total leasing cost of sharing machines, where the rental cost consists of fixed cost and variable cost. The online over-list model is focused on such that jobs with unit processing times are released one by one, and each job has to be assigned on its arrival to one of the currently rented machines for processing without the knowledge of any future jobs. Moreover, the decision on leasing one more external machine may be made concurrently by the manufacturer. Several fundamental properties are presented for an offline optimal solution, and a lower bound 1+6a－312a－3+118a+(6b+3)12a－3+6b2+6b－1 of competitive ratio is proved, where a and b (0≤b<a) are the coefficients of fixed and respectively variable costs, and both are assumed to be integers. The lower bound approaches 4/3, provided that a approaches infinity and the ratio of b to a approaches zero. Secondly, an online algorithm named TS is proposed, which assigns arrival jobs almost evenly between the manufacturer’s own machines or between the rented external machines. The difference between the upper bounds of the number of jobs assigned to the above two types of machines is equal to either b or b+1. It is proved that TS is of a competitive ratio of 4/3 for a=2 and 1.89 for a≥3, respectively. The results indicate that when the manufacturer has to make decisions on the processing schedule of jobs and the time points for machine leasing in the online mode, the total cost spent is less than twice of the optimal one.

Key words: shared manufacturing; online scheduling; parallel machine scheduling; competitive analysis; total completion time