Online inventory replenishment scheduling of temporary orders

This paper studies the online inventory replenishment scheduling problem, in which orders from retailers arrive and depart at arbitrary times at one supplier and each order needs to be replenished at least once every constant periods. The supplier needs to assign each order to some vehicle such that the maximum number of vehicles ever used over all time is minimized, while each vehicle can replenish only one order per period. We present a Combined First Fit algorithm and improve the upper bound of the competitive ratio for this problem to be 3.0913 from 5. When offline algorithm is unrestricted, the Combined First Fit algorithm is proved to be 6.1826-competitive.