The coordination of transportation and batching scheduling

Abstract

a b s t r a c tWe study a coordinated scheduling problem of production and transportation in which each job is transported to a single batching machine for further processing. There are m vehicles that transport jobs from the holding area to the batching machine. Each vehicle can transport only one job at a time. The batching machine can process a batch of jobs simultaneously where there is an upper limit on the batch size. Each batch to be processed occurs a processing cost. The problem is to find a joint schedule of production and transportation such that the sum of the total completion time and the total processing cost is optimized. For a special case of the problem where the job assignment to the vehicles is predetermined, we provide a polynomial time algorithm. For the general problem, we prove that it is NP-hard (in the ordinary sense) and present a pseudo-polynomial time algorithm. A fully polynomial time approximation scheme for the general problem is obtained by converting an especially designed pseudo-polynomial dynamic programming algorithm.Crown

New Results on the Coordination of Transportation and Batching Scheduling

“…The contributions of this paper are the following: we show that the complexity results in [1,3] are still valid when the processing cost is removed from the objective, thus reducing to more "classic" scheduling objectives; we assess the complexity status of the relevant problem variants with free m; and we establish that the weighted-completion-time objective F = w j C j leads to an intractable problem even with a single transporter, contrary to the unweighted case.…”

“…In a general application, however, one would typically expect m to be free, or at least O(n). By changing the base assumptions as such, previous pseudo-polynomial-time algorithms [1,3] become exponential-time. In the next sections, we show that both the problem variants are strongly NP-hard when m is free, excluding the existence of a pseudo-polynomial-time algorithm (unless P = NP).…”

“…, C n }, the maximum completion time or makespan. Using a method similar to [1], he provides a pseudopolynomial-time algorithm and FPTAS for any fixed m, thus again concluding NP-hardness in the ordinary sense; he also describes a polynomial-time algorithm for TBS with F = C max + α(b) when m = 1. In a general application, however, one would typically expect m to be free, or at least O(n).…”

“…Tang and Gong [1] address a planning problem that coordinates transportation and batch processing in the iron and steel industry. A set N = {1, 2, .…”

“…In the production stage, up to c jobs can be processed as one batch on the batching machine; the processing time of (all jobs of) each batch is equal to p, which is a constant. Following Tang and Gong [1], the resulting optimization problem is denoted as TBS, short for transportation and batching scheduling problem. A formal definition is as follows: TBS Input: job set N = {1, 2 .…”