Online computation and competitive analysis
Online computation and competitive analysis
SIAM Journal on Discrete Mathematics
Supply chain scheduling: Batching and delivery
Operations Research
Online scheduling in a parallel batch processing system to minimize makespan using restarts
Theoretical Computer Science
On-line scheduling with delivery time on a single batch machine
Theoretical Computer Science
Order Assignment and Scheduling in a Supply Chain
Operations Research
Supply Chain Scheduling: Conflict and Cooperation in Assembly Systems
Operations Research
Dynamic supply chain scheduling
Journal of Scheduling
Batching and delivery in semi-online distribution systems
Discrete Applied Mathematics
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We consider two-level supply chain scheduling problems where customers release jobs to a manufacturer that has to process the jobs and deliver them to the customers. Processed jobs are grouped into batches, which are delivered to the customers as single shipments. The objective is to minimize the total cost which is the sum of the total flow time and the total delivery cost. Such problems have been considered in the off-line environment where future jobs are known, and in the online environment where at any time there is no information about future jobs. It is known that the best possible competitive ratio for an online algorithm is 2. We consider the problem in the semi-online environment, assuming that a lower bound P for all processing times is available a priori, and present a semi-online algorithm with competitive ratio $\frac{2D}{D+P}$ where D is the cost of a delivery. Also, for the special case where all processing times are equal, we prove that the algorithm is $1.045\sqrt{\frac{2-u}{u}}$ -competitive, where u is the density of the instance.