Single-machine scheduling in the context of Operations Research

Logistics is the part of supply chain management that deals with the efficient forward and reverse flow of goods, services, and related information from the point of origin to the point of consumption according to the needs of customers, and a logistician is a professional working in the field of logistics management. Logistics management is a component that holds the supply chain together. The resources managed in logistics may include tangible goods such as materials, equipment, and supplies, as well as food and other edible items.Military logistics is concerned with maintaining army supply lines with food, armaments, ammunition, and spare parts, apart from the transportation of troops themselves. Meanwhile, civil logistics deals with acquiring, moving, and storing raw materials, semi-finished goods, and finished goods. For organisations that provide garbage collection, mail deliveries, public utilities, and after-sales services, logistical problems must be addressed.

Logistics deals with the movement of materials or products from one facility to another; it does not include material flow within production or assembly plants, such as production planning or single-machine scheduling.

Identical-machines scheduling is an optimization problem in computer science and operations research. We are given n jobs J₁, J₂, ..., J_n of varying processing times, which need to be scheduled on m identical machines, such that a certain objective function is optimized, for example, the makespan is minimized.

Identical machine scheduling is a special case of uniform machine scheduling, which is itself a special case of optimal job scheduling. In the general case, the processing time of each job may be different on different machines; in the case of identical machine scheduling, the processing time of each job is the same on each machine. Therefore, identical machine scheduling is equivalent to multiway number partitioning. A special case of identical machine scheduling is single-machine scheduling.