Alpha:

Single machine

Identical machine in parallel

Machine in parallel with different speeds

Unrelated Machine parallel

THE QUESTION IS: Why Alpha is not in charge of Machine in Series? Why just Single machine, Identical machine in parallel, Machine in parallel with different speeds, Unrelated Machine parallel and why not in series?

## Expert Answer

**Answer:**

A scheduling problem is described by a triplet i.e. **α, β, and γ** they represents **machine, constraints, and objective** respectively. The machine environment is described by α and it contains a single entry.

In order to minimize the average weighted completion time subject to release date, machine environment is the area of concern. It is well known that list scheduling in order of random alpha-points drawn from the same schedule results in an on-line algorithm.

Machine in Series are involved for completion of task where insted of single machine or machines in parallel there are machines in series. After an item has completed its processing in on upstream machine, it goes down to downstream machine for further processing.

However, Alpha is not in charge of Machine in Series because, in case of machine in series the basic approach utilized is to first relax the integer programming constraints to linear ones, than using the binary search to find a smallest feasible solution to the linear program, and then round to obtain the integer programming solution.