1.     1..P —products

2.    1..M — machines

3.     1..W — jobs

4.    T_p  – Processing time 

5.     Tech_p — Processing of job j on machine i

,

 

6.     NTech_p – the steps that are included to technological process of production P-products

7.     k – step of technological operation   k = 1..NTech_p

8.      – operative time

9.      – number of technological operations

10.                        – The cost of the machine changeover from one type of job to another

11.                      

We also present a two-dimensional array  M x W, where c_m,w defines costs of carrying w job on m machine in one unit time (if w job impossible to perform on m machine, then c_m,w = +∞). 

Unknown quantity:

The unknowns are the set of vectors jobs X_m, m = 1..M.

Each plan describes the tasks vector download m machine, and сvector set of tasks describes the production plan of the enterprise for the production of P products.

K_m — sum total of of tasks for m machine (a vector)

d_m,k — number of the product processing m mschine in k tasks

x_m,k —the number of process steps production d_m,k

s_m,k — the time at which begins k tasks  m machine.

X_m –  the loading plan m machine   m = 1..M (a vector)

Restrictions:

On duration of operations:

 

By number of technological operations:

 

k = 1..NTech_p

On technological processes:

 

Objective function

Is necessary to minimize costs (Accounts) for the execution the production plan:

.

 

The objective is a task without interruption type of Job Shop. In the above formulation of this problem is NP-complete.