A small manufacturing company is currently designing a new production system, organized in job shops. It is installing 3 different departments (M1, M2, M3), which will serve to produce at least 3 types of product (A, B, C). We have the following information:
| Product | Production process (Department, Cycle Time [min / pcs]) | Average annual demand (pieces) |
| A | (M1, 15) – (M2, 10) | 15000 |
| B | (M1, 9) – (M3, 8) | 25000 |
| C | (M2, 17) – (M3, 7) | 35000 |
The production system will work 3 shifts of 7 hours per day, 240 days/year. Departments have different coefficient. M1 considers a human coefficient (HC) of 0.96 and an Availability (A) of 0.96. M2 considers a human coefficient (HC) of 0.95 and an Availability (A) of 0.93. M3 considers a human coefficient (HC) of 0.91 and an Availability (A) of 0.93. The scheduling efficiency (SE) must be set equal to 0.82. M1 scrap rates (SR) is equal to 0.07, M2 scrap rates is equal to 0.05, while M3 scrap rates is equal to 0.09. In M1 department, setup lasts 2.8 hours for each change of production; in M2 setup lasts 2.3 hours for each change of production; in M3 setup lasts 1.9 hours for each change of production. It is expected to produce average batches of about 1000 pieces (regardless of the type of product). The objective is to determine the number of machines and the rate of saturation for each department.
Solution:
| Product ID | M1 (min/pcs) | M2 (min/pcs) | M3 (min/pcs) | pieces/year |
| A | 15 | 10 | 0 | 15000 |
| B | 9 | 0 | 8 | 25000 |
| C | 0 | 17 | 7 | 35000 |
| Setup (h) | 2,8 | 2,3 | 1,9 | |
| Setup (min) | 168 | 138 | 114 | |
| Average batch (pieces) | 1000 | 1000 | 1000 | |
| pieces | 40000 | 50000 | 60000 | |
| Number of setup | 40 | 50 | 60 | |
| Setup (min) | 6720 | 6900 | 6840 | |
| Scrap Rate | 0,07 | 0,05 | 0,09 | |
| Production (min) | 483870,9677 | 784210,5263 | 489010,989 | |
| A | 0,96 | 0,95 | 0,91 | |
| HC | 0,96 | 0,93 | 0,93 | |
| NH (min) | 532325,27 | 895427,87 | 585904,51 | |
| 240 | days | |||
| 3 | shift | |||
| 7 | hours | |||
| WH (h) | 5040 | |||
| WH (min) | 302400 | |||
| SE | 0,82 | |||
| AH (min) | 247968,00 | 247968,00 | 247968,00 | |
| NM | 2,146749858 | 3,611062208 | 2,362823076 | |
| NM | 3 | 4 | 3 | |
| S | 0,715583286 | 0,902765552 | 0,787607692 |
