The Ace Machine Company is considering using a priority scheduling rule in its fabrication shop and must decide

whether to use: the critical rule, the order slack rule, the shortest operation next rule or the slack per operation rule.

The table below shows the company$$s current inventory and shop status.

Exhibit $1$

Order number

Manufacturing

Lead Time

Remaining

Time Remaining

Until Due Date

Current

Operation

Processing Time

$1$

$15$

$7$

Number of

Operations

Remaining

Total Processing

Time Remaining

$2$

$2$

$15$

$11$

$3$

$8$

$3$

$3$

$20-2$

$4$

$8$

$5$

$4$

$15-5$

$2$

$8$

$4$

$5$

$15$

$3$

$1$

$3$

$12$

$8$

Note: Time is measured in days. Manufacturing lead time remaining includes both the machine processing time and the length of time orders

spend moving and waiting to be processed in a machine queue. Current operating processing time $($as well as total processing time remaining$)$

includes no move or queue times.

$8$

a$)$ State the formula for calculating the priority index for each of sequencing rules given above.

b$)$ Compute the scheduling priority index for each order in Exhibit $1$ for the four sequencing rules.