HW#$5$

HW#$5$ from $9$th edition textbook: Problem $13($employee scheduling$),$

Problem $20($NPV$),25($ILP$),31($cash flow investment$)$

Problem $13$: Snookers Restaurant is open from $8$:$00$ a$.$m$.$ to $10$:$00$ p$.$m$.$ daily.

Besides the hours they are open for business, workers are needed an hour

before opening and an hour after closing for setup and clean up activities. The

restaurant operates with both full$-$time and part$-$time workers on the following

shifts:

Shift Daily Pay Rate

$7$:$00$ a$.$m$.11$:$00$ a$.$m$.$ $$32$

$7$:$00$ a$.$m$.3$:$00$ p$.$m$.$ $$80$

$11$:$00$ a$.$m$.3$:$00$ p$.$m$.$ $$32$

$11$:$00$ a$.$m$.7$:$00$ p$.$m$.$ $$80$

$3$:$00$ p$.$m$.7$:$00$ p$.$m$.$ $$32$

$3$:$00$ p$.$m$.11$:$00$ p$.$m$.$ $$80$

$7$:$00$ p$.$m$.11$:$00$ p$.$m$.$ $$32$

The following numbers of workers are needed during each of the indicated time

blocks:

Hours Workers Needed

$7$:$00$ a$.$m$.11$:$00$ a$.$m$.11$

$11$:$00$ a$.$m$.1$:$00$ p$.$m$.24$

$1$:$00$ p$.$m$.3$:$00$ p$.$m$.16$

$3$:$00$ p$.$m$.5$:$00$ p$.$m$.10$

$5$:$00$ p$.$m$.7$:$00$ p$.$m$.22$

$7$:$00$ p$.$m$.9$:$00$ p$.$m$.17$

$9$:$00$ p$.$m$.11$:$00$ p$.$m$.6$

At least one full time worker must be available during the hour before opening

and after closing. Additionally, at least $30\%$ of the employees should be full$-$

time $(8-$hour$)$ workers during the restaurant$$s busy periods from $11$:$00$ a$.$m$.$

$1$:$00$ p$.$m$.$ and $5$:$00$ p$.$m$.7$:$00$ p$.$m$.$

a$.$ Formulate an ILP for this problem with the objective of minimizing total

daily labor costs.

b$.$ Implement your model in a spreadsheet and solve it$.$

c$.$ What is the optimal solution?