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Assignment 1 Staff Schedule

ShiftDaily 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
HoursWorkers 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

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:

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

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. Question 1. Formulate an ILP for this problem with the objective of minimizing total daily labor costs. Question 2. Implement your model in a spreadsheet and solve it. What is the optimal solution?

Question 1

Formulate an ILP for this problem with the objective of minimizing total daily labor costs.

Insert Your Answer Here.

Question 2

S h i f tWorkers
Hours1234567AvailableRequired
7:00 – 8:00

Cliff Ragsdale: Constraint cell
8:00 – 9:00

Cliff Ragsdale: Constraint cell
9:00 – 10:00

Cliff Ragsdale: Constraint cell
10:00 – 11:00

Cliff Ragsdale: Constraint cell
11:00 – 12:00

Cliff Ragsdale: Constraint cell
12:00 – 1:00

Cliff Ragsdale: Constraint cell
1:00 – 2:00

Cliff Ragsdale: Constraint cell
2:00 – 3:00

Cliff Ragsdale: Constraint cell
3:00 – 4:00

Cliff Ragsdale: Constraint cell
4:00 – 5:00

Cliff Ragsdale: Constraint cell
5:00 – 6:00

Cliff Ragsdale: Constraint cell
6:00 – 7:00
7:00 – 8:00
8:00 – 9:00
9:00 – 10:00
10:00 – 11:00
Pay Rate
Workers0
Cliff Ragsdale: Variable cell

Cliff Ragsdale: Constraint cell
0
Cliff Ragsdale: Variable cell

Cliff Ragsdale: Constraint cell
0
Cliff Ragsdale: Variable cell

Cliff Ragsdale: Constraint cell
0
Cliff Ragsdale: Variable cell

Cliff Ragsdale: Constraint cell
0
Cliff Ragsdale: Variable cell
0
Cliff Ragsdale: Variable cell
0
Cliff Ragsdale: Variable cell
Minimum
FT WorkersReq’d FT Workers
11:00 – 1:00

Cliff Ragsdale: Constraint cell

Cliff Ragsdale: Constraint cell

Cliff Ragsdale: Variable cell
5:00 – 7:00

Cliff Ragsdale: Constraint cell

Cliff Ragsdale: Objective cell

Cliff Ragsdale: Variable cell

Snookers Restaurant

Implement your model in a spreadsheet and solve it.

1. Weedwacker Company

Hours Required per Trimmer
ElectricGasHours Available
Production0.20.410,000
Assembly0.30.515,000
Packaging0.10.15,000

The Weedwacker Company manufactures two types of lawn trimmers: an electric model and a gas model. The company has contracted to supply a national discount retail chain with a total of 30,000 electric trimmers and 15,000 gas trimmers. However, Weedwacker’s production capability is limited in three departments: production, assembly, and packaging. The following table summarizes the hours of processing time available and the processing time required by each department, for both types of trimmers:

The company makes its electric trimmer in-house for $55 and its gas trimmer for $85. Alternatively, it can buy electric and gas trimmers from another source for $67 and $95, respectively. How many gas and electric trimmers should Weedwacker make and how many should it buy from its competitor in order to fulfill its contract in the least costly manner? a. Formulate an LP model for this problem in “Answer a” tab. b. Create a spreadsheet model for this problem in “Answer b” tab and solve it using Solver.

Answer a.

Answer b

ElectricGas
Number to Make
Number to Buy
Cost to Make
Cost to BuyTotal Cost
Total Available
Total Needed
Resources Req’dUsedAvailable
Production

A satisfied Microsoft Office user: Constraint cell
Assembly

A satisfied Microsoft Office user: Constraint cell
Packaging

A satisfied Microsoft Office user: Constraint cell

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Constraint cell

A satisfied Microsoft Office user: Objective cell

A satisfied Microsoft Office user: Constraint cell

Weedwacker Company

Minimize: E8 By Changing: B4:C5 Subject To: B10:C10=B11:C11 D14:D16<=E14:E16 B4:C5>=0

2. Rent-A-Dent

Costs of Transporting Cars Between Locations
Location 3Location 4Location 5Location 6
Location 1$54$17$23$30
Location 2$24$18$19$31

The Rent-A-Dent car rental company allows its customers to pick up a rental car at one location and return it to any of its locations. Currently, two locations (1 and 2) have 16 and 18 surplus cars, respectively, and four locations (3, 4, 5, and 6) each need 10 cars. The costs of getting the surplus cars from locations 1 and 2 to the other locations are summarized in the following table.

Because 34 surplus cars are available at locations 1 and 2, and 40 cars are needed at locations 3, 4, 5, and 6, some locations will not receive as many cars as they need. However, management wants to make sure that all the surplus cars are sent where they are needed, and that each location needing cars receives at least five. c. Formulate an LP model for this problem in “Answer c” tab. d. Create a spreadsheet model for this problem in “Answer d” tab and solve it using Solver.

Answer c.

Answer d.

Transportation Costs
Location 3Location 4Location 5Location 6
Location 1
Location 2
Redistribution Plan
Location 3Location 4Location 5Location 6ShippedAvailable
Location 1

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Variable cell
Location 2

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Variable cell
Actual

A satisfied Microsoft Office user: Constraint cell

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Constraint cell

A satisfied Microsoft Office user: Constraint cell

A satisfied Microsoft Office user: Variable cell

A satisfied Microsoft Office user: Constraint cell

A satisfied Microsoft Office user: Constraint cell

A satisfied Microsoft Office user: Constraint cell
Min
Max
Total Cost:

A satisfied Microsoft Office user: Objective cell

Minimize: E16 By Changing: C10:F11 Subject To: G10:G11=H10:H11 C12:F12>=C13:F13 C12:F12<=C14:F14 C10:F11>=0

Rent-A-Dent

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