Question

Multiple objective linear programming (MOLP) problem: The Chick'n Pick'n fast-food chain is considering how to expand its operations. Three types of retail outlets are possible: a lunch-counter operation designed for office buildings in downtown areas, an eat-in operation designed for shopping malls, and a stand-alone building with drivethrough and sit-down facilities. The following table summarizes the number of jobs, start-up costs, and annual returns associated with each type of operation:

Lunch Counter Mall Stand-alone

Jobs 9 17 35

Costs   $150,000 $275,000 $450,000

Returns $85,000 $125,000 $175,000

The company has $2,000,000 available to pay start-up costs for new operations in the coming year. Additionally, there are five possible sites for lunch-counter operations, seven possible mall locations, and three possible stand-alone locations. The company wants to plan its expansion in a way that maximizes annual returns and the number of jobs created. a. Formulate an MOLP for this problem b. Determine the best possible value for each objective in the problem c. Implement your model in a spreadsheet and solve it to determine the solution that minimizes the maximum percentage deviation from the optimal objective function values. What solution did you obtain? d. Suppose management considers maximizing returns to be three times as important as maximizing the number of jobs created. What solution does this suggest? Please submit your final solutions in a single Excel workbook containing each spreadsheet model on a separate worksheet. Please include the actual model formulation and answer any written questions in a textbox within the corresponding worksheet.

Just if you could ellaborate on the deviation/weighted percentages and target value please on the forumlas and constraints that goes into solver would be great.

https://www.chegg.com/homework-help/chick-n-pick-n-fast-food-chain-considering-expand-operations-chapter-7-problem-21qp-solution-9781285418681-exc

Here is a link to one already done. Im just having trouble  on the deviation/weighted percentages and target value please on the forumlas and constraints that goes into solver those steps. if you could just hit those on detail a bit and minimax if you can, dont worry about part A even i just need excel. Thank you.

Answer 1

Let,
X1 = number of lunch counter units built
X2 = number of mall units built
X3 = number of standalone units built

MAX   85X1 + 125X2 + 175X3 (returns)
MAX   9X1 + 17X2 + 35X3 (jobs created)
Subject to,
150X1 +   275X2 +   450X3 ≤ 2,000
X1 ≤ 5
X2 ≤ 7
X3 ≤ 3
Xi ≥ 0

Solution	Lunch counter	Mall	Standalone	Return	Jobs
1	5.0	4.5	0.0	993.2 (best)	122.3
2	0.0	2.4	3.0	820.5	145.2 (best)

The solver needs to be run twice - once for Objective = F20 and next for Objective = F21

MOLP formulation

MIN Q
Subject to,
150X1 +   275X2 +   450X3 ≤ 2,000
X1 ≤ 5
X2 ≤ 7
X3 ≤ 3
(993.2 - 85X1 - 125X2 - 175X3) / 993.2 ≤ Q
(145.2 - 9X1 - 17X2 - 35X3) / 145.2 ≤ Q
X1, X2, X3 ≥ 0
[Note the weights to the last two constraints taken equal to 1]

	Lunch counter	Mall	Standalone	Q
Nos.	5.0	1.3	2.0	0.1
Objective (Q)	0.1
Constraints				Original
Return	85	125	175	934.3	0.1	0.1
Jobs	9	17	35	136.6	0.1	0.1
Fund	150	275	450		2000	2000
Capacity X1	1				5.00	5
Capacity X2		1			1.28	7
Capacity X3			1		1.99	3