Reference no: EM132532230
Case 1
Recycling is an important and complex activity in Country A. To enable timely operations, the country is divided into 10 sectors and recycling operations are commenced simultaneously in each sector. The recyclable garbage is collected from public bins, loaded into trucks, and transported to recycling sites. Each site can accommodate different amounts of recyclable garbage because of its available land size at the facility. The annual capacities for five recycling sites are given in the table below (in megatonnes):
|
|
Recycling Site
|
|
|
|
1
|
2
|
3
|
4
|
5
|
|
Capacity
|
20
|
20
|
30
|
15
|
15
|
Each recycling site is installed with facilities that have different recycling efficiencies which are summarised in the table below (in percentages):
|
|
Recycling Site
|
|
|
|
1
|
2
|
3
|
4
|
5
|
|
Efficiency
|
35%
|
40%
|
20%
|
60%
|
55%
|
The cost of collecting and transporting recyclable garbage primarily depends on the distance between the sectors and the recycling sites. The following table summarises the distances between each sector and each recycling site (in kilometres):
|
|
Recycling Site
|
|
|
Sector
|
1
|
2
|
3
|
4
|
5
|
|
1
|
13.6
|
5.6
|
19.6
|
29.6
|
37.2
|
|
2
|
9.6
|
8.4
|
33.2
|
36.4
|
35.2
|
|
3
|
5.6
|
11.6
|
14.8
|
37.6
|
34.4
|
|
4
|
10.4
|
14.4
|
18.0
|
32.8
|
35.6
|
|
5
|
6.0
|
12.4
|
8.4
|
31.6
|
35.2
|
|
6
|
16.8
|
19.6
|
26.0
|
30.8
|
24.4
|
|
7
|
19.2
|
24.8
|
39.6
|
24.8
|
22.8
|
|
8
|
21.6
|
24.0
|
20.8
|
30.4
|
19.6
|
|
9
|
12.4
|
16.4
|
26.4
|
30.0
|
28.8
|
|
10
|
12.8
|
26.0
|
28.4
|
24.0
|
33.2
|
Using historical data, the country estimates the annual volume of the recyclable garbage for each sector in the coming year shown in the table below (in megatonnes):
Estimated Recyclable Garbage
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
10
|
8
|
4
|
7
|
5
|
6
|
10
|
8
|
5
|
6
|
It will cost approximately $113,918 to move one megatonne of recycling garbage for one kilometre. The management would like to maximise the amount of recycled garbage and minimise the transportation cost.
a. Formulate a multiple-objective linear programming (MOLP) model for this problem in a Word file with a brief description of an equation, and implement it in an Excel spreadsheet.
b. Determine the optimal value for each objective in the problem.
c. Suppose the management considers maximising the amount of recycled garbage to be two times as important as minimising the transportation cost. Formulate a GP model to optimise both objectives simultaneously with a brief description of an equation in a Word file, and implement the MOLP model in an Excel spreadsheet. What do the results suggest?
Case 2
Company B is a retailer of mobile phones in Australia that works 250 days in a year. The manager is determining a minimum-cost inventory plan for an upcoming phone to be launched in the market. She has collected the following information:
• Annual demand: 900 phones
• Phone cost: $1,079 each
• Phone RRP: $1,199 each
• Net weight: 163 g each
• Tare weight: 277 g each
• Annual inventory holding cost: 15%
• Cost per order to replenish inventory: $75
• Annual in-transit holding cost: 10%
• Freight rate: $7.50 per kg
• Time to process order for freight: 1 days
• Freight transit time: 3 days
Solve this problem using a non-linear programming (NLP) model to determine the followings:
a. Economic order quantity for the phone in units and in kg
b. The total cost for purchasing the phones
c. The total cost for ordering
d. The total cost for holding the inventory
e. The total cost for transportation
f. The total cost for holding the phones during transit
g. The total cost for this inventory plan
h. The number of orders
i. Ordering point
j. The profit from this inventory plan
Case 3
Paul is planning to buy a new car for his work as a trader. After narrowing his choices down to three models (X, Y, and Z) within his budget, he is having difficulty in deciding which one to purchase. He has compared each model against one another on the basis of four criteria: price, safety, economy, and comfort. His comparisons are summarised below:
|
Price Safety
|
|
|
X
|
Y
|
Z
|
|
|
X
|
Y
|
Z
|
|
X
|
1
|
3
|
2
|
|
X
|
1
|
1/4
|
2
|
|
Y
|
1/3
|
1
|
1/2
|
|
Y
|
4
|
1
|
3
|
|
Z
|
1/2
|
2
|
1
|
|
Z
|
1/2
|
1/3
|
1
|
|
Economy Comfort
|
|
|
X
|
Y
|
Z
|
|
|
X
|
Y
|
Z
|
|
X
|
1
|
1/5
|
1/2
|
|
X
|
1
|
2
|
1/2
|
|
Y
|
5
|
1
|
1/3
|
|
Y
|
1/2
|
1
|
3
|
|
Z
|
2
|
3
|
1
|
|
Z
|
2
|
1/3
|
1
|
Paul wants to incorporate all of the four criteria into his final decision. However, the criteria are not equally important. The following matrix summarises his comparisons of the importance of the criteria:
|
|
Criteria
|
|
|
|
Price
|
Safety
|
|
Economy
|
Comfort
|
|
Price
|
1
|
1/3
|
|
2
|
1/2
|
|
Safety
|
3
|
1
|
|
2
|
1/2
|
|
Economy
|
1/2
|
1/2
|
|
1
|
1/3
|
|
Comfort
|
2
|
2
|
|
3
|
1
|
Use analytic hierarchy process to compute the overall score for each car. What do the results suggest?