Chisnall Collieries Ltd (CCL) has three collieries (coal mines) each extracting four grades of coal to service five regions. Each of the mines has a daily maximum capacity for each grade and also a total capacity that may not be exceeded
The selling prices of each grade are different for each region and each region has daily requirements for each grade that must be fulfilled.
CCL wish to devise a daily production and delivery schedule that would maximise profit. Specifically, they need to know how much of each grade of coal to extract from each mine and deliver to each region.
Mine processing costs per tonne for each grade at each mine are:
Mine
Grade
1
2
3
1
14
12
13
2
12
12
11
3
11
10
10
4
9
8
9
Transportation costs per tonne from each mine to each region are:
Region
Mine
1
2
3
4
5
1
10
12
15
14
18
2
14
16
15
18
22
3
20
18
17
15
14
Daily mining capacities in tonnes for each grade at each mine are:
Mine
Grade
1
2
3
1
200
150
180
2
200
190
210
3
220
220
220
4
300
350
350
Total daily mining capacities in tonnes at each mine are 900, 800 and 950 respectively.
Requirements of each grade at each region are:
Region
Grade
1
2
3
4
5
1
100
90
95
105
100
2
120
110
105
115
110
3
140
132
125
110
100
4
180
200
210
185
190
Selling prices for each grade within each region are:
Region
Grade
1
2
3
4
5
1
150
152
148
145
153
2
140
135
140
138
142
3
125
128
122
125
127
4
90
90
88
92
91
1. Formulate the problem as a linear program using sigma notation. Define clearly the decision variables and parameters necessary to model the problem.
2. Model the problem in MS Excel and obtain the optimal solution using Solver.
3. Write a business report highlighting and explaining the optimal solution. Include a production and delivery schedule for CCL.
Submit for marking a verbal description of your model, the mathematical model, a printout of your Excel model together with the solution output and the report. | 
发表于 2008-11-16 09:01:51
