3)CoalCo has five different coal mines: A, B, C, D and E and has to ship the coa
ID: 381951 • Letter: 3
Question
3)CoalCo has five different coal mines: A, B, C, D and E and has to ship the coal to powr p Total coal demand for the power plant is 240 million ton (Mton). There is fixed and variable transportation. The capacity of coal mines and cost figures for procurement of shipment from each plant are: coal and fixed cost of Mine Capacity (MTon) Cost (Ton) Fixed Cost of 300 180 450 190 400 300 250 200 400 300 10 12 For the power plant the coal supply should satisfy the following conditions: . There should be no supply from D when there is supply from A, B or C . If there is supply from A and B, then there should be a supply from E If there is a supply from C, then there should be supply from A but no supply from B. Transportation cost varies for each mine. There is fixed and variable cost of transportation. The variable costs for A, B and D are 1, 2 and 9 respectively. For C and E, the transportation cost on the Mtons shipped as follows: Range (Mtons) 0-100 100 and over Formulate the problem as a MIP which minimizes total cost incurred. Define all variables clearly Cost(E)
Explanation / Answer
MIP model
Decision variables: A is a binary variables such that if A = 1 represents supply from mine A , A = 0 represents no supply from mine A. Similarly variables B,C,D,E represent the same condition for mines B,C,D and E repsectively.
XA, XB, XD represent the quantity supplied from mines A,B and D respectively
XC1 represent the quantity supplied from mine C if it is less than 100 ton
XC2 represent the quantity supplied from mine C if it is more than 100 ton
XE1 represent the quantity supplied from mine E if it is less than 100 ton
XE2 represent the quantity supplied from mine E if it is more than 100 ton
YC is a binary variable such that YC=1 represents that quantity supplied from mine C < 100 and YC=0 indicates quantity supplied from mine C >= 100
YE is a binary variable such that YE=1 represents that quantity supplied from mine E < 100 and YE=0 indicates quantity supplied from mine E >= 100
Objective: Min 300A+250B+200C+400D+300E+10XA+11XB+11(XC1+XC2)+12XD+9(XE1+XE2)+1XA+2XB+9XD+1XC1+2XC2+7XE1+6XE2
s.t.
A+B+C+3D <= 3
A+B-E <= 1
C - A <= 0
C + B <= 1
300A - XA >= 0
180B - XB >= 0
450X - XC1 - XC2 >= 0
190D - XD >= 0
400E - XE1 - XE2 >= 0
100YC - XC1 >= 0
XC2 >= 100*(1-YC)
100YE - XE1 >= 0
XE2 >= 100*(1-YE)
A,B,C,D,E,YC,YE = 0,1
XA,XB,XC1,XC2,XD,XE1,XE2 >= 0
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