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\Problem name: sample.lp
Maximize
100z1 + 346.5z2 + 115.6z3 + 375.1z4 + 34.1z5
Subject To
-1z1 +y7 >= 0
-2z2 +y1 +y2 >= 0
-2z3 +y5 +y6 >= 0
-2z4 +y13 +y12 >= 0
-4z5 +y2 +y6 +y12 +y13 >= 0
Max.storage
constraint
30z1 + 115.5z2 + 18.7z3 + 170.5z4 + 12.1z5 <= 100
Min. revenue
constraint
520z1+1640.1z2+394.4z3+2421.1z4+174.9z5>=600
y1 +y2 +y5 +y6 +y7 +y12 +y13 >= 5
y1 +y2 +y5 +y6 +y7 +y12 +y13 <= 10
lower & upper
bounds
Binaries
z1 z2 z3 z4 z5
y1 y2 y5 y6 y7 y12 y13
End
Fig. 1.
Sample problem
sample.lp
Integer optimal solution: Objective = 2.4970000000e+002
Solution time = 0.03 sec. Iterations = 0 Nodes = 0
CPLEX> dis sol var -
Variable Name Solution Value
z1 1.000000
z3 1.000000
z5 1.000000
y7 1.000000
y2 1.000000
y5 1.000000
y6 1.000000
y13 1.000000
y12 1.000000
All other variables in the range 1-12 are zero.
Fig. 2.
Solution of sample ILP using CPLEX
$600 is $249.70. The three best item packages to stock are X
1
, X
3
and X
5
which
correspond to the binary decision variables z
1
, z
3
and z
5
respectively. Further, the
particular items in the optimal set to store are 7, 2, 5, 6, 12 and 13 (corresponding to
the decision variables
y
7
y
2
y
5
y
6
y
12
y
13
. The remaining item packages and items do
not participate in the optimal solution.
We now present the results from the retail dataset as described at the beginning of
the section. We note that the number of distinct frequent item sets, namely k = 929.
To build the model, for each item i, we have randomly generated the corresponding
selling price (sp
i
), cost price (c
i
) and storage space (s
i
) with its profit around 25%.
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