Question

                                    A         B          C          D         E

Fixed Startup Cost        $3400 $2200 $2750 $1800 $1200
Cost per MW-hr          $6        $5        $7        $7        $8
Maximum Capacity      2200    1900    2600    1600    3200

Part A: Formulate a Binary-Integer Problem that minimizes the total cost. Write the complete algebraic form, and clearly state the decision variables, objective function, and the constraints.

Hint: Some binary variables and big number constraints are needed in this problem

Part B: Set up and solve a linear spreadsheet model to determine the operating plan that will minimize their overall costs. For full credit, the model must be linear (no multiplication of changing cells, no IF statements, no MAX statements, etc.)

Answer 1

PART A

Binary integer programming model is following:

Min = 3400*A+2200*B+2750*C+1800*D+1200*E+6*Xa+5*Xb+7*Xc+7*Xd+8*Xe;

2200*A-Xa >= 0;
1900*B-Xb >= 0;
2600*C-Xc >= 0;
1600*D-Xd >= 0;
3200*E-Xe >= 0;
Xa+Xb+Xc+Xd+Xe >= 7000;

@BIN(A);
@BIN(B);
@BIN(C);
@BIN(D);
@BIN(E);

Solution using LINGO is following:

B) The set-up and solution can be obtained in the excel file given in the dropboxlink below:

https://www.dropbox.com/s/libqbkq4i42jv2n/20170325_Binary_Optimization.xlsx?dl=0

Screenshot for reference:

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