Question

2. The Versatech Corporation has decided to produce three new products. Five branch plants now have excess production capacity. The unit manufacturing cost of the first product would be $31, $29, $32, $28, and $29 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the second product would be $45, $41, $46, $42, and $43 in Plants 1, 2, 3, 4, and 5, respectively. The unit manufacturing cost of the third product would be $38, $35, and $40 in Plants 1, 2, and 3, respectively, whereas Plants 4 and 5 do not have the capability for producing this product. Sales forecasts indicate that 600, 1000, and 800 units of products 1, 2, and 3, respectively, should be produced per day. Plants 1, 2, 3, 4, and 5 have the capacity to produce 400, 600, 400, 600, and 1000 units daily, respectively, regardless of the product or combination of products involved. Assume that any plant having the capability and capacity to produce them can produce any combination of the products in any quantity.

3. (a) Write down an optimization formulation for this problem. Remark: You need to write down the abstract optimization formulation, explain the meaning of each optimization variable and explain what are the data.

4. (b) There is no “transportation” in the problem statement (there is no “truck”, no “route”). Nevertheless, the formulation is similar to a transportation problem. Ex- plain how to view this problem as a transportation problem.

5. (c) Solve the problem and report the optimal solution and optimal cost. You can use software to solve the problem; if so, please provide the code (e.g. copy the code to the solution file, or take a snapshot and paste the picture in the solution file).

Answer 1

(a)

Optimization model is as follows:

Let Xij be the number of product i to be produced in plant j

Minimize 31X11+29X12+32X13+28X14+29X15+45X21+41X22+46X23+42X24+43X25+38X31+35X32+40X33

s.t.

X11+X12+X13+X14+X15 = 600

X21+X22+X23+x24+X25 = 1000

X31+X32+X33 = 800

X11+X21+X31 <= 400

X12+X22+X32 <= 600

X13+X23+X33 <= 400

X14+X24+X34 <= 600

X15+X25+X35 <= 1000

X34, X35 = 0

Xij >= 0

---------------------------------------------------------------------------------------------------------------

(b)

There is no "transportation" in the problem statement. However, the problem is about deciding how many products of each type to be produced in each plant. In transportation analogy, each product type is a demand node, each plant is a capacity node and manufacturing cost is equivalent of transportation cost.

---------------------------------------------------------------------------------------------------------------

(c)

Create spreadsheet model as follows:

Enter Solver Parameters as follows:

Click Solve to generate the solution. After that, values appear automatically in yellow cells (B11:F13).

Click OK

-----------------

Alternatively, solution can be obtained by LINGO as follows:

---------------------------------------------------------------------------------------------------------------