PROBLEM # 3-(15 POINTS) TANCO is a manufacturing company that produces water tan

Question

PROBLEM # 3-(15 POINTS) TANCO is a manufacturing company that produces water tanks. The company wants to schedule production over the next four months. Demand for their water tanks is expected as follows: PRIVATE January FebruaryMarchApril Month Demand (Units) 20 15 19 24 Regular time capacity is 17 units per month. By using overtime, an additional 5 units can be produced per month. A tank produced on regular time costs $400 to manufacture; on overtime the same tank costs $600 to manufacture. The holding cost to carry a tank in inventory from one month to the next is $50. Use the transportation model to formulate the production planning linear programming model for the company. Do not solve. Make sure to define every decision variable and write the objective and all the constraints

Explanation / Answer

Linear programming model using transportation model

Decision variables:

Rij = Regular production quantity produced in month i and consumed in month j , j >= i. i,j = 1,2,3,4

Oij = Overtime production quantity produced in month i and consumed in month j , j >= i. i,j = 1,2,3,4  

Objective: Minimize 400(R11+R22+R33+R44) + 600(O11+O22+O33+O44) + 450(R12+R23+R34) + 650(O12+O23+O34) + 500(R13+R24) + 700(O13+O24) + 550R14 + 750*O14

s.t.

R11+R12+R13+R14 <= 17

R22+R23+R24 <= 17

R33+R34 <= 17

R44 <= 17

O11+O12+O13+O14 <= 5

O22+O23+O24 <= 5

O33+O34 <= 5

O44 <= 5

R11+O11 = 20

R12+O12+R22+O22 = 15

R13+O13+R23+O23+R33+O33 = 19

R14+O14+R24+O24+R34+O34+R44+O44 = 24

Rij, Oij >= 0

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