Mantel produces a toy carriage, whose final assembly must include four wheels an

Question

Mantel produces a toy carriage, whose final assembly must include four wheels and two seats. The factory producing the parts operates three shifts a day. The following table provides the amounts produced of each part in the three shifts. Ideally, the number of wheels produced is exactly twice that of the number of seats. However, because production rates vary from shift to shift, exact balance in production may not be possible. Mantel is interested in determining the number of production runs in each shift that minimizes the imbalance in the production of the parts. The capacity limitations restrict the number of runs to between 4 and 5 for shift 1, 10 and 20 for shift 2, and 3 and 5 for shift 3. Formulate the problem as a goal programming model.

Explanation / Answer

Let the number of seats produces in each shift be S1,S2 and S3 ;
We know that S1 = 300; S2=280 and S3= 360

Similarly, let the number of wheels produced in each shift be W1,W2 and W3,
We know that W1=500 ; W2= 600 and W3=640

We are to minimise the imbalance, that is, produce seats and wheel in the ratio of 1:2

So, we are to minimise: | Total number of wheels produced - 2* total number of seats produced |
Let shift 1 go on for r1 runs; It is given that r1 = [4,5]

Similarly shift 2 for r2 runs and shift 3 for r3 runs;
r2 = [10,20] and r3= [3,5]

Our goal programming problem is to :

Minimise | r1( w1-2s1) + r2 ( w2-2s2) + r3(w3-2s3) ]
Such that 4<= r1<=5
10<= r2 <= 20
3<= r3 <= 5

and r1,r2 and r3 are integers

We have been asked to only formualt the problem so there is no requirement to solve it.

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