Problem 1 Bharat Ispat (5pt)

The steel, or Ispat, industry is a large industry employing millions of people in a variety of management jobs and skilled and unskilled labor jobs. Bharat Ispat is a large steel maker. They are facing a problem in their western division. Their CFO describes the problem as follows.

We produce 16 steel products coded as AA, AB etc. In simple terms Ax products are plate steel such as for auto and railcar body, and Bx products are rolled steel products such as rails and bars. We have three existing mills, Mill 1 at Bhiwandi, Mill 2 at Parel, Mill 3 at Vasai and a new Mill 4 at Dapoli. The table below shows the cost in USD/klb in the xC column and processing time in hours/klb in the xT column according to which mill does the work. klb is one thousand pounds. Thus it costs $104/klb and 0.8 hours/klb to produce plate product AC at Bhiwandi. A missing value indicates that the mill cannot produce the product because it does not have the equipment, skills or environmental approvals to do so. The Demand column indicates the division-wide demand in thousands of pounds per week for the upcoming week.

We have a labor problem at Bhiwandi. Our labor agreement will expire next week. We intend to form a new agreement only if we expect to use this mill to produce at least 65 klb of products.

The Bhiwandi, Parel and Vasai mills have a production capacity of 800, 480 and 1280 hours per week respectively. The engineering team at Dapoli suggests an initial capacity not to exceed 960 hours in the upcoming week. Additional production capacity hours may be added at Dapoli but because it is a new mill with a lot of new equipment it will cost $8000/hour to perform inspections and checks for each additional hour of operation. The hard limit is 1000 hours.

Mill-1 Mill-2 Mill-3 Mill-4 Demand 1C 1T 2C 2T 3C 3T 4C 4T AA 90 0.8 75 0.7 70 0.5 63 0.6 100 AB 80 0.8 70 0.7 65 0.5 60 0.6 630 AC 104 0.8 85 0.7 83 0.5 77 0.6 500 AD 98 0.8 79 0.7 80 0.5 74 0.6 980 AE 123 0.8 101 0.7 110 0.5 99 0.6 720 AF 113 0.8 94 0.7 100 0.5 84 0.6 240 AG 160 0.9 156 0.5 140 0.6 75 AH 142 0.9 150 0.5 130 0.6 22 BA 140 1.5 110 0.9 122 1.2 50 BB 124 1.5 96 0.9 101 1.2 22 BC 160 1.5 133 0.9 138 1.2 353 BD 143 1.5 127 0.9 133 1.2 55 BE 202 1.5 150 0.9 160 1.2 125 BF 190 1.5 141 0.9 140 1.2 35 BG 190 1.0 220 1.5 100 BH 175 1.0 200 1.5 10

(Q1) Write the pure form model for Bharat Ispat and solve it. Indicate your answer clearly.

(Q2) Should Mill-1 at Bhiwandi continue operations after the first week? Explain with sound reasoning based on the model.

(Q3) Should Mill-4 Dapoli add production capacity (hours)? Why or why not? Explain with sound reasoning based on the model.