Step 1 – Identify the BOTTLE NECK – in this case, the 2nd reactor (Fluidized Bed) was the bottleneck at the 4th step of the 7step process. The 2nd reactor is limited to 400 tons per cycle and each cycle takes 4 hours to complete. Since this is a continuous process system, it is important to ensure the 2nd reactor is always full as it has limited capacity. From there, we worked backwards through the previous three steps to arrive at the initial tons of material required for each process.
Divide input at 2nd reactor (400) by (1-mass loss) and (1-yield loss) to arrive at input for the 1st reactor, and repeat the process to arrive at inputs for the preceding two stages. The result of this calculation is a starting requirement of 576.5 tons of iron ore fines entering the system to ensure 400 semi-processed tons enter the 2nd reactor.
The 356.4 tons of outflow from the 2nd reactor (400 x 1- yield loss x 1- mass loss) is the input to the next step. We continued to take the outflow from each step and multiply by (1- the yield loss) to arrive at the final value of 321.5 tons of Hot Briquetted Iron (HBI), per cycle.
The number of cycles in a year was determined to be 1839.6. This was arrived at by multiplying 365 days x 24 hours/day x (1 – total downtime) divided by 4 hour cycle time (cycle time for the 2nd reactor or bottleneck). Downtime in this production process is additive since the process is continuous.
Variable cost = cycles per year x input value for process (calculation above) x the variable cost for that process from Exhibit 11. Combining the variable costs for each of the steps results in a total variable cost of $57,004,012. We then added the fixed costs of $20,790,000 from Exhibit 12 to arrive at a total cost of $77,794,012.
We then divided the resulting value by the total yield (cycles times output per cycle) of 591,447 to arrive at cost per ton of HBI of: $131.53.