Give explanation and calculation for full points Your company has a production a

Question

Give explanation and calculation for full points

Your company has a production area that can produce three parts: A, B and C. The time required to produce each part is 25, 80 and 10 minutes for each, respectively. The values of the parts are $5, $20 and $1 per minute, respectively. How would you schedule the parts through the area to minimize the value of work - in - process inventory? You must explain your logic/algorithm CLEARLY, step - by - step in order to receive full credit. Your answer is not complete if you do not compute the value of the work - in - process inventory from the resulting sequence. Assume that: (1) all 1 unit per part type, (2) all parts are available at t = 0, (2) there are no setup times, (3) there is no job preemption, (4) no job splitting and (5) no batch processing.

Explanation / Answer

to minimize the value of work in process inventory, we need to arrange the parts by minimum weighted processing time.

this means we have to sequence parts in an increasing ratio of t/w where t is processing time and w is the corresponding weight.

weights can be simply taken as the values of the parts i.e. $5, $20, $1.

or the weidhts can be calculated as : 5/(5+20+1), 20/(5+20+1), 1/(5+20+1).

we can use any one of them since the denominator is same in all of them.

So weighted processing time for the parts are:

part A: 25/5 = 5

part B: 80/20 = 4

part C: 10/1 = 10

so the order should be B-A-C.

this gives you a value of work in process inventory = [5*80] + [1*(80+25)] = 400 + 105 = 505

Note: all other sequencs give a larger value of work in process inventory. i have checked for all.

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