10.Wayne enterprises is about to begin the production of a new product. The mana
ID: 365827 • Letter: 1
Question
10.Wayne enterprises is about to begin the production of a new product. The manager of the department that produces one of the components wants to know how often the machine used to produce the item will be available for other work. The machine will produce the item at a rate of 300 units a day. Eighty units will be used daily in assembling the final product. Assembly will take place five days a week, 50 weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run at a cost of $400. The inventory holding costs will be $15 a year. a.What run quantity should be used to minimize the total annual costs? b.How many days does it take to produce the optimal run quantity? c.What is the average amount of inventory (in units/day)? d.If themanager wants to run another job between runs of this item and needs a minimum of 10 days per cycle for the other work, will there be enough time? e.Given the answer to part d above, the manager wants to explore options that will allow the other job to be performed using this equipment. Name three options the manager could consider. f.Suppose the manager decides to increase the run size of the new product. How many additional units would be needed to just accommodate the other job? How much will that increase the total cost?
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Explanation / Answer
Production rate, p = 300 units per day
Demand rate, d = 80 units per day
Setup cost, S = 400
Holding cost, H = 15
Working days in a year = 5*50 = 250
Annual demand, D = 80*250 = 20000
a) Optimal run quantity as per EPQ model = sqrt(2DS/H)/sqrt(1-d/p) = sqrt(2*20000*400/15)/sqrt(1-80/300)
= 1206 units
b) Number of days it takes to produce the optimal run quantity = Q/p = 1206/300 = 4 days (approx, excluding setup time)
c) Average amount of inventory = (Q/2)*(1-d/p) = (1206/2)*(1-80/300) = 442
d) Cycle time = 1206/80 = 15 days , including the production time of 4 days, therefore idle number of days = 15 - 4 - 1 day for setup = 10 days
Therefore, 10 days can be spared per cycle for other work. This is enough time to run the other job, which requires a minimum of 10 days per cycle.
e) The manager can explore following other options:
i) Increase the batch size or run size of the new product, so the lead time is longer and the other item could be also be produced.
ii) Reduce the setup time and production time, so that both the setup and production can be finished in 1 day so that there are 10 days available for the other job.
iii) Reduce the processing time of the other job, so that its batch run can be finished in 7 days instead of 10 days.
f) Let x be the new run size to accommodate the other job
x/80-x/300 - 1 = 10
300x - 80x = 300*880
220x = 300*880
x = 300*880/220 = 1200 units
Therefore, new run size should be 1200 units.
Additional units = 1200-1206 = -6 units
As there is negligible change in batch size, so there will be no change in annual total cost
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