Ise 513 Homework2

1) a. When the holding cost is assessed on a period by period basis, the holding cost would be the function of the maximum quantity hold during a period, especially when the carrying cost increase significantly along with the quantity, such as the insurance cost. Also, there are some products take up great space such as automobiles, ships and airplanes, each pieces need a certain amount of space, which makes the cost higher along with the increase of product quantity.
b. Since the holding cost=rv∙Imax=rvQ, TRC=ADQ+rvQ
∂TRC∂Q=ADQ2+rv=0, we can get EOQ=ADrv

2) a. the holding cost h=$0.3/300=$0.001 per working day
b. EMQ=2ADrv(1-DP)=2×48×20000.001×(1-20008000)=16000pounds
c. (1) Maximum inventory: Imax=Q1-DP=12000 (2) Average inventory: 12Imax=6000 (3) Average annual holding cost: 12Imax($0.3 /unit/year)=$1800 (4)Interval between orders: T=QD=160002000=8days (5) Reorder point: DL=2000×5=10000units d. Assuming that we get replenishment of 8000 pounds of flour on Monday and Tuesday respectively, the bakery will consume the first 8000 pounds from Monday till Thursday, and next 8000 pounds from Friday. However, the flour would be expired after 7 days, in this case on next Tuesday; while we only consume 4000 pounds before next Tuesday. Therefore, the maximum economic lot size under this scenario would be 8000+4000=12000 pounds.

3) Special order quantity: Q*=1000
TRCdon't =2ADh+v0DQ*D=2×20×100×5×0.252+0.03+5×100×1000100=5140
TRCdo =v1Q*+A+h1Q*I(t1)D+12h1Q*D=4750+20+4.75×0.252+0.03×1000×150100+12×10002100×4.75×0.252+0.03=5084
Since TRC(don’t) > TRC(do), it is a way of risk to take the order.

4) a. EOQ=2ADrv=2×5×40000.25×0.04=2000
b. T=EOQD=20004000=0.5 year=6 months
c. TRCEOQ=ADEOQ+vrEOQ2=4000×52000+0.04×0.25×20002=20
While based on 3-month supply rule, Q=1000,
TRCQ=ADQ+vrQ2=4000A1000+0.04×0.25×10002=4A+5
TRCEOQ>TRCQ, 203.75
Therefore, as long as A>3.75, a 6-month supply is