The hospital inventory manager from Problem 1 switches to a periodic review peri
ID: 422531 • Letter: T
Question
The hospital inventory manager from Problem 1 switches to a periodic review period ordering, where orders are place once a week. The lead time for receiving an order is now 2 weeks. The syringe cost is reduced to $12.50 apiece. The forecast remains 1475 units per month which equates to 340 per week (the CV remains 8%). The annual holding cost rate remains 25%, the ordering cost remains $80, and the desired cycle service level remains 99%. a. Calculate the order up to level (OUL) and the order quantity if there are 245 syringes in inventory and another 630 in transit. b. Why isn’t the holding cost or ordering cost considered in this model? c. Re-calculate Part a if the lead time to receive an order is reduced to one week.
Explanation / Answer
Lead time, L = 2 weeks
Annual demand, D = 1475*12 = 17,700 units
Weekly demand, d = 340
Standard deviation of weekly demand, s = 340*8% = 27
Annual holding cost, H = 12.5*25% = 3.125
Ordering cost, S = 80
Service level = 99%
z = NORMSINV(99%) = 2.33
a)
EOQ = SQRT(2DS/H) = SQRT(2*17700*80/3.125) = 952
Review period, P = (Q/D)*52 = (952/17700)*52 = 2.8 weeks
Order upto level, OUL = d*(L+P) + z*s*SQRT(L+P) = 340*(2+2.8) + 2.33*27*SQRT(2+2.8) = 1770
Inventory position, IP = On hand + In transit = 245 + 630 = 875
Order quantity = OUL - IP = 1770 - 875 = 895
b) holding cost and ordering is not considered in this model, because in this model, inventory is reviewed on a fixed interval, rather than continuously.
c) Considering, L = 1 week
Order upto level, OUL = d*(L+P) + z*s*SQRT(L+P) = 340*(1+2.8) + 2.33*27*SQRT(1+2.8) = 1415
Inventory position, IP = On hand + In transit = 245 + 630 = 875
Order quantity = OUL - IP = 1415 - 875 = 540
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