2. Periodic Review System (P-System) or Periodic Order Quantity (POQ) or Fixed Interval Reorder System or...

2. Periodic Review System (P-System) or Periodic Order Quantity (POQ) or Fixed Interval Reorder System or Periodic Reorder System. (10 Points)

Wood County Hospital consumes 1,000 boxes of bandages per week and the hospital operates 52 weeks per year.
The price of bandages (v) is $ 35 per box and the cost of holding one box for a year is 15 percent of the value of the material (r).
The cost of processing an order is $ 15.
Demand is normally distributed, with a standard deviation of weekly demand of 100 boxes (Sigma t).
The lead time is 2 weeks (L).
Cycle-service level is 97 percent.

A. What is the EOQ for this item?

B. What is the time between reviews or P in weeks? Please do not round the number.

C. What is the average demand during the production interval (Xbar P+L)?

D. What is the desired safety stock (SS)?

E. What is the target inventory level (T)?

F. What is the ordering cost at the lot size of EOQ?

G. What is the holding cost at the lot size of EOQ?

H. What the safety stock cost?

i. What is the total cost?

Solutions

Expert Solution

Average weekly demand, d = 1,000 boxes
No. of weeks per year = 52
Unit price, C = $35
Unit holding cost, h = 15% of C = $5.25
Order processing cost, K = $15
The standard deviation of weekly demand, σ_t = 100 boxes
Average lead time, L = 2 weeks
CSL = 97%

Annual demand, D = 52*d = 52,000

EOQ = Q^* = (2.D.K / h)^1/2 = SQRT(2*52000*15 / 5.25) = 545 units

The time between reviews, P = EOQ / d = 545 / 1000 = 0.545 weeks

X̄_P+L = d.(P+L) = 1000*(0.545+2) = 2,545 units

CSL = 97%, So, Z = Normsinv(0.97) = 1.88

Safety stock (SS) = Z.σ_t.√(P+L) = 1.88*100*√2.545 = 300 units

Target Inventory level, T = X̄_P+L + SS = 2545 + 300 = 2,845 units

Annual ordering cost = (D/Q^*) * K = (52000/545)*15 = $1,431.19

Annual holding cost = (Q^*/2) * h = (545/2)*5.25 = $1,430.63

Safety stock cost = SS * h = 300*5.25 = $1,575

Total annual cost = Annual ordering cost + Annual holding cost + Safety stock cost + Annual cost of purchase

= 1,431.19 + 1,430.63 + 1,575 + 52000*35

= 1824436.82

keosha answered 2 months ago

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