EXERCISES 11.1 A product used in a laboratory of the hospital costs $60 to order
ID: 457854 • Letter: E
Question
EXERCISES
11.1 A product used in a laboratory of the hospital costs $60 to order, and its carrying cost per item per week is one cent. Demand for the item is six hundred units weekly. The lead time is three weeks and the purchase prices is $0.60.
a. What is the economic order quantity for this item?
b. What is the length of an order cycle?
c. Calculate the total weekly costs.
d. What is the investment cost for this item?
e. If ordering costs increase by 50 percent, how would that affect EOQ?
f. What would be the reorder point for this item if no safety stocks were kept?
g. What would be the reorder point if one thousand units were kept as safety stock?
Economic Ordering Quantity (EOQ) Model Demand [D] (week or year) 800 Ordering Cost [S] 30 Carrying Cost/item [H]* 50 Price of the Item [p] 250 EOQ = 31 Order Cycle = 25.8 times (in a week or year) Average Inventory = 15 Holding Cost = $774.60 Carrying Cost = $774.60 Total Cost = $1,549.19 Investment Cost = $7,745.97 (If price of item is known) * must be calculated as same period length of Demand.Explanation / Answer
Weekly Demand(d)=600 Annual Demand(D)=600*365/7= 31286 Ordering Cost(O)=60 Carrying Cost per unit/week=0.01 per unit Carrying cost per unit per yr(H)=0.01*365/7= 0.521429 Purchase price(P)=0.6 Lead time(L)=3 weeks a) EOQ=sqrt(2*D*O/H)=sqrt(2*31286*60/0.5214)= 2683 b)Length of order cycle= 365/number of orders=(365/annual demand)*EOQ=365*2683/31286= 31.30138 days c) Total Weekly Cost= (total annual cost/365)*7= (D*O/EOQ+EOQ*H/2)*(7/365) (31286*60/2683+2683*0.5214/2)*(7/365)= 26.8322 d)Total Investment Cost=Total Annual cost+price*annual demand=(31286*60/2683+2683*0.5214/2)+0.6*31286 Cost= 20170.71 e) if the ordering cost increases by 50% the EOQ will increase by sqrt(1.5)= 1.224745 times f) Reorder point=weekly dmeand*lead time=600*3=1800 g) Reorder point with safety stock=weekly demand*lead time +safety stock=1800+1000=2800
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