Ollah\'s Organic Pet Shop sells bags of cedar chips for pet bedding or snacking
ID: 425433 • Letter: O
Question
Ollah's Organic Pet Shop sells bags of cedar chips for pet bedding or snacking (buyer's choice). The supplier has offered Ollah the following terms Order 1- 300 bags, and the price is $7.25 a bag Order 301 or more bags, and the price is $5.00 a bag Annual demand is 860, fixed ordering costs are $5 per order, and the per-bag holding cost is estimated to be around $3 per year Click the icon to view the table of z values a. The economic order quantity for the bags is. (Enter your response rounded to the nearest whole number.) b. Ollah should order bags at a time to take advantage of the lower cost per unit. (Enter your response rounded to the nearest whole number.) c. Suppose the lead time for bags is a constant 1.2 weeks, and average weekly demand is 12.8 bags, with a standard deviation of 1.5 bags. If Ollah wants to maintain a 95% service level, what should her reorder point be? The reorder point is bags. (Enter your response rounded up to the nearest whole number.) More Info z value 1.28 1.65 2.05 2.33 3.08 Associated service level 90% 95% 98% 99% 99.9% Print Done Enter your answer in each of the answer boxesExplanation / Answer
Answer to question # a :
Following details are provided :
Annual demand = D = 860
Ordering cost = Co = $5 per order
Annual unit holding cost per bag = Ch = $3
Economic order quantity ( EOQ ) which minimizes total cost of annual ordering cost plus annual inventory holding cost
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 5 x 860 / 3 )
= 53.54 ( 54 rounded to nearest whole number )
THE ECONOMIC ORDER QUANTITY FOR THE BAG = 54
Answer to question #b :
We will compare total cost for EOQ of 54 bags vs order quantity of 301 bags ( which is the starting point of the next quantity slab )
Total cost = Annual purchasing cost + Annual ordering cost + Annual holding cost
Annual ordering cost
= Ordering cost x Number of orders in a year
= Ordering cost x Annual demand / order quantity
Annual inventory holding cost
= annual unit inventory holding cost x average inventory
= annual unit inventory cost x Order quantity / 2
Annual purchase cost = Unit cost x annual demand
Data for order quantity = 54 bags :
Annual ordering cost = $ 5 x 860/54 = $79.63
Annual inventory holding cost = $3 x 54/2 = $81
Annual purchasing cost = $7.25 x 860 = $6235
Total annual cost = $79.63 + $81 + $6235 = $6395.63
Data for order quantity = 301 :
Annual ordering cost = $ 5 x 860/301 = $14.28
Annual inventory holding cost = $ 3 x 301/2 = $451.50
Annual purchasing cost = $5 x 860 = $4300
Total annual cost = $14.28 + $451.50 + $4300 = $4765.78
Since total annual cost is less for order quantity of 301 , same should be ordered
OLLAH SHOULD ORDER 301 BAGS AT A TIME TO TAKE ADVANTAGE OF LOWER COST PER UNIT
Answer to question c :
Weekly standard deviation of demand = 1.5 bags
Lead time = 1.2 weeks
Therefore , standard deviation of demand during lead time = 1.5 x square root ( 1.2) = 1.5 x 1.0954 = 1.6431
Z value for 95% service level = 1.65
Therefore ,
Safety stock = Z value x Standard deviation of demand during lead time = 1.65 x 1.6431= 2.71
Reorder point
= average weekly demand x lead time (weeks) + safety stock
= 12.8 x 1.2 + 2.71
=15.36 + 2.71
= 18.07 ( 18 rounded to nearest whole number )
THE REORDER POINT IS 18 BAGS
THE ECONOMIC ORDER QUANTITY FOR THE BAG = 54
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