Groundz Coffee Shop uses 4 pounds of a specialty tea weekly; each pound costs $1
ID: 447837 • Letter: G
Question
Groundz Coffee Shop uses 4 pounds of a specialty tea weekly; each pound costs $16. Carrying costs are $1 per pound per week because space is very scarce. It costs the firm $8 to prepare an order. Assume Groundz is open 52 weeks per year, and closed on Mondays.
a. How many pounds should Groundz order at a time?
b. What is the total annual cost of managing this item?
c. The lead time for orders to arrive is 1.5 (work) weeks. If the standard deviation of weekly demand is 1.2 pounds, and Groundz wishes to achieve at least a 98% customer satisfaction level, what is the reorder point?
d. Groundz has been contacted by a new supplier who is offering to sell the same tea for $12 per pound. In return, Groundz can place orders only once a month. Inventory and ordering costs would remain the same. Is it more cost-effective for Groundz to switch suppliers? Should Groundz switch?
Explanation / Answer
Yes it is cost effective to switch suppliers as total cost reduces from $3744 to $3060 and hence Groundz should switch
Annual Demand (4*52) 208 Ordering Cost $ 8.00 Holding Cost - $1 per week $ 52.00 a. EOQ = 2AO / H where A = Annual Demand O = Ordering Cost per order H = Holding Cost per unit per annum EOQ = 2AO / H = (2 * 208 * 8) / 52 = 8 units Groundz should order 8 pounds per week Total Holding Cost (Average Inventory * Holding Cost per unit = EOQ/2 * $52) (A) $208.00 Total Ordering Cost (No of orders * Ordering Cost = Annual Demand/EOQ * $8) (B) $208.00 Total Annual Cost of Managing this item (A+B) $416.00 Mean Demand 4 Standard Deviation of Weekly Demand (SDw) 1.2 Lead Time (weeks) 1.5 Standard Deviation of Lead Time (SDl) = SDw * Lead Time = 1.2*1.5 = 1.47 1.47 Service Level Desired 98% Z Value at 98% 2.054 Safety Stock for 98% service level Z value * Standard Deviation (Demand Lead Time) = 2.054 * 1.47 3 Lead Time Demand ( Lead Time * Avg Demand = 1.5 * 4) 6 Reorder Point = Lead Time Demand + Safety Stock 9 Current Order Cycle = 208/8 = 26 orders per year As per new proposal, number of orders = 12 Order Size = Annual Demand / No of orders = 208/12 = 18 (Rounding Off) Average Inventory = Order Size / 2 = 18 / 2 = 9 Inventory Order Size (A) 18 8 Price (B) $12.00 $16.00 Direct Cost (Price * Annual Demand = B*208) (C) $2,496.00 $3,328.00 No of orders (Annual Demand/Order Quantity per order = 208 / A) (D) 12 26 Ordering Cost (No orders * $ 8 = D *$8) ( E) $96.00 $208.00 Carrying Cost per unit (F) $52.00 $52.00 Carrying Cost (Order Size / 2 * Carrying Cost per unit per annum = A/2 * F) (G) $468.00 $208.00 Total Cost (B+E+G) $3,060.00 $3,744.00Related Questions
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