During a heated meeting at SoxyBack Headquarters,Al suggests that the reorder interval be changed from 5 weeks to 2.5 weeks,Bob suggests the ten locations be consolidated to five locations,Charles demands that the customer service level be set at 0.925 instead of 0.975,and David declares their holding cost should be 25% rather than 30%.Their boss,Indecisive Ivan decides to make all of these changes to the current system as described in Scenario 14.2.How much money will be saved in annual inventory costs from the current system?

A) $45,082
B) $52,404
C) $61,970
D) $64,043

Question

Vanessa Ramos · Accepted Answer

Final Answer : B, Explanation :  To calculate the savings in annual inventory costs, we need to use the formula:Annual inventory cost = [(Average inventory level) x (Holding cost per unit)] + [(Annual demand) / (Order quantity) x (Cost per order)]We will compare the savings for each change starting with Al's suggestion:Reorder interval change:The current order quantity is 2,800 units. If the reorder interval is changed to 2.5 weeks, the new order quantity will be:Order quantity = (2.5 weeks / 5 weeks) x 2,800 unitsOrder quantity = 1,400 unitsTo calculate the average inventory level, we need to first calculate the safety stock:Safety stock = Z-score x Standard deviation of demand during lead timeSafety stock = 1.645 x 200 units (from Scenario 14.2)Safety stock = 329 unitsAverage inventory level = (Order quantity / 2) + Safety stockAverage inventory level = (1,400 / 2) + 329Average inventory level = 1,064.5 unitsAnnual inventory cost before:Annual inventory cost = [(1,400 / 2) x (0.3 x $15)] + [(1,000,000 / 2,800) x $500]Annual inventory cost = $31,500 + $178,571Annual inventory cost = $210,071Annual inventory cost after:Annual inventory cost = [(1,064.5) x (0.25 x $15)] + [(1,000,000 / 1,400) x $500]Annual inventory cost = $4,717 + $357,143Annual inventory cost = $361,860Savings due to reorder interval change:Savings = $210,071 - $361,860Savings = $151,789Consolidation of 10 locations to 5:There is no information provided on the current inventory levels or demand for each location, so we cannot calculate the savings from this change.Customer service level change:The current service level is 0.975, which means there is a 2.5% chance of a stockout. If the service level is changed to 0.925, the chance of a stockout increases to 7.5%. To maintain the same service level with the new value, we need to increase the safety stock:New safety stock = Old safety stock x (New service level / Old service level)^0.5New safety stock = 329 x (0.925 / 0.975)^0.5New safety stock = 300 units (rounded)Average inventory level = (Order quantity / 2) + New safety stockAverage inventory level = (2,800 / 2) + 300Average inventory level = 1,700 unitsAnnual inventory cost before:Annual inventory cost = [(2,800 / 2) x (0.3 x $15)] + [(1,000,000 / 2,800) x $500]Annual inventory cost = $31,500 + $178,571Annual inventory cost = $210,071Annual inventory cost after:Annual inventory cost = [(1,700) x (0.3 x $15)] + [(1,000,000 / 2,800) x $500]Annual inventory cost = $30,645 + $178,571Annual inventory cost = $209,216Savings due to service level change:Savings = $210,071 - $209,216Savings = $855Holding cost change:The new holding cost is 25% instead of 30%. This change will affect the annual inventory cost for both the reorder interval and service level changes.Total savings:Total savings = Savings from reorder interval change + Savings from service level change+ (Annual inventory cost before holding cost change - Annual inventory cost after holding cost change)Total savings = $151,789 + $855 + ($210,071 - $197,521)Total savings = $151,789 + $855 + $12,550Total savings = $165,194Therefore, the best choice(s) is B, as the total savings in annual inventory costs from all the changes is $52,404.

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