Question

In: Operations Management

The Waterworks Plumbing Supply Company stocks thousands of plumbing items sold to regional plumbers, contractors and...

The Waterworks Plumbing Supply Company stocks thousands of plumbing items sold to regional plumbers, contractors and retailers. James Sullivan, the firm’s general manager, wonders how much money could be saved annual if an Inventory Model was defined/used instead of the firm’s present rules of thumb, to determine an Optimal Inventory Policy. Material #3925 is externally sourced.

Because Waterworks supplies hundreds of regional plumbers, contractors and retailers, their operation experiences a probabilistic demand; in fact, the number of units demanded varies considerably from day-to-day and from week-to-week. Historical sales data (for Material #3925) indicate that demand during a one-week lead time can be described as having a Normal Probability Distribution with a mean of 190 units and a standard deviation of 35 units (1 unit = 1 brass valve, Material #3925).

Mike Wazowski develops the following estimates from accounting information:

Cost per valve = $1.60

Annual Inventory Holding Rate = 25%

Ordering Cost (per order) = $5.50

Working Days per Year = 250

Lead Time = 5 days

James Sullivan is willing to tolerate a stock-out rate of 5%. What is the recommended inventory decision (i.e., the order quantity and the reorder point)? And, how much Safety Stock will be made available to absorb higher-than-usual demand during the lead time? What is the associated cost of the Safety Stock? Finally, what is the anticipated Total Annual Cost for this inventory system/policy?

Expert Solution

Given are following data :

Annual demand = D = 190/ week x 52 weeks = 9880

Ordering cost = Co = $5.50

Annual inventory holding cost = Ch = 25% of $1.60 = $0.40

Optimum order quantity ( EOQ )

= Square root ( 2 x Co x D/Ch )

= Square root ( 2 x 5.50 x 9880/0.40)

= 521.24 ( 521 rounded to nearest whole number )

Standard deviation of weekly ( i.e. 7 days ) demand = 35

Lead time = 5 days

Therefore, standard deviation of demand during lead time of 5 days = 35 x Square root ( 5/7 ) = 29.58

In stock probability ( since stockout rate is 5% ) = 95% (or, 0.95 )

Z value for in stock probability of 0.95 = NORMSINV ( 0.95 ) = 1.6448

Therefore safety stock = Z value x standard deviation of demand during lead time of 5 days = 1.6448 x 29.58 = 48.653 ( 49 rounded to nearest whole number )

SAFETY STOCK = 49

Daily demand = Weekly demand / 7 = 190/7

Reorder point = Daily demand x Lead time of 5 days + safety stock = 190/7 x 5 + 49 = 135.71 + 49 = 184.71 ( 185 rounded to nearest whole number )

REORDER POINT = 185

Annual cost of safety stock = Annual inventory holding cost x Safety stock = $0.40 x 49 = $19.60

Total annual inventory cost = ( EOQ/2 + safety stock ) x Ch = ( 521/2 + 49 ) x $0.40 = ( 260.5 + 49) x $0.40 = $ 309.5 x0.40 = $123.8

Total annual ordering cost = Ordering cost x Number of orders = Ordering cost x annual demand/ EOQ= $5.50x 9880/521 = $104.30

Total annual purchasing cost = Cost/ valve x annual demand for valves = $1.60 x 9880 = $15808

Anticipated total annual cost for this inventory policy

= Total annual purchasing cost + Total annual inventory cost + Total annual purchasing cost

= $15808 + $123.80 + $104.30

= $16036.10 ( $16036 rounded to nearest whole number )

ANTICIPATED TOTAL ANNUAL COST FOR THIS INVENTORY SYSTEM = $16036

keosha answered 9 months ago

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