Thomas Toys Ltd. uses a periodic review invenlory masagement system. One importa
ID: 328867 • Letter: T
Question
Thomas Toys Ltd. uses a periodic review invenlory masagement system. One important item for the company is building blocks, which sell, on average, five sets per day. How ever, the standard deviation of demand is two sets per day. The company checks the staas of inventory for building blocks every 21 days. When blocks are reondered from the plier, it takes 14 days to be replenished. Thomas has just checked its inventory and found that it currently has 160 sets in stock. The company desires to maintain a 975 percent service level. How many sets of building blocks should Thomas Toys arder? Plastics makes and sells, among many other things, specialty plastic display Johnson cases for retail stores. Johnson's expected demand for the display cases is 1,000 units, and average daily demand is 4 units. The production process is most efficient when 16 units per day are produced at a cost of $100 per unit. Setup cost is $$0. Inventory carrying cost at Johnson is determined to be 10 percent annually. What is the best pro- duction order quantity, and how many days is a required production run? Concert Productions is planning an appearance of the top band Iggy Wiggy. It plans to buy custom-designed t-shirts to sell at the stadium where the concert will take place. The t-shirt will sell for $25.00 and the cost per shirt is $8.00. Previous experience at Concert Productions suggests that after the concert is over, t-shirts can still be sold, but the selling price will be only $5.00 per shirt. Based on analysis of previous similar concerts, the company estimates sales of the t-shirt will be 6,000 units. However, the analysis also shows that the standard deviation in similar situations is 800 units. How many Iggy Wiggy t-shirts should the company order?Explanation / Answer
Answer to first question :
Average demand for building blocks = m = 5 per day
Standard deviation of daily demand = Sd = 2 per day
Review interval = T = 21 days
Lead time of supply = L = 14
Therefore , Protection period = P = T + L = 35 days
Z value for 97.5 percent service level = NORMSINV ( 0.975 ) = 1.96 ( rounded to 2 decimal places )
Therefore standard deviation of demand during protection period
= Sd x Square root ( P )
= 2 x Square root ( 35 )
= 2 x 5.916
= 11.832
Safety stock = Z value x Standard deviation of demand during protection period = 1.96 x 11.832 = 23.19
Reorder point = Average daily demand x Protection period + safety stock = 5 x 35 + 23.19 = 175 + 23.19= 198.19 ( 198 rounded to nearest whole number )
Number of building blocks currently in stock = 160
Therefore , number of building blocks Thomas Toy should order = reorder point – Quantity in stock = 198 – 160 = 38
NUMBER OF BUILDING BLOCKS THOMAS TOY SHOULD ORDER = 38
Answer to second question :
Given are following details :
Annual demand = D = 1000 units
Daily demand = d = 4 units
Daily production rate = p = 16 units
Set up cost = Cs = $ 50
Annual unit inventory cost = Ch = 10 percent of $100 = $10
Best production quantity ( EPQ )
= Square root ( 2 x Cs x D / Ch x ( 1 – d/p))
= Square root ( 2 x 50 x 1000 / 10 x ( 1 – 4/16))
= Square root ( 2 x 50 x 1000/ 10 x 0.75 )
= 115.47 ( 115 rounded to nearest whole number )
Number of days of production run = EPQ/ daily production capacity,= 115/16 = 7.187 days
BEST PRODUCTION ORDER QUANTITY = 115
NUMBER OF DAYS OF PRODUCTION RUN = 7.187 DAYS
Answer to third question :
Selling price of t shirt = P = $25
Cost of t shirt = C = $8
Salvage price of t shirt = S = $5
Therefore ,
Underage cost = Cu = P – C = $25 - $ 8 = $17
Overage cost = Co = C – S = $8 - $5 = $3
Therefore,
Critical ratio = Cu / ( Cu + Co ) = 17 / 17 + 3 = 17/20 = 0.85
Critical ratio is the in stock probability
Therefore in stock probability = 0.85
Corresponding Z value = NORMSINV ( 0.85 ) = 1.0364
Estimated sale of t shirt = m = 6000
Standard deviation of sale of t shirt = Sd = 800
Therefore,
Number of T shirts to be ordered = m + Z x Sd = 6000 + 1.0364 x 800 = 6000 + 829.12 = 6829.12 ( 6829 rounded to nearest whole number )
NUMBER OF T SHIRT COMPANY SHOULD ORDER = 6829
NUMBER OF BUILDING BLOCKS THOMAS TOY SHOULD ORDER = 38
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