Question 2 (50 marks) Shoe-R-Us buys leather soles from its supplier The Leather
ID: 2469411 • Letter: Q
Question
Question 2 (50 marks) Shoe-R-Us buys leather soles from its supplier The Leather Company (TLC). TLC offers volume discount to Shoe-R-Us as shown in the table below. The cost of placing an order is $10 at YOSR. Its annual inventory holding cost per unit is 20% of the unit price. The annual demand at Shoe-R-Us is about 625 pairs of soles. Determine the most cost-effective ordering policy for the leather soles at Shoe-R-Us. Step 1. Calculate EOQ assuming the lowest possible unit holding cost. Step 2. The EOQ amount found in Step 1 falls into the volume discount range __________________, whose unit price is ______________. Use this unit price to re-calculate EOQ. Step 3. Calculate the overall annual cost that includes total inventory cost and total cost of goods if Shoe-RUs uses the order quantity Q* calculated in Step 2. Step 4. The discount range next to the range of the EOQ found in Step 2 is __________________ , whose price is ____________ per pair. Calculate the overall annual cost that includes total inventory cost and total cost of goods if YOSR uses the smallest amount of the discount range as the order quantity. Step 5. Is there a discount range next to the range in Step 4? Yes No If Yes, that range is __________________ , whose price is ____________ per pair. Calculate the overall annual cost that includes total inventory cost and total cost of goods if Shoe-RUs determines that the order quantity equals to the smallest amount of the discount range. If No, go to Step 6. Step 6. Pick the lowest overall annual cost from those calculated in Step 3, 4, and 5, and determine the best order quantity that is associated with the lowest cost.
Pairs of soles in one order Price/Pair 1-50 $ 8.00 51-100 $ 7.60 101 and up $ 7.40Explanation / Answer
Given:
D = annual demand = 625 pairs of soles;
H = Holding cost = 20% of price = 8 * 20% = $1.6 per pair;
S =ordering cost = $10 per order
1. Calculate EOQ assuming the lowest possible unit holding cost.
Solution: formula for EOQ = Squareroot of 2DS / H
= Squareroot of 2*625 * 10 / 1.6
= Squareroot of 12,500 / 1.6
=Squareroot of 7,812.5
= 88.388 = rounded off to 88 pairs is the EOQ
Step 2. The EOQ amount found in Step 1 falls into the volume discount range 51 - 100, whose unit price is $7.6. Use this unit price to re-calculate EOQ.
Re-calculating EOQ = Squareroot of 2DS / H
here, H = Holding cost = 20% of price = 7.6 * 20% = $1.52 per pair
EOQ = Squareroot of 2*625 * 10 / 1.52
= Squareroot of 12,500 / 1.52
= Squareroot of 8,223.68
= 90.68 = rounded off to 91pairs is the re-calculated EOQ
Step 3. Calculate the overall annual cost that includes total inventory cost and total cost of goods if Shoe-RUs uses the order quantity Q* calculated in Step 2.
overall annual cost = total inventory cost + total ordering cost
total inventory cost = Average inventory * hosting cost per pair
= recalculated EOQ /2 * 1.52 = 91 / 2 * 1.52 = 45.5 * 1.52 = 69.16
total ordering cost = Number of orders * cost per order
= annual demand / EOQ * 10per order = 625 / 91 * 10 = 69
overall annual cost = total inventory cost + total ordering cost = 69.16 + 69 = $138.16
Step 4. The discount range next to the range of the EOQ found in Step 2 is 101 and up , whose price is $7.40 per pair. Calculate the overall annual cost that includes total inventory cost and total cost of goods if YOSR uses the smallest amount of the discount range as the order quantity.
overall annual cost = total inventory cost + total ordering cost
total inventory cost = Average inventory * hosting cost per pair
= recalculated EOQ /2 * (7.4 * 20%) = 91 / 2 * 1.48 = 45.5 * 1.48 = 67.34
total ordering cost = Number of orders * cost per order
= annual demand / EOQ * 10per order = 625 / 91 * 10 = 69
overall annual cost = total inventory cost + total ordering cost = 67.34 + 69 = $136.34
Step 5. Is there a discount range next to the range in Step 4? No Calculate the overall annual cost that includes total inventory cost and total cost of goods if Shoe-RUs determines that the order quantity equals to the smallest amount of the discount range. If No, go to Step 6.
order quantity equals to the smallest amount of the discount range
New EOQ =Squareroot of 2DS / H
here, H = Holding cost = 20% of price = 7.4 * 20% = $1.48 per pair
= Squareroot of 2*625 * 10 / 1.48
=Squareroot of 12,500 / 1.48
= Squareroot of 8,445.9
= 91.9 = rounded off to 92 pairs New EOQ
overall annual cost = total inventory cost + total ordering cost
total inventory cost = Average inventory * hosting cost per pair
= New EOQ /2 * (7.4 * 20%) = 92 / 2 * 1.48 = 46* 1.48 = 68.08
total ordering cost = Number of orders * cost per order
= annual demand / New EOQ * 10per order = 625 / 92 * 10 = 67.9
overall annual cost = total inventory cost + total ordering cost = 68.08 + 67.9 = $135.98
Step 6. Pick the lowest overall annual cost from those calculated in Step 3, 4, and 5, and determine the best order quantity that is associated with the lowest cost.
Frome the abouve 3 steps the lowest cost associated is step 5 i.e, cost = $135.98
and the new EOq = 92 pairs
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