SCM-2230-A01, HW 2

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University of Manitoba *

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Industrial Engineering

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Jan 9, 2024

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docx

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1. Amazon sells 20,000 units of consumer electronics from Samsung every month. Each unit costs $100 and Amazon has an annual holding cost of 20 percent. The fixed clerical and transportation cost for each order Amazon places with Samsung is $4,000. What is the optimal size of the order that Amazon should place with Samsung? With the goal of reducing inventories, Amazon would like to reduce the size of each order it places with Samsung to 2,500 units (allowing it to get eight replenishment orders every month). How much should it reduce the fixed cost per order for an order of 2,500 units to be optimal? D = 240,000/year, C = $100/unit, S =$ 4000/lot, h = 0.2 a. Q = SQRT((2*240,000*4000)/(0.2*100)) = 9,798 a. For Q = 2,500 to be optimal, amazon must reduce its fixed cost per order to S = 260.42, reducing fixed costs by 3,739.58 2. Amazon sells 10,000 Lenovo PCs every month. Each PC costs $500 and Amazon has an annual holding cost of 20 percent. For what fixed cost per order would an order size of 10,000 units be optimal? For what fixed cost per order would an order size of 2,500 units be optimal? D = 120,000/year, C = $500/unit, h = 0.2 a. 2,500 = SQRT((2*120,000*S)/(0.2*500)), S = $2604/lot a. 10,000 = SQRT((2*120,000*S)/(0.2*500)), S = $41,667/lot 3. A steel rolling mill can produce I-beams at the rate of 20 tons per week. Customer demand for the beams is 5 tons per week. I-beams cost the mill $2,000 per ton and the mill has an annual holding cost of 25 percent. To produce I-beams, the mill must go through a setup that requires changing to the appropriate rolling patterns. The mill would like to produce I-beams in batches of 40 tons (resulting in a production batch every eight weeks). For what changeover cost would this batch size be optimal? D = 260/year, C = $2,000, h = 0.25, P = 1040/year 40 = SQRT((2*Cc*260)/((2,000*0.25)*(1 – 260/1040))), Cc = $1154 4. Demand for fasteners at W.W. Grainger is 20,000 boxes per month. The holding cost at Grainger is 20 percent per year. Each order incurs a fixed cost of $400. The supplier offers an all unit discount pricing scheme with a price of $5 per box for orders under 30,000 and a price of $4.90 for all orders of 30,000 or more. How many boxes should Grainger order per replenishment? D = 240,000/year, h = 0.2, S = $400/lot
C ₀ = $5, C ₁ = $4.90 q ₀ = 0, q ₁ = 30,000 Q ₀ = SQRT((2*240,000*400)/(0.2*5)) = 13,856 Q ₁ = SQRT((2*240,000*400)/(0.2*4.9)) = 13,997 Adjusted to q: Q ₀ = 13,856, Q ₁ = 30,000 TC ₀ = ((240,000/13,856)*400)+((13,856/2)*0.2*5)+(240,000*5) = $1,213,856 TC ₁ = ((240,000/30,000)*400)+((30,000/2)*0.2*4.9)+(240,000*4.9) = $1,193,900 TC ₁ < TC ₀ ∴ Order Q ₁ = 30,000 per lot at a price of C ₁ = $4.90 5. Now, consider Exercise 13 with a marginal unit quantity discount. Demand for fasteners at W.W. Grainger is 20,000 boxes per month. The holding cost at Grainger is 20 percent per year. Each order incurs a fixed cost of $400. The supplier offers a marginal unit discount pricing scheme with a price of $5 per box for the first 30,000 and a price of $4.90 per unit for each unit above 30,000 in an order. How many boxes should Grainger order per replenishment? D = 240,000/year, h = 0.2, S = $400/lot C ₀ = $5, C ₁ = $4.90 q ₀ = 0, q ₁ = 30,000 V ₀ = 0, V ₁ = 5*(30,000-0) = $150,000 Q ₀ = SQRT((2*240,000*(400+0-(0)))/(0.2*5)) = 13,856 Q ₁ = SQRT((2*240,000*(400+150,000-(30,000*4.9)))/(0.2*4.9)) = 40,808 Adjusted to q: Q ₀ = 13,856, Q ₁ = 40,808 TC ₀ = ((240000/13856)*400)+((0+(13856-0)*5)*(0.2/2))+((240000/13856)*(0+(13856- 0)*5)) = 1,213,856 TC ₁ = ((240000/40808)*400)+((150000+(40808-30000)*4.9)*(0.2/2))+ ((240000/40808)*(150000+(40808-30000)*4.9)) = 1,216,292 TC ₀ < TC ₁ ∴ Order Q ₀ = 13,856 per lot at a price of C ₀ = $5
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