Assignment 4: Part (A) Problem 1: A toy manufacturer uses approximately 32000 silicon chips annually. The Chips are used at a steady rate during the 240.

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Presentation transcript:

Assignment 4: Part (A) Problem 1: A toy manufacturer uses approximately 32000 silicon chips annually. The Chips are used at a steady rate during the 240 days a year that the plant operates. Annual holding cost is 60 cents per chip, and ordering cost is $24. Determine a) How much should we order each time to minimize our total cost b) How many times should we order c) what is the length of an order cycle (working days 288/year) d) What is the total cost

What is the Optimal Order Quantity D = 32000, H = .6, S = 24

How many times should we order Annual demand for a product is 9600 D = 32000 Economic Order Quantity is 1600 EOQ = 1600 Each time we order EOQ How many times should we order ? D/EOQ 32000/1600 = 20

what is the length of an order cycle working days = 240/year 32000 is required for 240 days 1600 is enough for how many days? (1600/32000)(240) = 12 days

What is the Optimal Total Cost The total cost of any policy is computed as The economic order quantity is 1600 This is the total cost of the optimal policy

Assignment 4: Part (B) A small manufacturing firm uses approximately 3400 pounds of chemical dye per year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The ordering cost is $100 and inventory carrying cost is 51 cents per unit per year. D= 3400, S= 100, H=.51 a) The supplier has just announced that orders of 1000 pounds and more will be filled at a price of $2 per pound. Determine the order size that will minimizes the total cost. b) If the supplier offered a discount at 1500 pounds instead of 1000 pounds, what order size will minimize total cost?

Ordering and Carrying Costs The Total-Cost Curve is U-Shaped Annual Cost Ordering Costs QO (optimal order quantity) Order Quantity (Q)

Total Cost Cost Adding Purchasing cost doesn’t change EOQ TC with PR TC without PR PR EOQ Quantity

Price Discount p1 Cost p2 Quantity

Total Cost Including Purchasing Cost EOQ Quantity

Total Cost Including Purchasing Cost EOQ Quantity

Total Cost Including Purchasing Cost Quantity Q

Total Cost Including Purchasing Cost EOQ Quantity

The Problem A small manufacturing firm uses approximately 3400 pounds of chemical dye per year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The ordering cost is $100 and inventory carrying cost is 51 cents per unit per year. D=3400, S= 100, H=.51 a) The supplier has just announced that orders of 1000 pounds and more will be filled at a price of $2 per pound. Q P 0-999 3 ≥1000 2

The Problem A small manufacturing firm uses approximately 3400 pounds of chemical dye per year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The ordering cost is $100 and inventory carrying cost is 51 cents per unit per year. D=3400, S= 100, H=.51 b) Determine the order size that will minimizes the total cost. If the supplier offered a discount at 1500 pounds instead of 1000 pounds, what order size will minimize total cost? Q P 0-... 3 ≥1500 2

Assignment D= 3400, S=100, H= .51 TC = HQ/2 + SD/Q + PD b) If the supplier offered a discount at 1500 pounds instead of 1000 pounds, what order size will minimize total cost? Q P 0-... 3 ≥1500 2 D= 3400, S=100, H= .51 TC = HQ/2 + SD/Q + PD TC ( Q = 1155 , P = 3) = .51(1155)/2 + 100(3400)/1155 + 3(3400) TC = 294.5 + 294.5 + 10200 = 10789 TC ( Q = 1500 , P = 2) = .51(1500)/2 + 100(3400)/1500 + 2(3400) TC = 382.5+226.7 +6800 = 7409.2