Week Five Homework Assignment - Inventory Control

Current Ordering Model

A wholesale distributor stocks and sells low flow toilets to contractors for use in commercial office buildings. The estimated annual demand for the toilets is 5,475 units. The estimated average demand per day is 15 units. The purchase cost from the toilet manufacturer is $125.00 per unit. The lead time for a new order is 3 days. The ordering cost is $100.00 per order. The average holding cost per unit per year is $2.50. The distributor has traditionally ordered 250 units each time they placed an order. Answer questions 1-5 based upon the preceding information regarding the distributor’s current ordering model.

1. What is the average number of units in inventory based upon ordering 250 units each time an order is placed?

o 250o 125o 75o 140

2. How many orders per year will be necessary based upon ordering 250 units each time an order is placed?

o 40o 67o 22o 357

3. What is the average dollar value of inventory based upon ordering 250 units each time an order is placed?

o $31,250.00o $9,375.25o $17,500.50o $15,625.00

4. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon ordering 250 units each time an order is placed?

o $626,125.00o $578,900.00o $721,345.25o $686,877.50

5. What is the optimal reorder point based upon ordering 250 units each time an order is placed?

o 30o 45

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o 60o 15

Economic Order Quantity (EOQ) Model

The president of the wholesale distributor has recently heard about the EOQ model and is interested in learning whether or not using this model would allow the company to reduce its annual costs by optimizing the number of orders placed each year and the number of toilets purchased in each order. The estimated annual demand for the toilets, estimated average demand per day, purchase cost from the toilet manufacturer per unit, lead time for a new order, ordering cost per order and average holding cost per unit per year remain the same as stated in the scenario for the current ordering model. Answer questions 6-11 based upon using the EOQ model.

6. What is the economic order quantity (EOQ) that will minimize inventory costs?o 661.8o 456.5o 371.7o 278.3

7. What is the average number of units in inventory based upon ordering using the EOQ?o 343.6o 228.3o 330.9o 139.2

8. What is the average dollar value of inventory based upon ordering using the EOQ?o $48,135.10o $21,750.01o $35,735.76o $41,363.48

9. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon using the EOQ?

o $721,100.42o $686,029.54o $578,900.29o $652,380.39

10. What is the optimal reorder point based upon using the EOQ?o 30o 45o 60o 75

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11. How many orders per year will be necessary based upon using the EOQ?o 20.5o 15.9o 23.4o 29.1

EOQ Without Instantaneous Receipt Model (a.k.a., Production Run Model)

The wholesale distributor has traditionally relied upon an instantaneous receipt model in which the material associated with each order is received in a single batch. The toilet manufacturer has suggested to the president of the wholesale distributor that he might want to consider agreeing to accept receipt of ordered material incrementally over a period of time rather than in a single batch as a means for reducing total annual costs. The toilet manufacturer has advised that his factory’s daily production rate is 20 toilets and the set-up cost for each production run is $250. The estimated annual demand for the toilets, estimated average demand per day, purchase cost from the toilet manufacturer per unit, lead time for a new order, ordering cost per order and average holding cost per unit per year remain the same as stated in the scenario for the current ordering model. Answer questions 12-18 using the EOQ without instantaneous receipt model (production run model) in which goods are incrementally delivered at the same they are being still being produced.

12. What is the optimal order quantity without instantaneous receipt (material is accepted over time)?

o 2,092.84o 980.65o 580.38o 350.78

13. What is the maximum number of units in inventory without instantaneous receipt (material is accepted over time)?

o 265.98o 416.33o 326.87o 523.21

14. What is the average number of units in inventory without instantaneous receipt (material is accepted over time)?

o 132.99o 132.59o 261.61o 208.17

15. What is the average dollar value of inventory without instantaneous receipt (material is accepted over time)?

o $20,430.00

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o $32,700.70o $26,020.82o $10,373.75

16. What is the total annual cost (i.e., Purchase Cost + Ordering Cost + Holding Cost) without instantaneous receipt (material is accepted over time)?

o $685,683.03o $627,081.67o $578,893.72o $652,480.15

17. What is the optimal reorder point without instantaneous receipt (material is accepted over time)?

o 30o 45o 50o 57

18. How many set-ups per year will be necessary without instantaneous receipt (material is accepted over time)?

o 1.65o 7.89o 4.41o 2.62

Quantity Discount Model

The toilet manufacturer has proposed a quantity discount schedule for toilets as reflected in the following table for consideration by the president of the wholesale distributor as a means to potentially reduce his total annual costs.

Discount Number Quantity Ordered Unit Cost Discount1 0 to 1,000 0%2 1,001 to 2,000 10%3 2,001 and over 15%

The estimated annual demand for the toilets, estimated average demand per day, purchase cost from the toilet manufacturer per unit, lead time for a new order, ordering cost per order and average holding cost per unit per year remain the same as stated in the scenario for the current ordering model. Answer questions 19 and 20 based upon using the quantity discount model.

19. What order quantity will allow the wholesale distributor to minimize their total annual inventory costs (Purchase Cost + Ordering Cost + Holding Cost) by taking advantage of the proposed discount pricing?

o 250

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o 751o 2,001o 662

20. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon taking advantage of the proposed discount pricing?

o $626,128.89o $601,698.43o $584,118.43o $487,998.00

Minimizing Total Annual Costs

21. Which ordering model is least effective with regard to minimizing total annual cost (i.e., results in the highest total annual cost)?

o Current ordering modelo EOQ modelo Production run modelo Quantity discount model

22. Which ordering model is most effective with regard to minimizing total annual cost (i.e., results in the lowest total annual cost)?

o Current ordering modelo EOQ modelo Production run modelo Quantity discount model

Safety Stock

The president of the wholesale distributor is concerned about the possibility of stockouts causing a loss of customer confidence and loyalty and is interested in maintaining safety stock in inventory to prevent potential stockouts. Answer questions 23 through 25 based upon using the safety stock models.

23. Assuming demand is normally distributed with a mean of 15 units and a standard deviation of 3 units, and a constant lead time of 3 days, what is the reorder point necessary to provide a 97% level of service?

o 54.77o 45.14o 34.41o 60.49

24. Assuming demand is constant at 15 units per day, and lead time is normally distributed with a mean of 3 days and a standard deviation of 1 day, what is the reorder point necessary to provide a 97% level of service?

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o 80.48o 64.87o 73.21o 53.18

25. Assuming that demand is normally distributed with a mean of 15 units and a standard deviation of 3 units, and lead time is normally with a mean of 3 days and a standard deviation of 1 day, what is the reorder point necessary to provide a 97% level of service?

o 59.69o 81.20o 66.46o 74.86

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