Question

1.    This basic information applies to all of the related questions:

Alpha Assemblies produces a wide variety of products in their central Nebraska facility. Many of these products fit within a line of standard truck and trailer parts. Within this is a set of hitches that can be made in two sizes (1-1/4 and 2) and three strengths (light duty, medium duty, and heavy duty). All of the hitches in this line have "natural" finishes so no additional steps are necessary after they are cast. The machine used to cast these six hitch variations is available for 2000 hours per year. Operators are paid $15.00 per hour including benefits.

Simone is working to establish her reputation at Alpha Assemblies as part of her internship opportunity. She is looking for a way to improve the operations. She has been working on the hitch project and is looking at possible ways to cut costs. At this point she has studied the processes and their associated costs, and completed forecasts for the next year's demand.

Hitch A is the 1-1/4 inch, light duty, natural hitch. Simone has forecast the demand for this hitch at 6,000 units for the next year. It takes one operator 5.2 hours to perform a setup to produce a batch for this hitch and no other setup costs are incurred when setting up the machine. In addition, the holding costs for this item are $4.19 per unit per year. This hitch has a current batch size of 1,500 units per production run.

Simone has determined that traditional EOQ is applicable for this problem. Determine the order quantity (EOQ) Simone should use if this determination is correct.

Don't round any numbers in the middle of the problem. Provide your answer to two (2) decimal places.

2.    All of the basic information from Problem 1 still applies along with the additional information provided here for Hitch B.

Hitch B is the 1-1/4 inch, medium duty, natural hitch. This hitch has a forecast annual demand for next year of 3,000 units and has a current batch size of 1,500 units per production run. The unit processing time for this hitch is 0.0420 hours per unit, setup time using a single operator is 6.6 hours per setup and the holding cost per unit per year is $4.90. No additional costs are incurred in the setup process.

It was suggested that Simone had oversimplified her analysis because it would take longer get the same number of units produced if she used EOQ instead of the current batch sizes. How much longer (in hours) will it take to setup for and produce Hitch B if it is produced at its EOQ volume instead of at the current batch size?

Don't round any numbers in the middle of the problem. Provide your answer to two (2) decimal places.

3. All of the information from Problems 1 and 2 continue to apply to this problem where necessary. Hitch C is the 1-1/4 inch, heavy duty hitch.

Hitch C has a forecast annual demand for next year of 7,000 units and a current batch size of 1,500 units. It takes 0.0400 hours to produce each unit and the setup time for a production run is 8.9 hours. Hitch C has a holding cost of $3.96 per unit per year. The value of each Hitch C as it is stored in inventory is $32.21 per unit. As with Hitches A and B, it takes 1 worker to perform the setup and no other costs are incurred in the setup process.

On average, how much more cash is tied up in inventory using the current batch size for Hitch C than would be tied up if batch sizes were determined using EOQ as Simone suggests? Note: this is not the holding cost, it is the actual value of inventory on hand on average.

Don't round any numbers in the middle of the problem. Provide your answer to two (2) decimal places.

4. All of the information that is included in Problems 1, 2, and 3 that is relavent is carried forward to this problem. Hitch D is the 2 inch, light duty, natural hitch.

Hitch D has a forecast annual demand for the next year of 10,000 units. It takes 5.9 hours to complete a setup using a single worker and there are no other costs incurred during the setup process. The holding cost per unit per year is $2.97. The current batch size is 2,000 units. The unit processing time for Hitch D is 0.0380 hours per unit.

How much more time (in hours) will be spent on setups if Hitch D is produced using Simone's recommendation of EOQ than with the current batch size?

Don't round any numbers in the middle of the problem. Provide your answer to two (2) decimal places.

5. All of the relavent information from Problems 1 through 4 carry through to Problem 5. Hitch E is the 2 inch, medium duty, natural hitch.

Hitch E has a forecast annual demand of 8,400 units for next year. It is currently produced in batches of 1500 units. It takes 0.0375 of an hour to produce Hitch E. Each setup requires 4.4 hours for one employee and no other costs are incurred in the setup process. The cost to hold inventory of Hitch E is $4.40 per unit per year.

How much will be saved in ordering and holding costs if they switch from the current batch size to the EOQ value recommended by Simone?

Don't round any numbers in the middle of the problem. Provide your answer to two (2) decimal places.

6. All of the relavent information from Problems 1 through 5 moves forward for Problem 6. Hitch F is the 2 inch, heavy duty, natural hitch.

After discussions with the production manager, Simone has come to realize that her assumption on EOQ is not appropriate. Since EOQ is designed for situations where all of the inventory shows up all at once, which would often be the case for a purchased items and in some cases for manufactured items when everything must move forward as a full batch, and the situation here is that each item may move into inventory as soon as it comes out of production (without waiting for the other items) EOQ with gradual deliveries (sometimes called Economic Run Length (ERL) or Economic Production Quantity (EPQ), among other things) would be more appropriate.

The forecast annual demand for next year of Hitch F is 9,400 and the current batch size is 2,000 units. It takes 0.038 hours to produce each Hitch F. Production and demand both occur 250 days per year. The facility operates 8 hours per day.

How many of Hitch F can be produced per 8 hour day without considering time set aside for setups?

Don't round any numbers in the middle of the problem. Provide your answer to two (2) decimal places.

7. All of the relavent information from Problems 1 through 6 moves forward for Problem 7. Hitch F is the 2 inch, heavy duty, natural hitch.

After discussions with the production manager, Simone has come to realize that her assumption on EOQ is not appropriate. Since EOQ is designed for situations where all of the inventory shows up all at once, which would often be the case for a purchased items and in some cases for manufactured items when everything must move forward as a full batch, and the situation here is that each item may move into inventory as soon as it comes out of production (without waiting for the other items) EOQ with gradual deliveries (sometimes called Economic Run Length (ERL) or Economic Production Quantity (EPQ), among other things) would be more appropriate.

The forecast annual demand for next year of Hitch F is 9,400 and the current batch size is 2,000 units. It takes 0.0480 hours to produce each Hitch F. The setup time is 7.1 hours per setup conducted by a single operator with no other setup costs incurred. The holding cost is $2.42 per unit per year. Production and demand both occur 250 days per year. The facility operates 8 hours per day.

What is the recommended batch size using EOQ with Gradual Deliveries (ERL, EPQ)?

Hint: This isn't in the book, it will take some extra digging.

Don't round any numbers in the middle of the problem. Provide your answer to two (2) decimal places.

Answer 1