Question

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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 G 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 G is 9,400 and the current batch size is 2,000 units. It takes 0.0480 hours to produce each Hitch G. The setup time is 6.6 hours per setup conducted by a single operator with no other setup costs incurred. The holding cost is $1.81 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

Current scenario

No. of batches needed to complete the demand = 9400/2000 = 5

Time taken to produce a batch = 6.6+ 2000 x0.048 hours = 102.6 hours

Time taken to produce entire quantity = 4x102.6 + 6.6 x 1400 x0.048 = 410.4+443.52 = 853.52

Number of days needed to complete this order = 853.52/8 = 107, which is far less than the given time of 250 days

as there is no set up cost involved, the holding cost is the only factor that needs to be minimised

If n be the ERL, then, no. of runs needed = 9400/n

Hours incurred in each run = 6.6+0.048x n

Total hours for completing the order = 9400/n ( 6.6+0.048n) = 250x8

62040/n+ 451.2 = 2000

n = 40.05 =41

Number of runs = 9400/41 = 230

Hence 41 units in a run will give the least holding cost i.e. 41/2 x 1.81 = 37.1