Skip to main content

A new business graduate has been given the task of determining the best production quantity for a new product that will be produced on a new...

The Economic Order Quantity (EOQ) is the optimal solution for how much product to order, assuming that you are buying from a vendor and all orders will be filled completely and immediately. For producing a product, the optimal solution would actually be the Economic Production Quantity (EPQ), but in this case we couldn't determine that because we didn't know the production rate.

For an order/setup cost of K, a demand rate of D, a holding cost of F, and a production rate of P, these are the equations for each quantity:

EOQ = sqrt(2DK/F)

EPQ = sqrt(2DK/(F(1-D/P))

Thus, the two quantities differ only by a ratio of 1/sqrt(1-D/P). We are given that the demand rate is 80% of the production rate, so D/P = 0.8, and 1/sqrt(1-D/P) = 2.24.

Therefore, we are not holding enough of the product, by a factor of 2.24. In other words, we are only holding 44.7% of the quantity we should be. This is because the production rate is only slightly faster than the demand rate, so we can barely keep up with demand if we don't hold onto inventory and thus end up incurring a lot of per-run costs by doing so many different production runs.

The sensitivity analysis formula says that the ratio in average cost between the actual production and the optimal production is, for actual quantity Q and optimal quantity Q*, the average of their ratios:

AC(Q)/AC(Q*) = 1/2 * (Q/Q* + Q*/Q)

Since Q/Q* = 2.24 and Q*/Q = 0.447, we just substitute in:

AC(Q)/AC(Q*) = 1/2 (2.24 + 0.447) = 1.3435

So, we are paying 34% more than we should be.

Still, I think the consultant can make a good case that the EOQ was a reasonable choice; it would be the best choice if production rate is much higher than demand rate, and even in this particular case it was not wildly wrong. The employer, on the other hand, might argue that they should have made some ballpark assumption for the production rate and gone with that, say assume that D/P = 0.5; because effectively using the EOQ assumes D/P = 0, which is obviously not realistic.

Comments

Post a Comment

Popular posts from this blog

etymology - Origin of the greeting "Sweet dreams".

Does anybody know the etymology of the phrase "sweet dreams"? I tried googling but did not find anything satisfying. Is this a relatively new phrase of the modern world or has this been in use for some time? I think it's the latter one. Answer The OED has the interjection as "a farewell to someone going to bed" from the 20th century: 1908 Sears Roebuck Catal. 198/1 Tenor Solos..Good Bye, Sweet Dreams, Good Bye. But it goes back until at least the 19th and possibly 18th centuries. John Wolcot, writing under the pseudonym of Peter Pindar, used it in his poem "Orson and Ellen; A Legendary Tale" published in 1801: Also from 1801 in The infernal Quixote (Page 287) by Charles Lucas: In the March 1776 of The Universal Magazine was published "The Serenade. A Pastoral Tale. From the German of Gesner" , where the shepherd Daphnis watches over his beloved as she sleeps and sings: The same tale appears in 1776's as Idyl XI, " Daphnis ...
Post a Comment
Read more

Is there a word/phrase for "unperformant"?

As a software engineer, I need to sometimes describe a piece of code as something that lacks performance or was not written with performance in mind. Example: This kind of coding style leads to unmaintainable and unperformant code. Based on my Google searches, this isn't a real word. What is the correct way to describe this? EDIT My usage of "performance" here is in regard to speed and efficiency. For example, the better the performance of code the faster the application runs. My question and example target the negative definition, which is in reference to preventing inefficient coding practices. Answer This kind of coding style leads to unmaintainable and unperformant code. In my opinion, reads more easily as: This coding style leads to unmaintainable and poorly performing code. The key to well-written documentation and reports lies in ease of understanding. Adding poorly understood words such as performant decreases that ease. In addressing the use of such a poorly ...
Post a Comment
Read more

What are the similarities between the relationships of the characters in The Outsiders and Romeo and Juliet?

At first glance, it might appear as if the characters in  The Outsiders  by S. E. Hinton and  Romeo and Juliet  by William Shakespeare do not have much in common; however, when one isolates the core of the conflicts, it becomes clear that the relationships in both stories are rooted in rivalry and secrecy.  In both  The Outsiders  and  Romeo and Juliet , an overarching theme is rivalry. While   socioeconomic status separates the greasers from the Socs in The Outsiders , last names separates the Montagues from the Capulets, who appear to be relatively equal in terms of socioeconomic status. Due to these rivalries, there are instances of deadly interactions in both stories. In  The Outsiders , Johnny kills Bob (whether his actions were justified or not is debatable). In  Romeo and Juliet , Romeo kills Tybalt and Paris, and Tybalt kills Mercutio. These deaths have profound effects on the main characters. In Ponyboy's case, the Johnny's death and other events in the novel inspire h...
Post a Comment
Read more