## Tuesday, February 12, 2013

### How Much to Order? A Revised EOQ Model

How much to order is an important question in inventory management. The case study introduces us a cost model, to provide an economic approach to determine order side. Economic Order Quantity (EOQ) is a simple and widely used inventory control model. Following are the figure and results from the case study.

Many assumptions have been implicitly made in developing the EOQ formula, and one of the assumptions attracts big interest of me, that is there are no quantity discounts, which means the unit cost holds constant regardless of how many we order. However, it sounds unrealistic to me. In most situations, the more you buy the cheaper price you will get, like the price of coke in supermarket is one for \$2 and 12 for \$10. The case study indicates the EOQ model could be modified to accommodate discounts, and I am going to try to revise the model with quantity discounts, and help companies to find the optimal lot size, also whether should take the discount price or not.

Now, consider this situation, if the lot size is less thanQ1, the unit cost would be C1
If the lot size lies between Q1 and Q2, the unit cost would be C2
So we can summary the total annual cost equation:

Differ from the function in case study, we cannot simply use derivation to find the minimum value. Because of quantity discounts, the cost curve becomes discontinues at point Q=Q*. Based on Figure 1, I draw a new diagram, which clearly shows the correlation between TAC and lot size when we include quantity discounts in the EOQ model.(forgive my unskillful hand drawing. )
We can see that, this TAC curve is not smooth anymore, instead, it consist of several smooth curve, which are also part of the TAC curve from the original EOQ model. Thus we can still use the EOQ formula to find the lowest points of every smooth curve contained in the discontinuous TAC curve:
Based on the example from case study, consider ABC Company buys replacement lamp bulbs from the bulb factory, their monthly demand has been forecast as 100 units. The cost of preparing an order is \$8, and the unit cost is \$35. the bulb factory offers ABC Company a discount according to the quantity they ordered, which is if they order more than 75 units they can get a discount price of \$32.5. The inventory holding charge is 12 percent per year of the unit cost.

1)         Starting from the lowest price, C1=32.5, the optimal lot size is
2)         We continually look for the optimal lot size of the second lower price, C2=35, which is
3)         Next, we need to compute the Total Annual Cost according

Questions:
Until now, we only include the traditional economic criteria within the model to control the cost. After controlling the cost, sustainability is the next emerging requirement for a better business practice in supply chain management. In achieving sustainability, what else considerations should we adopt, besides economic criteria?

We only consider single organization in this EOQ model. If considering multiple organizations and analyzing the terms of coordination among supply chain members with those added criteria from above question, what kind of new insights for sustainable supply chain management can we conclude?

 Arslan, M. Can, and M. Turkay. EOQ revisited with sustainability considerations. Working paper, Koç University, Istanbul, Turkey. http://home. ku. edu. tr/~ mturkay/pub/EOQ_Sustainability. pdf (retrieved 02-10-2011), 2010.