10 Things You Have in Common With EOQ MODEL KEY POINTS


The Economic Order Quantity (EOQ) model is a mathematical model used in inventory management to determine the optimal order quantity for a product. Here are ten things that you may have in common with the key points from the EOQ model:


  • Both you and the EOQ model consider the cost of holding inventory: Holding inventory can be expensive, and both you and the EOQ model take this into account when making decisions about inventory levels.


  • Both you and the EOQ model consider the cost of placing an order: Placing an order for new inventory also incurs costs, and both you and the EOQ model take this into account when determining the optimal order quantity.


  • Both you and the EOQ model consider the cost of stock outs: Running out of inventory can lead to lost sales and damage to customer relationships, and both you and the EOQ model take this into account when making inventory decisions.


  • Both you and the EOQ model consider the relationship between inventory levels and demand: Inventory levels and demand are closely related, and both you and the EOQ model consider this relationship when determining the optimal order quantity.


  • Both you and the EOQ model consider the lead time of the product: The amount of time it takes for an order to be fulfilled and received is important in determining the optimal order quantity.


  • Both you and the EOQ model consider the carrying cost of inventory: Carrying cost of inventory is the cost of financing inventory, and both you and the EOQ model take this into account when making decisions about inventory levels.


  • Both you and the EOQ model consider the annual demand for the product: The annual demand for a product is an important factor in determining the optimal order quantity.


  • Both you and the EOQ model consider the cost of the product: The cost of the product is also an important factor in determining the optimal order quantity.


  • Both you and the EOQ model consider the safety stock: Safety stock is the extra stock held in inventory to protect against stock outs and both you and the EOQ model take this into account when making inventory decisions.


  • Both you and the EOQ model strive for efficiency: Both you and the EOQ model strive to make efficient and cost-effective decisions when it comes to inventory management.


Overall, the EOQ model is a useful tool for inventory management and it considers many of the same factors that you would consider when making inventory decisions. By understanding the key points of the EOQ model, you can make more informed decisions about inventory levels and improve the efficiency of your operations.


Example: Aggregating Multiple Products in a Single Order


  • Transportation is a significant contributor to the fixed cost per order.
  • Can possibly combine shipments of different products from the same supplier. Same overall fixed cost
  • Effective fixed cost for each product shared across multiple products is reduced
  • Lot size can be reduced for each product
  • Can be a single delivery coming from multiple suppliers or even a single truck delivering to multiple retailers.
  • Aggregating products, retailers or suppliers into a single order allows for a reduction in lot sizes for individual products as fixed ordering and transportation costs are now spread across multiple products, retailers or suppliers.


Example: Grouping multiple products into one order.


- Let's say in the previous example there are 4 computer products: Desk Pro, Light Pro, Med Pro and Hive Pro.


- Assume there is a demand of 1000 units per month for each.

- If each product is ordered separately:

Q* = 980 units for each product

- Total cycle list = 4(Q/2) = (4)(980)/2 = 1960 units

- Total orders of all four products:

Combined Q* = 1960 units

-For each product: Q* 1960/4 = 490

-Cycle inventory is reduced for each product

Total cycle inventory 1960/2 = 980 units

from 490/2 = 245 2

  • -Average flow time, inventory holding cost will be reduced
  • Lot Sizing with Multiple Products or Customers:
  • In practice, fixed ordering costs depend at least partially on the variation associated with ordering multiple models.
  • Part of the cost is related to transportation (independent of variety) 
  • Part of cost is related to loading and receiving (not independent of variety) 
  • Three scenarios
  • Lots are ordered and delivered independently for each product
  • Lots are ordered and jointly delivered for all three models -Lots are ordered and jointly delivered for a selected subset of models

Lot Sizing with Multiple Products or Customers

Demand per year.

-dl = 12,000; dm = 1,200; DH = 120

Common transportation cost, S = -$4,000.

Product specific ordering cost.

-SL = $1,000; SM = $1,000; H = $1,000

- holding cost, h = 0.2.Unit cost.

- CL = $500; CM = $500; CH = $500


Delivery Options:


  • No aggregation: Each product ordered separately.
  • Full Aggregation: All products delivered on each truck.
  • Customized Aggregation: Selected subsets of products on each truck.


77 No Aggregation: Order each product independently,


Lite Pro Med Pro Heavy Pro

Demand per annul 12,000 1,200 120

Fixed cost/order $5,000 $5,000 $5,000

Optimum Order Size 1,095 346 110

Order frequency 11,0 / year 3.5 / year 1.1 / year

Annual Cost $109.544 $34.642 $10.954

total cost = $155,140

Aggregation: Order all products combined.

S* = S + SL + SM + SH = 4000+1000+1000+1000 = $7000

n* = sqrt [(DLHCL+ DMCM+ DHhCH)/2S*]= 9.75

QL = DL/N*12000/9.75 = 1230

Qm = dm/n* = 1200/9.75 = 123

QH = DH/N* = 120/9.75 = 12.3

bicycle inventory = 0/2

Average flow time = (Q/2)/(Weekly demand)

78Full Aggregation: Order all products combined.

LitePro MedPro HeavyPro

Demand per annum 12,000 1,200 120

Order Frequency 9.75/year 9.75/year 9.75/year

optimal order

Shape

1.230 123 12.3

annual holding cost

$61.512 $6.151 $615

Annual Order Cost = 9.75 X $7,000 = $68,250

Annual Total Cost = $136,528


Lessons from Aggregation

  • Aggregation allows the firm to reduce lot size without increasing cost.
  • Full aggregation is effective if product specific fixed costs are a small fraction of joint fixed costs.
  • Optimized aggregation is effective when product specific fixed costs are a large fraction of joint fixed costs.