A – A1. Economic Order Quantity Model (EOQ)

The Economic Order Quantity Model will allow an organization to determine the optimal volume of inventory to order at a given time. The EOQ model provides the most optimized approach to inventory ordering as it considers, demand, ordering cost, and holding costs; to develop the volume of inventory to be ordered to maintain to minimum annual cost (Render, 2012).

Equation:

Variables:

Q* = optimal number to order

D = annual demand in units

Co = ordering cost

Ch = holding cost

Process Description:

Q or Q* meaning the optimal order of pieces per order, is equal to the square root of the equation of annual demand (D), multiplied by 2, then multiplied by the ordering cost (Co), which is then divided by the holding cost (Ch). The end result of the equation provides the optimal order of pieces per order or Q*.

Company A:

Demand (D) = 30,000 units per year

Ordering Costs (Co) = $36 per order

Per Unit Cost of inventory = $425

Holding cost rate = 4.5%

Holding cost (Ch) = $425 (.045) = $19.12

*Holding cost is the per unit cost of inventory multiplied by the holding cost rate

Step 1: Input variables into the equation

Step 2: Follow mathematical order of operations: simplify and solve for numerator 2(30000)(36) = 2160000 Step 3: Follow mathematical order of operations: Divide numerator by denominator 2160000/19.12 Step 4: Square roots your quotient and get your final result of the equation

= 336.11

Step 5: Round up to the nearest Unit to get you final answer.

In order to minimize total cost, the order size should be 337 when company A orders new inventory.

B – B1. Economic Production Lot Model

The Economic Production Lot Model is a variation of the EOQ model that allows businesses to determine optimal replenishment lot size. This model provides the most optimized approach this form of ordering as it considers, demand, available production, ordering

References: Render, B., Stair, R. M., & Hanna, M. E. (2012). Quantitative analysis for management (11th ed.). Upper Saddle River, N.J.: Pearson Prentice Hall.