The problem here is one of inventory management. Economic Order Quantity (EOQ) is a measure used in the fields of Operations, Logistics and Supply Management. It represents the number of units a company should add to inventory with each order to minimize the total costs of inventory—such as holding costs, order costs, and shortage costs.
To find the EOQ and the total cost, follow the given steps:
Step 1: Gather all required input variables. These are:
a. Fixed cost associated with ordering (K)
b. Annual demand (lambda)
c. Holding cost per year (h)
d. Variable per unit purchasing cost (c)
Remember, all these costs are usually given in monetary terms like dollars or euros.
Step 2: Calculate the order quantity that minimizes the total inventory cost - the EOQ - using the formula:
EOQ (Q) = sqrt((2 * K * lambda) / h)
Here, sqrt represents the square root function. This is the quantity that should be ordered at a time to minimize the total cost.
Step 3: Once the EOQ (Q) is calculated, proceed to calculate total cost.
The total cost (TC) is given by the equation:
TC = c * lambda + K * (lambda / Q) + h * Q / 2
This equation represents the total cost by including the purchasing cost (c times lambda), the ordering cost (K times lambda divided by Q), and the holding cost (h times Q divided by 2).
This is how you solve this problem given the inputs of fixed ordering cost, annual demand, holding cost per year, and variable purchasing cost. Please remember to input these parameters in the same units (for example, all in dollars or all in euros) for consistency.