Andler formula/Andler formula
Andler's formula calculates the optimal order quantity based on an order model in which total costs are minimal.
Brief description
The optimal order size is the result of time and quantity agreement:
- material requirements,
- procurement costs,
- storage costs
and aims to minimize total costs. In doing so, the purchasing behavior of the company within a certain range and at a certain time is considered. It is assumed that the consumption of the part runs evenly, and the possibilities for delivery as well as storage are determined to be unlimited. At the same time, it is assumed that the cost of ordering a unit of goods is independent of the size of the order.
If a very large batch is ordered at one time to cover the demand for the period under review, the fixed costs for each order can be sharply reduced. At the same time, storage costs increase. If orders run in small batches, then warehousing costs are lower; however, the fixed costs for each order will increase because orders must run more frequently. Therefore, an optimal order size is sought, at which the demand will be covered and the total costs consisting of warehousing and order costs are minimal. The calculation of the order size automatically results in the length of the order periods, that is, the optimal time between two orders.
Calculations
t(s) - cycle length between two orders
k(s) - fixed costs of a single order
k(L) - storage costs per quantity and time unit
T - total duration (period under study)
R - link demand in period T
q - lot size in units of goods
n - number of necessary orders
The number of necessary orders can be calculated with the help of the total order and batch size:
n = R / q
Similarly, the length of the order cycle can be determined from the defined quantities :
t(s) = T / n = T(q) / R
To calculate the total costs due to the length of the order cycle or the size of the order, use the formula:
K(q) = n * k(s) + k(L) * ((n * q * t(s)) / 2)
The linear part in costs represents the total storage costs in period "T" the other part represents the total order costs. We get the storage costs by dividing the area by the inventory function and multiplying by the warehouse cost function. We calculate ordering costs from the warehouse cost function and multiply by the number of orders in the period. The graphs of the inventory run and the total cost run are as follows:
Features and requirements
- One-step product development process
- Price discounts due to order size for larger orders are not taken into account
- No occurrence of fluctuations in the time of demand and releases from the warehouse
- Annual demand is accurately known
- Supply velocity is infinitely high
- No restrictions on financial resources and capacity
- All costs at the time of planning are known
Advantages and disadvantages
The advantage of Andler's formula is that it can be expanded at any time, for example in the case of multi-product production. The formula then becomes more extensive and complex, but remains quick and easy to use.
However, Andler's formula also has weaknesses:
- Assuming that there is constant and linear consumption
- Since the price per unit is assumed to be fixed and does not depend on the size of the order, it is not included in the calculation
- Problems if there is a sudden increase in resources
- Price-quantity differentiation is not taken into account
- Determining the fixed costs of a single order is difficult
- Availability of calculated demand (basic quantity)
- A single-article oriented view can lead to performance/throughput problems
- The Y-axis has two dimensions: storage costs are expressed in Euro/year and ordering costs are expressed in Euro/piece
Application
In practice, the above-mentioned requirements can never be met. It should also be noted that Andler's formula is only a basis and approximation for determining the optimal order size or lot size.