Economic Manufacturing Quantity (EMQ)

Calculate the economic manufacturing quantity (EMQ) for a finite replenishment rate inventory model. 
 syse.emq(a: float, d: float, h: float, r: float) float
Calculate the economic manufacturing quantity (EMQ) for a finite replenishment rate inventory model.
 Parameters:
A (float) – The cost to place one order.
D (float) – The number of units used per year.
h (float) – The holding cost per unit per year.
R (float) – The replenishment rate.
 Returns:
The EMQ that minimizes the total annual inventory cost.
 Return type:
float
Note
The EMQ formula assumes the same conditions as the EOQ formula (i.e., constant and known demand, no stockouts, constant and known ordering costs and holding costs), but also assumes that the replenishment rate is finite. The EMQ represents the optimal production quantity that minimizes the total annual inventory cost, including both holding costs and ordering costs, when production is constrained by a finite rate of replenishment. Note that the formula assumes that the replenishment rate is given in units per day, and that the annual demand is normalized to units per day by dividing by 365.
Examples:
Let’s say that a manufacturer produces widgets using a finite replenishment rate inventory model to manage its inventory of raw materials. The manufacturer purchases a raw material from a supplier and pays a fixed cost of $100 to place an order, regardless of the quantity ordered. The manufacturer uses 10,000 units of the raw material per year, and the holding cost per unit per year is $8. The supplier has a limited production capacity and can only replenish the manufacturer’s inventory at a maximum rate of 500 units per day. To determine the optimal production quantity, we can use the emq function:
A = 100 D = 10000 h = 8 R = 500 emq = syse.emq(A, D, h, R) print(emq) Output = 514.29
Important
Again, note that this example is simplified and does not take into account other factors that could influence the manufacturer’s decisionmaking, such as variability in demand and lead times, stockout costs, and other costs associated with ordering and holding inventory. Nonetheless, the EMQ model provides a useful starting point for inventory management decisions in a constrained production environment.