EOQ with price gap
From Supply Chain Management Encyclopedia
Consider the case of static demand.
The Basic Assumptions of the Model
- Number of units consumed per unit of time is a constant (demand rate);
- Price of the resource unit depends on order volume. If the order quantity does not exceed a certain level of , then the price is constant , otherwise - the price is a constant , where :
- Carrying cost of resource unit is a constant;
- Order cost is a constant;
- Lead time is zero.
The Basic Notation
- – demand rate;
- – marginal carrying costs;
- – fixed order costs;
- – order cycle time;
- – total costs per unit of time;
- – order quantity;
- – economic order quantity.
Inventory Optimal Control
Costs of resource per unit of time are a function of the size of orders:
Given the dependence of the order cycle time on the intensity of demand for the resource, , the cost of the purchase of products per unit time can be represented as:
The total cost per unit time can be represented as a function of order volume as the sum of acquisition costs of resource per unit of time, the cost of ordering and storage costs of the resource per unit time:
The graphs of the function and are the following, fig. 1:
Fig. 1. The function of total costs
The point is determined according to economic order quantity:
In the point the following inequality holds:
When graph equal to . When graph equal to . In correspondence with a graph, consider the three areas on the x-axis: , , , which are called, respectively: A, B and C. The optimum size of the order depends on what area is the point , Fig. 2, 3, 4:
Fig. 2. , .
Fig. 3. , .
Fig. 4. , .
Optimal inventory control in the model is the following:
Step 1. According to EOQ compute . If , then , else, go to step 2.
Step 2. Compute from the following equation:
to determine the border areas and . If , then , if , then .