# EOQ with price gap

### From Supply Chain Management Encyclopedia

**Russian: Экономичный размер запаса с разрывами цен**

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:

or:

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:

,

or:

,

then:

.

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 .