Inventory

These models use different variations of the economic order quantity ( EOQ ) model in order to determine proper order or production quantities. Besides the standard EOQ model, we include the economic production quantity ( EPQ ) model. For both the EOQ and EPQ model we allow shortages to be included. Finally, we allow quantity discounts for the EOQ model.

A second type of model is ABC analysis.

EOQ -Type Models

The following screen contains an example that includes both the data and the solution.

The data

Demand rate. The rate of demand or usage is to be entered here. Typically, this demand rate is an annual rate but it does not need to be. The time units for this demand rate must match the time units for the holding cost.

Setup cost. This is the fixed cost of placing each order or making each production run.

Holding cost rate. This is the cost of holding or carrying one unit of inventory for one time period. This cost is either given as a particular dollar amount or given as a percentage of the price of the item. That is, if you want the holding cost to be a percentage of the unit cost, enter a percent sign, '%', after the number. For example, '20' means 20 dollars but '20%' means 20% of the unit cost. If the holding cost is a percentage of the unit cost, you must enter the unit cost.

Unit cost. This is sometimes necessary but many times not since the EOQ is independent of the unit cost.

Reorder point. The option box above the data enables us to calculate the reorder point. Three lines of input are added in these cases. We must either enter a daily demand rate or enter the number of days in the year so that the daily demand rate can be computed from the annual demand rate. In addition, we must enter the number of days for the lead time.

Order quantity. Above the data is a textbox /scroll bar combination that allows you to enter a value for the order quantity. If you enter a number other than 0 then two sets of results will be displayed. One set will be for the EOQ while the other set will be for the specified order quantity.

The solution

The output screen appears in the preceding screen. In example 1, we have solved a standard EOQ model and ,in addition, found results when using an order quantity of 20 units. The model results are as follows:

Optimal order quantity. This is the most economical order quantity. If there is no quantity discount, this is the EOQ . However, when a quantity discount is available (as in example 3) this is either the EOQ or a discount point above the EOQ . In this example, the optimal order quantity is 16.33 units per order.

Maximum inventory level. It is useful to know the largest amount that will be in inventory. In the standard EOQ model, this is simply the amount that is ordered; in a production or shortage model this is less. In this example, the inventory will never exceed 16.33 units when using the EOQ or 20 units if 20 is the order quantity.

Average inventory level. If there are no backorders , the average inventory is half of the maximum inventory. Annual holding costs are based on the average inventory.

Orders per year. The assumed time period is one year and the number of orders is displayed. In this example it is 12.25 for the EOQ and 10 for an order quantity of 20 units.

Unit costs. This is the total cost for ordering the units. In many instances, the individual unit cost will be 0 and therefore the total unit costs will be 0.

Total costs. This is the total cost of both the inventory costs and the unit costs. This figure is useful for checking work on problems with discounts.

Reorder point. This is the product of the daily demand rate and the number of leadtime days. In this example we have a daily demand rate of .8 units and a lead time of 5 days which yields a reorder point of 4 units.

A graph of cost versus inventory is displayed next.

Example - Inventory with production

Following we display data for a problem with production. The data includes the usual parameters of demand rate, setup cost, holding cost, and unit cost. We also are displaying results for a policy of producing 300 units per run.

In this model, we are asked for a daily production rate and either a daily demand rate or the number of days per year. Notice in this example that we have set the days per year to 250. The program will compute the daily demand rate as 10,000/250. Alternatively, we could have entered the daily demand rate to compute the days per year.

The solution appears next. The daily demand rate has been found to be 40. The remaining results are the same as in the first example.

Example 3 - Quantity discounts

A screen for quantity discounts appears in the following illustration. Once again, the usual information is placed at the top. In addition, up to 4 price ranges may be given.

A detailed analysis of the order quantities and costs at each price range is available as shown below.

Backorder models

The software also has the capability to compute the EOQ or the production model with backorders . These models do not appear in all textbooks so we do not display them in this manual. If you have the software set for one of the Render texts then these models will not show up in the model submenu.

ABC Analysis

The goal of ABC analysis is to identify the most important items that are kept in inventory. Importance is measured by dollar volume. An example appears below for a problem with 6 items.

For each item, the information to be entered is:

Item name. As usual, a name can be entered on each line.

Demand. The demand rate for each item is to be given.

Item price. The cost or price of each item is to be given

Percentage of A and B items. In the example, we want 20% of the items to be A items and 30% to be B items. After the program sorts the items by dollar volume, the first 20% of 6 items (.6 items rounded to 1) will be classified as an A item and then 30% of 6 (1.8 items rounded to 2) will be classified as B items.

Notice that the items are sorted according to their dollar-volume percentages. That is, they do not appear in the same order as on the original screen of input. The output computed for each item are:

Dollar-volume = demand*price is computed for each item

Percentage of items = number of units/total number of units

Dollar-volume percentage = the item dollar-volume/total dollar volume is displayed

Cumulative dollar - volume percentage = a running total of dollar volume