Lot Sizing | 1. Introduction | 2. Example | 3. Main Menu | 4. Printing | 5. Graphs | 6. Modules |
Lot Sizing This model will perform lot-sizing for minimizing total holding and set-up costs when demands are not equal in each period. Methods include the Economic Order Quantity(EOQ) Period Order Quantity (POQ), lot for lot, part-period balancing method or Wagner-Whitin which finds the optimal schedule. Lot sizing is almost invariably discussed in association with MRP systems.
Consider the following example
| Week | Demand |
| July 11
July 18 July 25 August 1 August 8 August 15 |
5
2 4 8 9 3 |
Holding costs $2 per unit per week and the cost to set up a production run is $21. There is no initial inventory nor is there a lead time.
A data screen for our problem appears below. The data to be given includes demands on the left and costs and other information on the right of the table.
Five methods are available in the method box above the data.
Demands. The demands in each period are to be given. The demands are integers.
Produce. This column is used only for the user defined option. Enter the number of units to be produced. If an option other than user defined is chosen then the program will revise this column and display this column as output.
The information on the right includes:
Holding cost. The cost of holding one unit for one period is to be entered here. The holding cost is charged against the inventory at the end of the period. Under the user defined option it is possible for the inventory to be negative. (For example the user could define production to be 0 in every period). The holding cost will then be negative which makes very little sense. This negative cost appears in the holding cost column but is not included in the holding cost sum.
Note: We generally assume that the holding cost is charged against the inventory which is on hand at the end of the period.
Setup cost. This is the cost of each production run. It is charged only in the periods which have positive production.
Initial inventory. It is possible to allow for a situation where there is beginning inventory. Treatment is as you would expect.
Lead time. This will offset the requirements and produce n periods earlier.
Example 1 - A 6 period lot sizing problem
The solution for our example is displayed in the screen above. The production column has been derived by the program. The extra columns which are derived contain the following information.
Inventory. This is the amount of inventory on hand at the end of the period. In the example there are 6 units left after period 1, 4 units left after period 2 and 3 units on hand after period 5. The holding cost is charged against these amounts.
Holding Cost. This is the cost of holding inventory at the end of this period. It is simply the number of units on hand multiplied by the holding cost per unit, which in this example is $2.
Setup Cost. This is $0 if no production occurs or the setup cost if production occurs during this period. In the example setups occur in periods 1, 2 and 5 so the setup cost of $21 is listed in these three periods but not in the other three periods.
Totals. The total inventory, holding cost and setup costs are listed at the bottom of each column. Thirteen units were held for one month at a cost of $26.00. Three setups occurred at a total cost of $63.
Total Cost. The sum of the setup and holding costs are displayed in the bottom left hand corner. The total cost in this example is $89. Since we used Wagner-Whitin this solution is optimal.
One of the options for placing orders is to use the Economic Order Quantity. The EOQ is computed based on the average demand over the periods. In the example the EOQ is based on the demand rate of 31 units per 6 periods(31/6 = 5.167). Using the holding cost and setup cost with this demand generates an EOQ of 10 (after rounding) as shown near the bottom of the screen. The program will place an order for 10 units every time that the inventory is insufficient to cover the demand. For example, the first order for 10 units is placed in period 1. This covers the demand in period 1 and the demand in period 2. In period 3 we need another order of 10 units. Using this method in this example generates four orders (which total 40 units - not 31 units) and a total cost of $142.
Note that the EOQ method will likely order more units than needed and therefore have higher holding costs than necessary.
Example 3- Using the POQ
One of the options for placing orders is to use the Period Order Quantity. The POQ is the EOQ but expressed in time rather than units. In our example the POQ is the 10 units divided by the average demand rate and rounded off which is 2 periods as seen in the screen below. The program will place an order to cover every two periods.
Example 4 - Lot for Lot ordering
Lot for lot (not shown) ordering is very straightforward and a common way for MRP systems to operate. The exact amount demanded is always ordered. This is optimal if there is no setup cost.
Example 5 - User defined
In this option (not shown) the user can enter the production quantities directly.
| 1. Introduction | 2. Example | 3. Main Menu | 4. Printing | 5. Graphs | 6. Modules |
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