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Aggregate Planning

Aggregate (Production) Planning



Production planning is the means by which we prepare our production quantities for the medium term (generally one year). Aggregate planning refers to the fact that the production planning is usually carried out across product lines. The main difficulty is that demands vary from month to month. We want to keep production as stable as possible yet maintain no inventory and experience no shortages. We must balance the costs of production, overtime, subcontracting, inventory, shortages and changes in production levels. In some case aggregate planning problems might require the use of the transportation or linear programming modules.

The Model.

Production planning problems are characterized by a demand schedule, a corresponding production schedule and various costs. In addition, we have the following considerations.

Shortage handling. In production planning there are two models for handling shortages. In one model shortages are backordered. That is, demands can accumulate and be met in later periods. In another model the shortages become lost sales. That is, if you can not satisfy the demand in the period in which it is requested the demand disappears. This option is above the data table.

Initial Inventory. Often times we have a starting inventory from the end of the previous month


Production costs - regular time, overtime and subcontracting. These are the per unit production costs depending on when and how the unit is made.

Inventory (Holding) cost. This is the amount charged for holding one unit for one period. The total holding cost is charged against the ending inventory. Be careful because while most textbooks charge against the ending inventory some textbooks charge against average inventory during the period.

Shortage cost. This is the amount charged for each unit that is short in a given period. It is assumed that the shortages are backlogged and satisfied as soon as stock becomes available in a future month or are lost sales as indicated by the option box above the data table. Shortage costs are charged against end-of-month levels.

Cost to increase production. This is the cost due to having changes in the production schedule. It is given on a per unit basis. The cost for increasing production entails hiring costs. It is charged only against regular time production changes. If the initial production level is 0 then there will be no charge for increasing production in the first period.

Cost to decrease production. This is similar to the cost of increasing production and is also given on a per unit basis. However, this is the cost for reducing production. It is charged only against regular time production changes.

Example 1

Consider a situation where demands in the next four periods are for 1200, 1500, 1900 and 1400 units. Current inventory is 0 units. Suppose that regular time capacity is 2000 units per month and that overtime and subcontracting are not a consideration. The costs are $8 for each unit produced during regular time, $3 for each unit held per period, $4 for each period that we are short a unit, $5 for each unit that we increase production by from the previous period and $6 for each unit that we reduce production by from the previous period.


Five methods are available which we will demonstrate.

  1. Smooth production (equal production in every period). This can be set according to the gross demand of 6000 units or the net demand of 6000-100 units.

  2. Produce to demand which will create a production schedule which is identical to the demand schedule

  3. Constant regular time production followed by overtime and subcontracting if necessary

  4. Any defined in which case the user must enter the amounts to be produced in each period.

The Solution

In this example we have chosen the smooth production method and backorders. The demands are 1200, 1500, 1900 and 1400 and the regular time capacity of 2000 exceeds this demand. There is no initial inventory. The numbers represent the production amounts. The costs can be seen at the top of the columns.

The screen contains information on both a period by period basis and summary basis.

Regular time production amount. The amount to be produced in regular time is listed in the Reg time column. This amount is determined by the program for all options except user defined. In this example, because the gross (or net) demand is 6000 there are 1500 units produced in regular time in each of the 4 periods. If the total demand is not an even multiple of the number of periods then extra units will be produced in as many periods as necessary in order to meet the demand. For example had the total demand been 6001 then the production schedule would have been 1501 in the first period.

The ending inventory is represented by one of two columns -either holding or shortage.

Holding inventory. The accumulated inventory appears in this column if it is positive. In the example, there is a positive inventory of 300 units in periods 1, and 2, no inventory (actually a shortage) in period 3 and neither any inventory nor shortage at the end of period 4.

Shortages. If there is a shortage then the amount of the shortage appears in this column. In the example the 100 in the shortage column for period 3 means that 100 units of demand have not been met.

No increase or decrease from month to month occurs so these columns do not appear in this display.

Total. The total number of units demanded, produced, in inventory, short, or in increased and decreased production are computed. In the example 6000 units were demanded, 6000 units were produced, there was a total of 600 unit-months of inventory, 100 unit-month of shortage, and 0 increased or decreased production unit-months.

Costs. The totals of the columns are multiplied by the appropriate costs yielding the total cost for each of the cost components. For example, the 600 units in inventory have been multiplied by $3 per unit yielding a total inventory cost of $1800 as displayed.

Total cost. The overall total cost is computed and displayed. For this strategy the total cost is $50,200.


It is possible to display a graph of the cumulative production versus the cumulative demand.

Example 2 - Starting inventory and previous production

We have made two modifications to the previous example. These modifications can be seen in the screen below. In the demand column in the "Initial inventory" row we have placed a 100 and we have changed the method.

The output indicates that the total requirement is 5900 rather than the 6000 from the previous example due to the initial inventory. Thus we need only produce 1475 per month as seen to the right of the double bar. This is shown in the far right column.

Example 3 - Using overtime and subcontracting

In this example we take our original example (without starting inventory) and reduce the capacity to 1000 for regular time. We have included capacities of 100 for overtime and 900 for subcontracting and we have included unit costs for overtime and subcontracting of $9 and $11 respectively. This can be seen below.

Because there is not enough regular time capacity, the program looks to overtime and subcontracting. It first chooses the one which is less expensive. Therefore in this example, the program first makes 1000 units of regular time, then 100 units on overtime then 900 units on subcontracting.

Example 4 - when subcontracting is less expensive than overtime

Below we show a case where subcontracting is less expensive than overtime. That is, the only change we have made from the previous screen is to make the overtime cost $13 rather than $9. This time, the program first chooses subcontracting and since there is sufficient capacity overtime is not used at all.

Example 5 - Lost Sales - case 1

We have taken the previous example and we have changed from backorders to lost sales as can be seen below.

The output shows a shortage of 100 units at the end of period 3. In the next period we produce 1500 units even though we need only 1400 units. These extra 100 units are not used to satisfy the old shortage since these have become lost sales. The 100 units go into inventory as can be seen from the holding column in period 4. It does not make sense to use the smooth production model and have lost sales. The total demand is not really 6000 since 100 of the sales were lost.

Example 6 - The Produce to demand (No inventory) strategy

We have taken our first example and toggled the method to display the produce to demand strategy below.

Notice that the program has set the produce column equal to the demand column. The inventory column is always 0 because under this option with production equal to demand there will be no changes in inventory nor any shortages. The production rates will increase and/or decrease. In this example, production in period 1 was 1200 and production in period 2 was 1500. Therefore, the increase column has a 300 in it for period 2. Again, we remind you that the program will not list any increase in period 1 if no initial production is given. In total, the increases have been 700 and the decreases 500.

Increase. The change in production from this period to the last period occurs in this column if the change represents an increase. Notice that the program assumes that no change takes place in the first period in this example. In this example there is no change in other periods because production is constant under the smooth production option.

Decrease. If production decreases then this decrease appears in this column.

Example 7 - Increase and decrease charging

The previous example had increases and decreases in production. These increases and decreases only are accounted for by regular time production. Below we have reduced the regular time capacity in order to force production through all three methods of regular time, overtime and subcontracting.

Notice that the increase column only has a value in it in the second month when regular time production went from 1200 to 1500 units. The regular time production remains at 1500 and even though overtime and subcontracting have increases and decreases, these do not show up in the increase and decrease columns. We do not charge against such increases.



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