MRP is a tool for production planning and inventory control. This approach is used periodically, on a rolling-horizon basis.5
Applying MRP requires data on the components (raw material, semi-finished products) of each end item, quantity of each component, sequence in which the components are required and operations are performed, as well as the operation times.
The bill-of-material (BOM) is the key structure used to introduce these data.
4.4.2.1 Bill-of-material (BOM)
The BOM is the key input for the MRP system. It shows all of the components (both purchased and manufactured) at every level of the manufacturing process and the quantity of each component required. In the supply chain environment, the levels of the manufacturing process may take place in different companies. There is one BOM for each end item. It should be noted that purchased items do not require a BOM.
5A decision is made on a rolling-horizon basis if it is made periodically (period h) for a period H (h ≤ H), taking into account the information available when the decision is made.
An example of a BOM describes how a tablet box (TB) is produced. Tablets are presented in blisters. The final product (i.e., the tablet box) is made with a box (BX), a blister pack of tablets (BPT) and the instructions for use (IU). A blister pack of tablets is obtained from a blister (BL) and tablets (TA). The numbers associated with the arrows define the number of components required to obtain the item of the next upper level.
The BOM is presented in Figure 4.8. Another way to represent the BOM of the tablet box is Table 4.3. This BOM has three levels: level 0 (TB), level 1 (IU, BPT, BX) and level 2 (BL and TA).
TB
IU BPT BX
BL TA
1 1
1
1 20
Figure 4.8 An example of a BOM: The tablet box
Table 4.3 The tablet box BOM
Level Quantity Acronym Identification
0 1 TB Tablet box
1 1 IU Instruction for use
1 1 BPT Blister pack of tablets
1 1 BX Box
2 1 BL Blister 2 20 TA Tablets
4.4.2.2 Master Production Schedule (MPS)
The MPS is a production program for end items. It is a time-phased schedule of the production required to meet demand (in the case of make-to-order supply chain) or to maintain inventory levels.
The MPS is generated based, in particular, on the following information:
• forecasted demands;
• customers’ orders;
• inventory levels (including backlogs);
4.4 Echelon Stock Policies 135
• outstanding orders;
• the lead times (which are assumed to be constant).
The end items of the MPS are called “level 0” items.
4.4.2.3 Time-phased Gross Requirements
The gross requirement leads to component requirements by exploding the MPS using the BOM of each item.
Consider, for example, the BOM of the tablet box and assume that the operation times related to the components are given in Table 4.4. The operation times are given in terms of the number of elementary periods.
Figure 4.9 provides the cumulative lead time of the tablet box. It is equal to 7 elementary periods.
Table 4.4 Component requirements for tablet box
Level Operation Operation time Identification
0 Assembling IU, BPT and BX 1 TB
1 Making IU available 1 IU
1 Assembling BL and TA 3 BPT
1 Producing and making box available 2 BX
2 Producing and making blister available 2 BL 2 Producing and making tablets available 3 TA
BPT BX
IU TA
–1 –2 –3 –4 –5 –6 –7
BL
TB
Elementary periods
. Figure 4.9 Cumulative lead time for tablet box
This shows that if the due date of a tablet box (TB) is given:
• The TA item must be released into production 7 elementary periods before the due date.
• The BL item must be released into production 6 elementary periods before the due date.
• The BPT item must be released into production 4 elementary periods before the due date.
• The BX item must be released into production 3 elementary periods before the due date.
• The IU item must be released into production 2 elementary periods before the due date.
• The TB item must be released into production 1 elementary period before the due date.
The operation times, given in terms of elementary periods, are rough and often overestimated. Furthermore, these times apply whatever the number of elements and, last but not least, they are adjusted from time to time to respond to worker requirements, which often lead to increasing operation times.
4.4.2.4 Adjusting Production and Inventory Levels
The forecasted demand and production are computed, before entering MRP, in the master production schedule. The MRP system adjusts the production objectives and inventory levels from these data, as shown below for the end item and item BPT.
Table 4.5 concerns the end item TB. The first row deals with elementary periods. The second and third provide the demands and production quantities respectively, which are inputs of the MRP. The next rows are fulfilled by the MRP system. The fourth row presents the inventory levels corresponding to the two previous rows. Note that a stock is available at the end of an elementary period while a demand is due, and a quantity produced is available at the beginning of the corresponding period. The last row contains the corrective production introduced to suppress stock shortages. These orders are released taking into account the operation time, which is one elementary period in this example.
Table 4.5 Inventory and production management of the end item
Elementary period 1 2 3 4 5 6 7 8 9 10 11
Demand 0 10 15 10 8 14 15 13 11 25 12
Production 0 0 30 0 0 0 0 10 20 15 12
Inventory level 30 20 35 25 17 3 –12 –15 –6 –16 –16
Corrective production 0 0 0 0 0 12 3 0 1 0 0
4.4 Echelon Stock Policies 137 Table 4.6 Inventory and production management of the item BPT
Elementary period 1 2 3 4 5 6 7 8 9 10 11
Demand 0 20 10 15 10 20 20 18 12 20 10
Corrective demand 0 0 0 0 0 12 3 0 1 0 0
Production 0 0 15 0 0 15 40 0 20 10 50
Inventory level 30 10 15 0 –10 –27 –10 –28 –21 –31 –9
Corrective production 0 10 17 0 1 0 3 0 0 0 0
Table 4.6 concerns item BPT. The mechanism is the same as in Table 4.5, except that an additional row is introduced to modify the demands in order to take into account the corrective production introduced for the end product and the fact that only one BPT is required to perform one end product. When scheduling the corrective production, the system takes into account the fact that three elementary periods are required to produce item BTP. In this table, we assume that item BPT is a component of only the end item TB.
The above example is simple. In real situations, the number of end items (i.e., level 0 items) could be very high and a component can be used by several end items. So the computational burden is often very large: this explains why MRP is of utmost importance.
It should be noted that the MRP does not consider the capacity of the system.
As a consequence, the solution given by the MRP may be not admissible. In this case, the approach provides load profiles for the components of the system, and it is the responsibility of the user to modify the due dates of some items (load smoothing) based on the profiles and, if necessary, to launch the MRP system again, hoping that it will provide a feasible solution. The user may have to iterate several times before reaching a feasible solution.
In the above example we used a lot for lot policy. Some more complex lot- sizing rules are often applied in practice. They will be presented in the next section.
4.4.2.5 Some Remarks about MRP
The following advantages are usually mentioned:
1. reducing inventory and WIP levels;
2. reducing the number of late deliveries;
3. better adjustment to changes in the master production plan;
4. improvement of productivity;
5. better use of resources.
There are also several disadvantages when using MRP:
• Tendency to perpetuate the errors of the past, in particular to freeze overesti- mated operation times.
• The operation times are defined based on lot sizes that rarely coincide with ac- tual ones which makes it difficult to reach feasible solutions.
• The scheduling function is not included in the MRP.
• The necessity to carry out a parameterization phase using simulation to take into account the real lot-sizing rules and random factors.
• The nervousness of the system due to the frequent changes of production plan.
MRP is a widely accepted method for production planning. The MRP software solutions are employed readily. Most industrial decision makers have been made aware of them through all the commercial production control software. MRP software has a well-developed information system and has a proven track record.
Nevertheless, MRP is funded on the hypothesis that the demand and lead times are known. Release dates (replenishment order dates) are calculated for a series of discrete time intervals (time buckets) based on the demand and considering the fixed lead time (the release date is equal to the due date for the demand minus the lead time).
This premise of deterministic environment seems somewhat awry since often random events arrive and product lead times and finished product demands are rarely foreseen reliably due to machine breakdown, transport delay, customer demand variations, etc. Therefore, in real life, the deterministic assumptions embedded in MRP are frequently too limited.
Luckily, the MRP approach can be adapted for replenishment planning under uncertainties by determining the optimal values of its parameters. For random lead times, the planned lead time will be obtained as the sum of the forecasted lead time and the safety lead time (safety stock). These planned lead-time values are a compromise between overstocking and stock-out while optimizing total cost. This is called the MRP parameterization problem. State-of-the-art methods are reported and commented upon in (Dolgui and Prodhon, 2007).