Defining the placement of inventory buffers in the elements of the bill of materials for the manufacture of a product using the Critical Path (CPM / PERT) methodology
Introduction
This document describes how to use the CPM / PERT methodology to define the elements of a manufacturing process in which it would be useful to place Inventory Buffers to reduce the delivery time of a product and improve the level of Customer Service.
1. Background
Currently, there are methodologies or initiatives to improve Manufacturing and Supply Chain Effectiveness, which suggest the use of Inventory Buffers, which aim to reduce the time of manufacturing and delivery of products and with this improve the level of customer service.
The use of the Inventory Buffers is the Strategic Positioning of the Inventories, according to Demand Driven MRP (DDMRP), this is to define where to place the inventories in order to:
- Deliver the product in the Minimum Time Required by the Client Achieve the Delivery Time of Opportunity to obtain the Best Price or More Volume of Business Obtain the Minimum Time in which the Sales Orders are visualized so that they are delivered on time Have the Protection to mitigate the Demand or Supply Variability Have Leverage Inventory to Improve Service and Reduce Delivery Time Have Inventory to Protect Critical Processes for Capacity and Quality
The Inventory Buffers will be placed at the most appropriate points in the BOM structure.
2. The Bill of Materials or the Structure of Materials of a Product
The structure of the BOM in the following figure shows the integration of the purchased materials and the manufacture of the parts until the manufacture of the final item for sale.
Structure of Materials and Delivery Times for the Manufacture of the Final Product 101
3. The CPM / PERT Network
The structure of the bill of materials for the manufacture of article 101 represented in the form of a project network to make the analyzes with the CPM / PERT methodologies would be as follows:
Network for CPM / PERT analysis resulting from the Bill of Materials Structure
4. Delivery Times
The Delivery Times must be defined through a careful statistical analysis, the Delivery Times must reflect the efficiency of each operation, the delivery times are decisive to improve the process and in this case define the location of the Buffers, as well as also defining the size of the buffers.
In the CPM / PERT methodology the determination of the Expected Time is based on values of three types of times, an Optimistic Time, a More Probable Time, a Pessimistic Time; For the case of this example:
- Ti e mpo more likely: It is one in a series of data is the data that is presented more, is what in Central Tendency measures is defined as the mode of the data. Ti e mpo Optimist: This can be considered as the delivery time that is when everything goes perfectly, although this could be considered as its definition, but when everything goes perfect ?, is complicated to say, in reality an analysis of Data This is not exactly possible, so Optimistic Time should be considered as the average of a range of data that have a value less than the FASHION value. Ti and mpo Pessimistic:This would be the data of the worst time that is recorded or that results when most of the deficiencies of the process appear, but knowing when this is not easy, so the Pessimistic Time should be defined as the average of a range of data that have a value greater than the value of FASHION.
The Times and the Determination of the Expected Time
To develop the example of using CPM / PERT to determine the location of Inventory Buffers in a Bill of Materials Structure for the manufacture of an item, we will take the following delivery time data in units of days:
Ti and mpos Delivery and Statisticians Elements of Structure Materials
5. Investment in Inventories
The same CPM / PERT network that was built based on the structure of the bill of materials is used to visualize the transition of costs since the purchase of the materials is made, the expenses that are incurred for the supply of those materials and transformation costs in each of the processes until the final salable item is obtained.
Having inventories of materials, parts or finished products implies having an investment of money, which, although it has a merger, are also assigned resources that cannot be used in any other way. Whichever way you decide to consider the investment in Inventories, the amount of this investment is a parameter to better define the location of the Inventory Buffers.
The cost network below shows how costs are transferred in the BOM structure, from the purchase of materials to the final salable item.
The cost of the material is transferred from its purchase and increases with the purchase price of other materials as they come together in subsequent processes. For our effect, we will have separate the material cost data and we will also have the data of transformation costs and expenses in each process, as well as those accumulated or increased for each process. The transition of costs and expenses to article 101 are as follows: Materials Cost: $ 1,150, Supply Cost: $ 235, Transformation Cost of: $ 200, Accumulated Transformation Cost to the final article $ 1,000, Total Cost of Article 101: $ 2,385.
Transition of Costs in the CPM / PERT Network of the Bill of Materials Structure
6. The CPM / PERT Network - The Variance of the Processes
With the expected times that were determined and the variance of the processes we have the CPM / PERT network in which in the first instance we can observe three branches that lead to the manufacture of the final salable article, from these we can obtain the variance of each branch and the Greater variance indicates to us in which branch we must pay attention to reduce the times and consequently the variability of the processes of that branch will be reduced, in the network we observe that the greatest variance is in Branch 1 is 14.11, the next with the highest variance Branch 2 of 11.89 and Branch 3 has a variance of 11.78
7. The CPM / PERT Network - Determination of the Critical Path
CPM / PERT Network - Critical Path Determination
The initial Critical Path is on Branch 1 defined by: Supply of Material 501P, Manufacture of Parts 409, 301, and 201 and Manufacture of Final Article 101
The Critical Route for the manufacture of Final Article 101 is 31 days, this critical route has a total variance of 12.33 days and a Standard Deviation of 3.51 days. Achieving 31 days to have the article 101 available has a variation of 31 days +/- 2 Standard Deviations (7.02 days), it is expected to have the final article in a time of between 23.98 days and 38.02 days for a 95.46% probability.
8. Location of Inventory Buffers:
It is now appropriate to locate the Inventory Buffers, doing this will incur Inventory Investment costs with the benefit of reducing the Expected Manufacturing time of article 101.
The Inventory Buffer should be located in the Critical Path and in it it should be located first in the place where customer service is assured, so that Article 101 is delivered to the customer in the maximum number of days that customers are willing to wait, assuming customers want to receive the product in a minimum of 3 days including the delivery time, so since the Expected Delivery Time of item 101 in is 5 days, this is a longer time than required by the customer, then an Inventory Buffer must be placed for item 101
To place the Inventory Buffer for item 101 with the Critical Path CPM / PERT model, this is done by changing the Expected Delivery Time from 5 to 0 “zero days”. The Delivery Time will be zero days and already having Inventory Buffer for product 101, it will be sent to customers as soon as their orders are received. We see this in the following table of the model:
1. CPM / PERT Network - Placement of the Inventory Buffer for the Manufacture of Article 101
When locating the Inventory Buffer for item 101:
- Item 101 can be delivered immediately upon receipt of customer orders.Inventory Inventory costs per Item 101 Buffer have (Materials $ 1,150 and Total Costs $ 2,385). The variance of the Item 101 Manufacturing Process is now 0 "Zero" The critical route is maintained in Branch 1 with a time of 26 days of replenishment of the Inventory of article 101
The next step is to locate another Inventory Buffer also in the Critical Path, for this the criterion is to place the Inventory Buffer first in the element or process that has the longest Expected Delivery Time, or in the element that contributes to the further reduction of the Expected Replacement time of article 101, in this case it is the process of Purchase of 501P Material.
By placing the Inventory Buffer for the 501P Material, the Critical Path will move to Branch 3 (Critical Path 2), which is the one with the 23-day replenishment time, it is the immediate lower than 26 days of Branch 1
2 . CPM / PERT Network - Placement of the Inventory Buffer for the Purchase of 501P Material
The Inventory Buffer in Critical Route 2 is placed in the process or element with the longest Expected Delivery Time, this is the Purchase of Material 304P whose delivery time is 20 days, when placing in this process the Inventory Buffer the time delivery to be had is 0 "zero"
3 . CPM / PERT Network - Placement of the Inventory Buffer for the Purchase of Material 304P
Placing the Inventory Buffer for Purchased Material 304P reduced the total turnaround time for item 101, increasing the cost of Investing in Inventory. Critical Path now changed to Branch 2, the next step is now to locate an Inventory Buffer on the new Critical Path.
In the new Critical Route of Branch 2, there are two options for placing the Inventory Buffer, in the Purchase Process of the 404P Material and also in the manufacturing process of Part 203, both have an Expected Delivery Time of 8 days, by cost the Buffer should be located in the Purchase of the 404P Material, but for days of reduction in the replacement time it is more convenient to locate the Buffer in the Manufacture of Part 203.
In this case where we have two possible options for placing the Buffer, we choose to place the inventory (zero Expected Delivery Time) in the element of the Critical Path that makes the replacement time of article 101 have the greatest reduction.
The result of placing the Inventory Buffer in the manufacturing process of Part 208 can be seen in the following model view:
4 . CPM / PERT Network - Part 208 Manufacturing Inventory Buffer Placement
Placing the Part 203 Manufacturing Inventory Buffer again reduced the total turnaround time for item 101, increased the cost of Inventory Investment, and produced a new Critical Path.
Critical Path now changed back to Branch 1, the next step is now to locate an Inventory Buffer on the new Critical Path.
In the new Critical Route of Branch 1 (Critical Route 4), the option is to place the Buffer in the Manufacturing process of part 201 whose Expected Delivery Time is 8 days, it is the longest in that Critical Route, when placing the
Buffer in the Manufacture of Part 201 we can see that a new Critical Path is also generated again in Branch 2, the result is seen in the following model view:
5. CPM / PERT Network - Inventory Buffer Placement for Manufacturing Part 201
Having placed the Buffer in the Part 201 Manufacturing process, there are Buffers in: 1. Manufacture of Article 101, 2. Purchase of 501P Material, 3. Purchase of 304P Material, 4. Manufacture of Part 203 and 5. Manufacture from Part 201
At this point the Objective defined for the action of placing the Inventory Buffers was achieved, which was to reduce the Expected Delivery time by at least 50%, with the placed Buffers a reduction of 58% is being achieved, having reduced the Expected Delivery Time from 31 days to 13 days.
Results of the Process of Using the CPM / PERT Methodology for the Location of Inventory Buffers
Now the objective of reducing the Expected Delivery Time has been achieved, but the process can be continued with a greater reduction, if this is done, in the new Critical Route of Branch 2 it is where the Buffer should be placed, in this case the Greater Delivery Time is 8 days in the process of Purchasing the 404P Material, if we place the Buffer in this process the Total Expected Delivery Time is reduced to 10 days, but if we place the Buffer in the Part 305 Manufacturing process, The Total Expected Delivery Time is reduced to 8 days, for this reason, to have a greater decrease in the Delivery Time, it is decided to place the Buffer in the Manufacturing process of Part 305, so, the situation of the Model can be seen in the next view.
6. CPM / PERT Network - Part 305 Manufacturing Inventory Buffer Placement
By placing this last Inventory Buffer, the Critical Route of Branch 2 remains Critical and a new Critical Route appears in Branch 1 and now this is Critical in its two aspects of initiation, this happens because the more the Total Time is reduced Delivery Due to the placement of buffers, the difference between the branches of the routes is less and less. As there are two or more critical routes it will mean that to reduce the Expected Delivery Time more, with the placement of Buffers each time there will be a higher cost for the Investments in Inventory. The results up to this last Buffer, which may still be acceptable, are now shown:
Results of the Process of Using the CPM / PERT Methodology for the Location of Inventory Buffers
9 . Summary of Steps to use CPM / PERT to define the Position of the Inventory Buffers
- Define the structure of the list of materials From the structure of the list of materials define the CPM / PERT Network Determine the Delivery Times of the elements or processes (Optimistic Time, Most Probable Time - FASHION, Pessimistic Time), as well as Variance and Deviation Standard.In the CPM / PERT Network determine the Critical Path Locate the Inventory Buffers in the elements or processes of the CPM / PERT Network
- Establish the Target of% Reduction of Total Delivery Time Locate the Inventory Buffer in the Element or Process of the Critical Route that has the longest Delivery Time and that makes the greatest decrease in Total Delivery Time, the location of the Buffer is defined of Inventory making “zero” the Delivery Time of the process or element of the CPM / PERT Network, when locating the Buffer in the Critical Path that ceases to be Critical and generates another Critical Path Continue to locate the Inventory Buffers in the Critical Routes according they are generated in the progress of the procedure until the established reduction objective is reached or until after locating a Buffer, more than one Critical Path is generated.
