Process Flow Analysis
Definition of Processes

The Theory of Constraints (TOC) is a five-step procedure for operating a system producing several products on several machine resources. We list the steps below.

  • Step 1: Identify the system's constraint(s).
  • Step 2: Decide how to exploit the system's constraint(s).
  • Step 3: Subordinate everything else to the decisions of Step 2.
  • Step 4: Elevate the system's constraint(s).
  • Step 5: If a constraint is broken in Step 4, go back to Step 1.

In this section, we describe how process flow analysis is used to perform step 1, identify the system's constraints. At the same time we illustrate a number of the issues that arise while designing and operating a production process. We use an example taken from teaching materials provided by the Goldratt Institute. In the figure below, the left and bottom axes are labeled for indentification of the various system components. The components are the colored rectangles arranged in rows and columns. The manufacturing process starts at the bottom of the figure with raw materials entering at the row labeled RM. The raw materials are identified by their columns. There are five raw materials labeled A, B, E, F and G. The number adjacent to a rectangle in the RM row is the unit cost of the raw material.

Finished goods or products are indicated in the row labeled FG. Again we identify a finished good with its column. Thus we have finished goods A, C, F and G. The number to the left of a rectangle is the unit revenue for the product and the number within the rectangle is the maximum sales per week.

The unit-processes or operations used to translate the raw materials to finished goods are colored to indicate the machines that implement the operations. For the example, we have six machine types labeled W, M, R, C, G and B, refering to the colors Brown, Magenta, Red, Cyan, Green and Blue. (The color designations are the same as those used by Goldratt, and I don't know why Brown is labeled with a W). The number within a rectangle is the unit-processing time expressed in minutes. A particular operation is identified by its row and column. The flow of materials proceeds from raw materials to finished goods along the lines connecting the operations. Lines converging indicate assembly. For example, the outputs of operations A5 and B5 are assembled in operation A7. Diverging lines indicate that the output of an operation is used by more than one following operation. For example, operations B5 and B6 both require the units produced by B3. The numbers on the lines indicate work-in-process (WIP) at the beginning of a week of production.

At the bottom of the figure, we see that the system requires an operating expense of $4500 per week. Each week has 2400 minutes. The colored retangles at the bottom indicate the names, numbers and setup times for the machines of the system. The time capacity for a particular machine type is 2400 minutes multiplied by the number of machines.


There are many questions that must be answered regarding the operation of this system.

  • Can we produce all the products in the amounts equal to the weekly demand?
  • If all products cannot be produced to the maximum, how much of each product should be produced?
  • When should raw materials be purchased? How many units should be purchased?
  • What lot size should be used for each operation?

The decisions cannot be made independently. For example the lot size decision affects the amounts of finished goods that can be produced. In the following we illustrate the use of the Process add-in as well as aspects of the Theory of Constraints.

The first step of the TOC is to identify the bottleneck. To do this with the add-in we describe processes for each finished good. The figure below shows the operations necessary for finished good A. Although some of the operations are used for other products, the process for each product must be defined independently. The system results will be obtained by combining the data for the products.

The system is described for Excel using the menu items, dialog boxes and other interactive features provided by the Process add-in. See the add-in description for details. Processes are created on a worksheet by selecting Add Process from the menu.

The portion of the Excel worksheet describing the process for product A is below. The seven operations are numbered in column C. Column D shows the sequence of operations. As for most manufacturing situations, this is a pull system where the flow through the operations is pulled by the demand at the finished good operation. We see on the sheet several features of the problem including operation time (col. F), setup time (col. G), lot size (col. H), resource type (machine designations in col. I) and raw material types (col. K). Cell B4 holds the demand per week and cell G3 holds the number of minutes per week. Economic and capacity aspects of the situation will be considered later.

  We have chosen a lot size of 30 for our analysis. It is necessary to choose some lot size because setup times play an important role in this problem. It happens that the product demands are all multiples of 30, so this choice seems reasonable at this step of the analysis.

Finished good C is produced by the process shown in the figure and represented by the Excel table below.


Finished good E is produced by the process shown in the figure and represented by the Excel table below.


Finished good F is different than the others in that its operations are not shared by other finished goods. Since the operations use common machines, however, the production of F cannot be set independently of the other finished goods.

  After the process for each finished good has been defined, we choose the Process Economics option from the menu to perform a system analysis. Results for the example are on the next page.


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Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved