Queuing Analysis

#### Optimization Models

Drive/Structure

Models

Subassemblies

 Process Flow Analysis - Process Definitions

A manufacturing system is defined by collection of processes for the one or more products of the system. Data describes a process in terms of structure, operation sequence, push or pull flow, setup and operation times, lot sizes, recycle rates, scrap rates, defect rates, raw material use and machine requirements. Computations distinguish between processing and inspection operations, with processing operations producing defective items, and inspection operations discovering and scrapping defective parts. The main results of the add-in are the operation unit flows that indicate the rate of flow into each operation per unit of finished product. The add-in builds and formats the worksheet areas necessary for data entry and inserts the formulas necessary for analysis.

We repeat the process chart for product A for illustration.

Data concerning product A is entered by selecting the Add Process item from the OM_IE menu. The following dialog box is presented. Cells are provided for the Location and Name of the process. The check boxes indicate various features the data structure is to exhibit. For the present example, we include defects, proportions, resources and raw materials. The Tree structure option has been chosen because the the raw materials combine to make the finished good. The process chart has the tree structure. The Pull drive option indicates that the demand for the product is pulled from the final operation. The other structure and drive options are illustrated later.

The figure below shows the data structure after the information for product A has been entered. The other products differ only in the proportion of cards passing through the two lines. Note that the columns of the display include the required columns and columns necessary to model the items checked in the dialog box.

At the top of the display the name, structure, drive and flow out of the process are listed. The first three items are in a yellow field indicating that these values should not be changed. If they are mistakenly entered, delete the process and redefine it with correct values. The flow out can be changed to reflect different amounts of finished products. The data entries in cells G1, G2 and G3 define the time dimensions for characteristics of the problem. The Flow Time Interval is the dimension by which demand for the finished good is measured. For this example, the flow out of the process is 200 units per week.The Operating Time Interval is the dimension by which processing times are measured. For example the processing time for the SMT line is 0.03 hours. The Operating Interval per Flow Interval, tells for this example the number of processing hours during a week. We enter 40 here to indicate one shift operation for 5 days per week.

Also at the top of the display are summary results. In cell K1 we see the total time spent in the operations of the process measured in hours. Cell K2 holds the total Work-in Process for this process. The contents of these cells are computed with formulas as described below.

The table below shows the meanings of the various data columns. We only define here the columns used in the example. The data columns start in the worksheet column A in the example, and we use the Excel column designations to describe the items. There is no requirement, however, that the process definitions begin in column A, and the columns used by a particular data item will depend on the items selected in the dialog.

Data Items Describing a Process
 Column Title Explanation A Name Name to identify operation. The example has eight operations. The Start and End operations are added by the program. B Type The type is identified by the first two letters of this field. "Op" identifies a processing operation, delay or inventory. Defects introduced in "Op" operations are accumulated but not discarded. "In" identifies an inspection operation. "In" operations discard some proportion of the defects as waste. C Index This column specifies a unique number identifying an operation. The column is colored green to indicate that the add-in controls its contents. The numbers in this column will be sequential integers and the index assigned to a particular operation will change when operations are added or deleted using the Change Process command. The user should not bother these numbers. D Next This column gives the index of the following operation in the process. For the pull/tree option illustrated here all operations must have a unique following operation. The following node of the "End" operation is 0. Every pull/tree structure defines a unique vector of Next indices. This column is labeled Previous for a push tree. For the Network structure, this column will not be included unless the Defects option is selected on the dialog. E Pull Out The numbers in this column describe flows out of each node relative to 1. For the example, the only non-zero entry is the end operation (9). The total flow out of the process is the product of this number and the number in cell B4. Other numbers in this column are also relative. If 1/2 were entered in E10, flow in the amount of (1/2) times the number in cell B4 would be removed from the TH line. This allows the process to have several outputs. Note that all outputs are proportional to the number in B4. F Operation Time This is the time to process one item passing through the operation. G Defect Rate This is the percentage of products passing through a processing operation that receive defects. We assume a single defect warrants discard of an item, however, the defects are only discovered by an inspection. Defects do not change the flow except at an inspection operation. For an inspection operation, the defect rate is the proportion of defects not discovered and discarded. H Proportion For a pull system, this is the proportion of the flow entering the next node that comes from the operation specified by this data line. For product A, 50% of the flow of finished product comes from the SMT Inspection and 50% of the product comes from the TH Inspection. The other products differ with respect to these proportions. For a push system, this parameter is the proportion of the flow leaving the operation that goes to the next operation. I Resource Type This is the machine resource used by the operation. Machines are identified with names or numbers. Different operations and processes may use the same resources. The resource types are used to construct the from-to matrix. See the page describing this matrix for more details. J Resource Amount This is the number of resources used by the operation. For machines it is usually 1. For those rows without resources, the number has no meaning. K Raw Material Type This is the raw material identifier used by the operation. Raw materials are identified with names or numbers. Different operations and processes may use the same raw materials. L Raw Material Amount This is the number of units of raw material used by the operation. It has no meaning if the associated Raw Material Type is blank or 0.

The example includes two additional products, B and C. The products differ in the proportion of product that passes through the SMT and TH lines. In the case of B, 90% of the boards come through the SMT line, while 10% come through the TH line. All of the boards for product C come through the SMT line. The TH portion of the process could have been left out, but we leave it in to keep the three processes similar.

Note that we have defined all the processes in the example on the same worksheet with all process definitions starting in column A. This is not necessary as processes may be defined on different worksheets and at different locations within a worksheet. All the processes are assumed to comprise the complete system for the economic analysis. Use a different workbook for each system.

There is no limit to the number of operations in a process for the tree structure. The network structure is limited to about 50 operations. The analysis of the network structure requires a matrix inversion. Excel limits that computation to a matrix with fewer than 50 rows and columns.

The add-in limits the number processes, resources and raw materials to 50 for each. These numbers may be changed by changing the associated variables in the Declaration module of the add-in.

Change Process

Operations may be added or deleted with the Change Process item on the OM_IE menu. The example below will add a new operation after the operation indexed 1 (SMT Line). The start and end operations are fixed. Operations cannot be added before the start or after the end. Use the third button to delete an entire process.

Operations Management / Industrial Engineering
Internet
by Paul A. Jensen