   #### Process Flow Queuing Analysis

#### Optimization Models

Drive/Structure

Models

Subassemblies  Download Process Flow Analysis - Computation for Flow Analysis Spreadsheet formulas are included to compute a number of characteristics associated with the process. We repeat the data for the example together the results. The descriptions of the results columns follow. All of the cells in the analysis columns are colored yellow on the worksheet. The colored cells indicate that the cells contain formulas that should not be changed by the user. Some of the cells use functions defined by the add-in. If a model is created on one computer and opened on another, these functions will not compute. Use the Refresh Functions command to rewrite the functions. Not all the results column are shown in this example. We describe all the result columns below using the Excel column letter for identification.  Results for the Process Analysis Example

 Column Title Explanation M Defects Out For a processing operation ("Op"), this is the proportion of the items leaving an operation that have defects. We assume that the defect producing mechanisms in different operations are independent. The function in this cell combines the probabilities of defective parts entering the operation with the defect probability for the operation to obtain the probability that an item leaving the operation is defective. The computations are implemented in the defect user-defined function. For an inspection operation ("In"), the probability of a defective part leaving is zero if the inspection is perfect, that is inspections find and remove all defective items. If the inspection is not perfect, the function computes the probability that a defective item leaves the inspection. N Flow Removed For a processing operation, this cell contains the adjusted scrap rate for the operation. When the operation is an inspection, defective items are removed as waste. The proportion discarded is shown in this column. Again, these cells are computed with a function, remove1, provided by the add-in. O Ratio This is the ratio between output flow and input flow for an operation. When material is removed, the ratio is less than 1 as in the example. The ratio is also affected by the grouping factor for the operation. P Unit Flow For this example, this is the flow into the operation per unit flow out of the process (out of operation 9). In general for a pull system, there may be several operations from which flow is removed as described by the pull out column of the data. The unit flow is the effect of the combined output flows from the process. For the pull tree structure these cells are computed with an algebraic formula based on the unit flow of the next cell and the ratio and proportion for the operation. For a pull network structure the unit flows are computed with a matrix computation using the Excel matrix inverse function. Q Unit Time This is the resource (machine) time used by this operation per unit of the flow out from operation 9. For the example this is just the time used by a unit of product A. R Operation Flow This is the total flow rate into the operation. It is the Unit Flow multiplied by the flow out. For product A the flow out is in cell B4. The Operation Flow is this output flow divided by the number of operating hours per week that appears in cell G3 multiplied by the Unit Flow. S WIP This is the flow rate through the operation multiplied by the residence time in the operation. It is the operation flow (flow rate) multiplied by the operation time (residence time) . By Little's law, this must be the average work-in-process that resides at the operation, or the WIP. In column K near the top of the display we see two computed quantities. Cell K3 computes the total WIP in the process. It is the sum of the operation WIP values appearing in column S of the process display. Cell K2 holds the total WIP divided by the total flow rate out of the process. For the Pull system, the total flow rate out of the process is the sum of the external flows from column E of the data multiplied by the contents of cell B4. When the operations are arranged in a series system it is the average time interval between when raw materials enter the process and when the finished good leaves the process. Sometimes we call this the cycle time. When the structure is more general than a series system, it is the average time materials remain in the system.  The process results for products B and C are below.

Results for Process B Results for Process C   Operations Management / Industrial Engineering
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by Paul A. Jensen
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