Process Flow Models - Resources

Resources are used to manufacture products. A resource is characterized by time available during some interval of time, say 40 hours per week. Production during the week uses up the time available for resources, but the resources remain for the next week. Resources include machines, space and labor. In the context of an application a variety of resources might be defined. The economic analysis allows specification of resource investment costs, operating costs, number and availability. A variety of questions might be answered for which resources play an important role.

 Checking the Resource box in the dialog causes the process definition to include resource columns, one for name and another for amount. The resources described by these columns are called System Resources and are usually physical resources, such as machines, that are located in specific places in the plant. The other boxes checked in the figure, add other features specific to the example. The field labeled General Resources specifies the number of columns to include for resources that are used for several operations in the process. These usually are resources that do not involve physical location. We use labor as a general resource for the example. Although we do not specify that parameter columns be included, two columns are automatically created because they are necessary for the time functions. To illustrate we use a serial pull process with inventories and queues. The triangle for operation 1 represents the raw material inventory. The triangle for operation 7 represents the finished goods inventory. The d-shaped symbols for operations 2 and 4 are delays for the queues waiting for machining operations 3 and 5. We add a second pull location at the output of operation 6. The value of 0.2 indicates that for each unit leaving operation 7, 0.2 will leave at operation 6. The two pull amounts are not independent, the flow withdrawn from 6 will always be 20% of the amount withdrawn from 7. If independent demands at the two locations were required, separate processes would be defined for each pull location. Parameters for the operations are on the Excel worksheet below. The worksheet is shown in two parts for clarity. All operations use lot sizes of 10. Only operations 3, 5 and 6 have nonzero operation times. Nonzero scrap rates are at the three processing operations, so their ratios are less than 1, and the unit flows increase as we move backwards from operation 7. Defects are not included in the model, so there is no need for inspection. Operation 6 models a batch process where 10 items are processed at the same time. Each item passing through the operation has a processing time of 5 hours, but all items in the batch of 10 are processed at the same time, rather than sequentially. We model the batch process by assigning 1/10 to the resource amount for items passing through the machine 3. The denominator is the batch size. The process uses resources as listed in column J. The names of the resources are important, because the use of like-named resources by separate operations and separate processes are combined. The names of resources that appear in column J are also used to construct the from-to matrix. The four system resources for the example are: store, machine 1, machine 2 and machine 3. The entries in column J are called System Resources. Column K shows the number of units of each resource used by the operation. The dimension of capacity may differ between resources. In the example, the dimension of the store resource is square meter-hours, while the dimensions of the other three system resources are machine-hours. The RM Inventory operation (row 7), uses 1.5 square meters (col. K) for each unit of flow passing through the operation. The time required is 1.5526 hours (col. P). Thus each unit of demand uses 1.5*1.5526 = 2 sq. meter-hour (col. T) of the store resource. The numbers in column T are used in the Economic Analysis part of the model. Machine resources are measured in machine-hours. We note that the resource use for operation 6 is 0.1, indicating that 10 units, the size of the batch, will use up the entire capacity of machine 3. Labor is a general resource and its use is described in column L. The three processing operations require 1, 2 and 0.8 units of labor during the operation time. The total use of labor per unit of finished good, leaving operation 7 is determined in the economic analysis.

 Column Title Explanation J Resource Type This is the resource used by the operation. Resources are identified with names. Different operations and processes may use the same resource. The resource types defined in this column are system resources and are used for the economic analysis and also to construct the from-to matrix. K Resource Amount This is the number of resources used by the operation. For machines it is usually 1, although it could be less than 1 if the machine is not used during part of the operation time or the operation is a batch process. Resource amounts may be 0. The from-to matrix recognizes flow that passes from one system resource to another system resource. In the example, we identify the queues as using the resources of the machines they precede, but use 0 as the resource amount. This causes the flow to be passed from the store resource to the machine 1 resource. If the resource type were left blank for the Queue 1 operation, that flow to machine 1 would be lost. L General Resources The dialog allows the user to produce columns for general resources. An example is labor, where each operation may require a specified number of labor hours per operation hour. An entire column is provided for each general resource, so different operations may use the same resource. The name of a general resource is placed on the top of the column. A general resource should not use the same name as the names listed in the Resource Type column. The numbers in a general resource indicate the amounts of the resource used by flow passing through the operations.

Economic Analysis - Resource Availability and Use

The Economic Analysis option on the OM/IE menu produces the Project worksheet. All parts of the worksheet are constructed by the add-in with default data in several areas defined for user input. Generally, ranges with a white background and maroon outlines are for user data, yellow areas hold Excel formulas and green areas hold the output of computer computations. The user data for the example has been entered by the author to illustrate meaningful values.

Several of the ranges on this worksheet refer to resources. Although, not specifically showing resources, we include the Product portion of the worksheet because the product sales per week (cell I3) drives the total resource requirements. The number is initially taken from the Flow Out cell (B4) in the process definition, but can be changed here to investigate the impacts of different levels of sales. The example has only one process defined, otherwise there would be multiple lines in the Product portion. Although we choose to sell (and manufacture) 100 units of product A which is the output of operation 7 in the process, we also produce 20 units at operation 6. The product is identified by the process name.

Starting at row 8 for the example (row numbers will be different for other examples), we see the portion of the worksheet that accepts data and compiles information from the processes that are defined in the workbook. The current example only has one process, so all the information comes from that process (A).

Column E lists the resource names as compiled by the add-in from the process definitions. Column F shows the number of each resource used. For the first three resources, this is the number of machines used. In the case of store, this is the number of square meters, and for labor it is the number of workers. Except for machine 1, we have entered values large enough to provide sufficient resources to manufacture 100 of product A. column G holds the maximum number of the resources allowed. Here, we use the same as column F, but this column will provide an upper bound for the mixed integer programming model that optimizes the number of the resources. Column H implies that all resources work for 40 hours per week. Column I indicates the availability of the resources. Values less that 100% indicate downtime. Column J is provided to limit the utilization of resources. Although we exclude variability for our model, we recognize that WIP will explode when resources are used to high utilization when there is variability present. Here we allow the user to specify the maximum utilization allowed. Columns F through J are user data and can be changed to represent the system being modeled.

Column K is the hours available for each unit of resource considering the entries in columns H, I and J. Column L multiplies this by the maximum number of resources. Column M is the available hours given the number of resources used. Column N holds the computed amounts of the resources used given the sales of the product. For a feasible system, the entries in column M must be no less than the entries in N. Note that the row for machine 1 shows a slight deficit, indicating that the 100 units of production for process A is not quite obtainable.

The primary model assumption is that resource use is proportional to the number of items passing through an operation and the time required for the operation. This is valid in many, but not all, contexts. One case in which it is not valid is for a queue that uses the resource of space. The number in the queue, the time in the queue and subsequently the space required is a nonlinear function of flow.

Resource Cost

Starting in row 16 of the Project worksheet, a table of resource costs is provided.

Again, the resources are listed in column E. This list is constructed by the add-in. Data is entered in columns F through G. Column F has the space per resource unit. Any space measure can be used, but assume the numbers are in square meters. The first three entries are the space requirements for each of the machine types. Since the dimension of store is square meters, the space per unit is 1. We assume 4 square meters are allowed for each worker. Column G is the operating cost per hour for each resource. This cost is expended only for time used. Column H shows the investment cost amortized to the weekly interval of the analysis. These costs are fixed costs per unit of resource and do not depend on the utilization.

Columns I though J are computed with formulas based on the number of hours used to manufacturing 100 of the A product and the number of each resource provided. The latter was entered in the range F9:F13. The space requirement might be useful for a plant layout analysis. The operating and investment costs are used in the economic analysis. Totals are provided in row 22.

Unit Resource Use

This table starts in row 29 for the example. There will be as many data columns in the table as there are products, but here we only have one column. Again the resources are listed in column E. The green range in the table is computed by the add-in from the process definitions. Each entry is the amount of resource used per unit of product. For example, the definition shows two uses of resource store. The first is the RM Inventory that for each unit of finished good uses 1.5 meters for 2 hours. The second use of store is the FG Inventory that for each unit of finished good uses 2 meters for 5 hours. The total use is then (1.5*2 + 2*5) 13 hours per unit of finished good A. The Resource Operating Cost/Unit is the sum-product of the resource operating costs (G17:G21) and the contents of (F31:F35). This value is subtracted from the revenue per unit to obtain the operating profit column of the product portion of the worksheet (cell J3).

From-To Matrix

A matrix that is useful for plant layout analysis, is the from-to matrix. The flows between system resources are computed by the add-in and placed in the matrix display starting at row 45. The green area indicates the flows between the system resources listed in column J of the process definition. Columns and rows are also constructed for the general resources, Labor for the example. The default flow in these cells is zero, but if there is a flow from labor to or from any of the system resources, that flow can be entered into the cells provided.

Summary and Refilling

In the upper left corner of the Project worksheet there is a summary of the economic results. This summary is linked to the product sales and the results of the various data items and computations on the worksheet.

It may be that the user will want to change process definitions or add new processes. The contents of the Project worksheet may be updated after changes by clicking the button to "Fill usage matrices". The from-to matrix is updated by clicking the "Fill from-to matrix" button.

Operations Management / Industrial Engineering
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by Paul A. Jensen