In the Model window, use the Equation tab to specify the equation or initial value for a selected building block. The Equation tab is for assigning units to a building block and selecting options and parameters that affect the building block's equation.
To view the Equation tab, click the at the bottom of the Properties panel. For more information about using the Properties panel, see Using the Properties panel.
The options available in this section depend on the type of building block you select.
Type – Use this option to select how the initial value is calculated for the conveyor: Continuous or Discrete.
If you select Continuous, the initial value for the conveyor is spread evenly over the length of the conveyor, and flows out of it in a steady stream. Unless the inflow is from a queue, this is selected by default.
If you select Discrete, the initial value is separated into "packages", so it flows out of the conveyor in separate chunks. The initial value is spread over the conveyor, but the packages are stacked in the last DT of each conveyor slat. If the conveyor's inflow is from a queue, Discrete is automatically selected and can't be changed.
Accept – Use this option to select how much of the value you want the conveyor to accept from its inflows: One at a time or As much as possible.
If the conveyor's inflow is from a cloud and/or stock, the conveyor will accept as much material as possible; As much as possible is automatically selected and can't be changed.
If the conveyor's inflow is from a conveyor and/or oven, the inflow is determined by the upstream conveyor and/or oven; As much as possible is automatically selected and can't be changed.
If the conveyor's inflow is from a queue, you can select either option. If you select One at a time, the conveyor will take the next item in the queue, each DT, subject to the inflow limit and capacity constraint. As much as possible will make the conveyor take as much as it can from the queue.
Note: The quantity the conveyor can accept is always subject to the values in the conveyor's Capacity and Inflow limit parameters.
Split batches - This option is only available if the conveyor's inflow is from a queue.
Select this check box to let the conveyor take only a portion of the "next" item in the queue if the conveyor has reached its Inflow Limit or Capacity. If this check box is not selected, the flow from the queue will be set to zero (0) if the flow exceeds the values in the Capacity or Inflow limit parameters. This can lead to queue blockage.
Accept – Use this option to select how much of the value you want the oven to accept from its inflows: One at a time or As much as possible.
If the oven's inflow is from a cloud or stock, the oven will accept as much material as possible; As much as possible is automatically selected and you can't change it.
If the oven's inflow is from a queue, you can select either option. If you select One at a time, the oven will take the next item in the queue, each DT, subject to the oven's capacity. As much as possible will cause the oven to take as much as it can from the queue.
Note: The quantity the oven can accept is determined by its capacity, as specified in the Capacity parameter.
Tips: To represent a capacity-constrained situation, select the One at a time option, specify a long fill time, and specify a small capacity.
To represent a processor that takes only the "next" item from the upstream queue, select the One at a time option, select the DT builtin for the fill time, and specify a large capacity.
Split batches – This option is only available if the oven's inflows are all queues.
Select this check box to let the oven take a portion of the "next" item in the queue, in order to fill itself to capacity. If this check box is not selected, the flow from the queue will be set to zero (0) whenever the flow exceeds the values in the oven's Capacity parameter. This can lead to queue blockage.
When you first view the Equation tab for a flow, the type of flow you chose when you first placed it will be selected. To change the type, select the appropriate option here.
Uniflow – Select this option to have the flow move in only one direction. With uniflows, the flow volume only takes on non-negative values. Biflows can take on any value.
Biflow – Select this option to have the flow move in two directions. With biflows, the flow volume can be any value (negative or positive). If you select this option, a second, dashed, arrowhead will appear on the flow to point in the direction of the negative flow. It's not possible to have a biflow connected to a conveyor, queue, or oven.
Time stamp flow – Select this option to time stamp the flow, for use with cycle-time. This option is only available when you've selected Cycle-time as the integration method. If you select this, flows will be marked with a clock.
Unit conversion – Select this check box to convert the units of measure for the flow as material moves through the flow pipe. This is useful when you're modeling processes like assembly (which transforms raw materials into finished goods) or chemical processes (which involve molecular transformations).
When you select the Unit conversion check box for a flow, a shaded half-circle will appear in the flow regulator on the diagram, to indicate that unit conversion is taking place.
The Unit conversion check box is only available for uniflow flows that connect two stocks (where the flow is conserved). The default is no unit conversion.
Inflow multiplier – This box appears when the Unit conversion check box is selected.
The inflow multiplier is the value the upstream stock's value should be multiplied by. The resulting value becomes the downstream stock's value.
The value can be either a number or a model variable from the Required Inputs list. The default value is 1.0.
To specify a value in this box, you can type a number, use the calculator buttons to enter a number, or click a variable name in the Required Inputs list.
When the model runs, the software reports the values for the flow before unit conversion has taken place.
Leakage – This option is available if the flow is the second or subsequent outflow for a conveyor.
Select the type of leakage this flow represents: Linear or Exponential.
If you select the Linear option, the total amount that will leak for any given inflow will be the contribution of that inflow to the stock value (inflow*DT) multiplied by the leakage fraction. The leakage will be spread evenly in time over the leak zone. In steady state, the total leakage will be inflow*leak_fraction, and each slat in the leak zone will leak the total amount divided by the number of slats in the leak zone. In this case, the units of measure for the leakage fraction must be Dimensionless.
If you select the Exponential option, the amount that leaks from each slat within the leakage zone is equal to the slat contents times the leakage fraction, generating an exponential decay in the amount leaked across the leakage zone. In this case, the units of measure for the leakage fraction must be per time unit (e.g. Per Month, if the model is in Months).
For Linear leakage, the total amount leaked doesn't change with the length of the leakage zone, whereas for Exponential leakage, it does.
Note: To specify the leak fraction, use the Leak fraction box in the flow's Parameters section.
Select the Leak integers check box to round leakage flow to the nearest integer value. If the Discrete option is selected for the conveyor, the rounding will happen each DT. Otherwise, the rounding will happen each time unit.
The Leak zone is defined by the blue sliders. By default, the entire conveyor will be selected as the leak-prone section.
Use the sliders to specify the size of the leak zone. The leak zone is expressed as a percentage of the conveyor's transit time, which is applied to the inflow as it enters the conveyor.
To specify the leak zone, move the Start and End sliders to select the appropriate percentage. A leak zone percentage of 100 implies that the entire conveyor is leak-prone.
By default, the leak zone is 100%, and leakage occurs across the entire conveyor. To have the leakage occur at the end of the conveyor, move the start slider as far to the end as you can (99).
Tip: You can have multiple leakage flows from a conveyor; each leakage flow can have different leakage fractions, to create different leakage zones. For example, you can create a leakage flow of 10% for the first half of the conveyor and another leakage flow of 20% for the second half of the conveyor. Do this by adding additional flows and defining their leakage zones differently.
Overflow – This check box is available if the flow is the second or subsequent outflow for a queue.
Select this check box to make the flow an overflow. When a higher priority flow is blocked because of capacity constraints, the flow will be routed through the overflow. For more information about flow prioritization, see Flow prioritization.
This displays a list of all inputs that must be used in the equation for the selected variable. Required inputs are anything connected to the selected variable using connectors. This list only appears if the selected variable is a flow or converter.
Note:This list doesn't appear for Summing Converters, which can take any inputs.
Tips: You can also see a list of all allowable inputs for the selected variable (including required inputs) by using the Find window. You can then drag a listed input from the Find window into the Equation box. You can also drag a required input variable from the model diagram into the Equation box. For more information, see Finding Variables in Models.
This displays a list of builtins that you can include in the equation for the selected building block.
Note: Regarding converters, this list doesn't appear for summing converters, which create their equations automatically.
Tip: By default, the list displays all builtins in alphabetical order. To make it easier to find a specific builtin, select a category in the box at the top of the Builtins list.
This is the list of variables whose values will be added for the selected summing converter.
Note: This box only appears when a summing converter is selected on the model diagram.
Use the buttons in the Operators and Calculator sections to insert numbers and operators into the equation for the building block.
Note: The full calculator is only available when you're viewing the Equation tab for a stock, or when the Properties panel is sufficiently wide. For other variables, and when the Properties panel is at its default width, only the Operators section is available.
Tip: You can also insert operators and numbers into the equation by typing them.
Tips: To transpose arrays in an equation, you can use the apostrophe (') as a transposition operator. For example, to transpose the array A[X, Y] as A[Y, X] in an equation, you can type A'. The apostrophe operator doesn't appear as a button in the Operator section. You have to type it.
If you're defining an equation for an arrayed variable that has more than one dimension with the same name, use the @ operator instead of the dimension name to refer to a particular instance of the dimension. Use @1 for the first use of the dimension, @2 for the second use of the dimension, etc.
The options available in this section depend on the type of building block you select.
Tip: For parameters where you can specify a model variable as a value, you can type the variable's name in the parameter box, or drag a variable from the Find window.
Transit time – Use this parameter to specify the time it takes for material to pass through the conveyor.
To specify a constant transit time, type a single number in this box. When you specify a constant transit time, all material that enters the conveyor will use the number you specify for the transit time.
To specify a variable transit time, define an equation in this box. For an equation, you can use other model variables, builtins, algebraic operators, or a graphical function.
Note: If you're using a statistical builtin to generate a variable transit time, be sure to generate random numbers within the conveyor's equation. Don't generate random numbers in an external converter and use that converter to define the transit time. If you generate random numbers externally, the sequence of transit times won't conform to the distribution you've specified for the converter.
Sample – Use this parameter to sample the conveyor's transit time whenever the equation you specify equals anything other than zero (0).
To use this parameter, select the Sample check box and then type an equation in the box that appears.
Whenever the sample equation isn't equal to zero (0), the current value of the transit time equation will be used for the transit time of material flowing onto the conveyor. If the sample equation is equal to zero (0), the transit time doesn't change. Material will exit the conveyor when the sampled transit time has expired.
If you don't select the Sample check box, units will be assigned to the transit time so that it's calculated as the units enter the conveyor.
Inflow limit – Use this parameter to limit the inflow into the conveyor. Inflows per unit time won't be allowed to exceed the value you specify here. To allow an unlimited inflow limit for the conveyor, set the value to infinity by typing INF (or by pressing option-5 on a Mac).
This parameter isn't available if the conveyor's inflow is a conveyor or an oven, because, in that case, the flow rate is controlled by the upstream conveyor or oven.
Notes: If the Discrete option is selected for the conveyor, the entire inflow limit will flow during one DT.
If the conveyor has multiple inflows and there's an inflow limit set for the conveyor, the inflows are prioritized so that the multiple flows enter the conveyor in order of their priority. For more information about how flows are prioritized, see Flow prioritization.
Capacity – Use this parameter to limit the capacity of the conveyor. Inflows per unit of time won't be allowed to fill the conveyor to a greater capacity than the value you specify here. To allow an unlimited capacity for the conveyor, set the value to infinity by typing INF (or by pressing option-5 on a Mac).
Note: If the conveyor has multiple inflows and there's a Capacity limit set for the conveyor, the inflows are prioritized; multiple flows enter the conveyor in order of their priority. For more information about how flows are prioritized, see Flow prioritization.
This parameter isn't available if the conveyor's inflow is a conveyor or an oven, because, in that case, the flow rate is controlled by the upstream conveyor or oven.
Arrest – Use this parameter to have the converter stop whenever the equation you specify equals anything other than zero (0).
To use this parameter, select the Arrest check box and then type an equation in the box that appears.
Whenever the arrest equation is not equal to zero (0), the conveyor will stop. Inflows and outflows to the conveyor will be set to zero (0). The conveyor will start where it left off when the arrest equation is equal to zero (0).
Note: The Arrest option is disabled when an inflow to the conveyor comes from a conveyor or an oven.
Cook time – Use this parameter to specify how long the oven "cooks" a batch before opening its door and releasing the contents. Material exits from the oven when the cook time expires.
You can specify a constant cook time or a variable cook time.
To specify a constant cook time, type a single number. When the oven closes its door, it'll use this number as the cook time for the batch.
To specify a variable cook time, use model variables, builtins, algebraic operators, or a graphical function. The cook time that's calculated as the oven closes its door will be used for the batch.
Note: If you're using a statistical builtin to generate a variable cook time, be sure to generate random numbers within the oven's equation. Don't generate random numbers in an external converter and use that converter to define the oven time. If you generate random numbers externally, the sequence of cook times won't conform to the distribution you've specified for the converter.
Capacity – Use this parameter to specify how much material the oven can hold at once. When the capacity is reached or the fill time expires (whichever comes first), the oven will close its doors and begin "cooking" its contents.
To specify the oven's capacity, enter a value or an equation. For an equation, you can use required inputs, builtins, algebraic operators, or a graphical function.
Tips: To represent a capacity-constrained situation, select the One at a time option, specify a long fill time, and specify a small capacity.
To represent a processor that takes only the "next" item from the upstream queue, select the One at a time option, select the DT builtin for the fill time, and specify a large capacity.
Arrest – Use this parameter to have the oven stop whenever the equation you specify equals anything other than zero (0).
To use this parameter, select the Arrest check box and then type an equation in the box that appears.
Whenever the arrest equation is not equal to zero (0), the oven will stop. Inflows and outflows to the oven will be set to zero (0). The oven will start where it left off when the arrest equation is equal to zero (0).
Leak fraction – This parameter is available if the flow is a leakage flow from a conveyor. The leak fraction is used to determine the leakage flow volume. Whatever enters the conveyor, multiplied by the leakage fraction, exits through the leakage flow.
Define a leakage fraction by using a constant, other model variables, builtins, algebraic operators, or a graphical function. The leakage fraction must be in the 0-1 range. Numbers outside this range will be forced to the nearest endpoint.
For Linear leakage flows, the total amount to leak is equal to the inflow times the DT times the leakage fraction, and this amount is distributed evenly across the leakage zone of the conveyer (each slat leaks the total amount divided by the number of slats). The total amount leaked doesn't change with the length of the leakage zone.
For Exponential leakage flows, the amount that leaks from each slat within the leakage zone is equal to the slat contents times the leakage fraction, generating an exponential decay in the amount leaked across the leakage zone. The total amount leaked changes with the length of the leakage zone.
To specify the type of leak (Linear or Exponential) and the leak zone for the flow, use the options in the flow's Options section.
Use this box to specify the initial value or equation for the selected building block. The initial value specified here is used only at the start of a simulation run.
Note: The name and icon for the selected building block appear just above the Equation box.
The method for defining the initial value and equation depends on the type of building block you select. The following general procedures apply to defining equations for all types of building blocks. For information on defining equations for a specific type of building block, click the appropriate link below.
Note: You can also generate initial and subsequent values for variables, via a link from an Excel or .CSV file, by using the data import features. For more information, see Importing and Exporting Data.
Type a constant or define an algebraic expression that evaluates to a single value.
The initial value can be either a constant or an algebraic expression that evaluates to a single value. Use one of the following methods to define the initial value:
Type a single number in the Equation box. This value will be evenly spread over the length of the conveyor.
Note: When the Discrete option is selected, the conveyor will be initialized so that the material flows out in discrete "packets". The number you type will be portioned out over the conveyor, but stacked in the last DT of each conveyor slat.
Type a series of numbers, separated by commas; each number corresponds to a unit of time in the conveyor's Transit time. Any slats not initialized will default to the last value provided. The first number you type will be the first to exit from the conveyor.
Note: When the Discrete option is selected, the conveyor will be initialized so that the material flows out in discrete "packets". Otherwise, each initial value you provide will be spread over one time unit within the conveyor.
Type a single non-negative number that isn't greater than the oven's capacity.
Type a constant or define an algebraic expression that evaluates to a single value. All required inputs have to be used in the equation for the flow.
Type a constant or define an algebraic expression that evaluates to a single value. All required inputs have to be used in the equation for the converter.
This check box appears if the selected variable has been defined as an arrayed variable.
To apply a single equation to all elements in the array, select this check box, and then use the Equation box to define the equation like you would for a non-arrayed variable.
To provide a separate equation for each element in the array, clear this check box. If you clear this check box, a table will appear in the Equation box where you can provide values or equations for each element/dimension combination.
For more information about specifying equations for arrays, see Creating Arrayed Variables. You can also open the Arrayed Equation editing dialog by clicking on the button.
Use the options in this section to assign and manage units of measure.
Note: You can't assign or change units for a variable whose units are defined by other variables. For example, the unit of measure for a flow attached to a stock is defined by the stock's unit of measure. In this case, the flow's units are displayed in the Units box, but you can't edit them directly; to change the flow's units, change the stock's units.
If you're enforcing unit consistency, when you click at the bottom of the tab to apply your changes, the software will perform a unit consistency check on the equation.
For more information, see Assigning Units to Variables, Creating and Deleting Units, and Checking Unit Consistency.