NMOD Primer Ch 5

In Chapter 4 (Visio pages and ORMSware networks) we explained briefly how NMOD executes [sub]networks referenced in a network. In this chapter we will expand on the execution of Network nodes.

As you can gather from the network diagrams in Figure 6 window (click here if it is not already open), when execution thread reaches Network node [2]PiecesPerHour, it evokes the PiecesPerHour network in the model. When execution thread returns from PiecesPerHour network having calculated PiecesPerHour, NMOD executes n[2] as if it were a Normal node.

What is the significance of that? It offers many possibilities depending on the problem being modeled. Let us explore two possibilities with our example model.

In the current version of the model, PiecesPerHour is a function of production levels of Products A and B (see PiecesPerHour network in Figure 6 window). Suppose we want to see the impact of setting PiecesPerHour to a specific value (e.g. equal to 5) without worrying about production levels of A or B, but also want to be able to quickly switch back to calculating A and B levels when necessary.

Then, when we want to increase the granularity of the model by incorporating production levels of A and B into the calculations, all we have to do is change the Type property of n[2] to Network.

When n[2]'s Type is Network, NMOD will execute PiecesPerHour network, causing PiecesPerHourTemp to take on the value of PiecesPerHour in PiecesPerHour.[4]PiecesPerHour. When control returns to CostPerPiece.[2]PiecesPerHour, PiecesPerHour will take on the value calculated in the subnet and stored in PiecesPerHourTemp.

When n[2]'s Type is Normal, NMOD will not execute PiecesPerHour network and the value of PiecesPerHour variable will take on the value of PiecesPerHourTemp set in CostPerPiece.[6]Initializations.

To explore another possibility, suppose we want to investigate just the impact of PiecesPerHour on total cost per piece and locate that value of PiecesPerHour which minimizes CostPerPiece. One way to do this is to develop a CostPerPiece curve by plugging in various values of PiecesPerHour into the model.

We can do this by looping through the top network several times with various values of PiecesPerHour. However, if we are to use this approach, we do not want the values we are looping through to be replaced by PiecesPerHour value calculated in the PiecesPerHour [sub]network. We can prevent execution of PiecesPerHour network while also incorporating the looping process, by changing the Type property of n[2] to Arrival and adding a loop-back arc from PiecesPerHour to itself as shown in Figure 7. We will expand on Arrival nodes and another way to generate values for the curve a little later in this document.

Figure 7

Notes

In the case of our simple model so far, it is easy to find the value of PiecesPerHour that will yield minimum CostPerPiece by finding the root of the first derivative of the cost-per-piece function. If pieces per hour is x, labor cost per hour is z=$25, wear coefficient is a=0.1 and wear exponent is b=1.8, minimum value of

x = { z / [a * ( b - 1 ) ] } ^ ( 1 / b ) = { 25 / [ 0.1 * ( 1.8 - 1 ) ] } ^ ( 1 / 1.8 ) = 24.32359647.

Whenever it is possible to find the desired value of a variable analytically that way in a real situation, we should incorporate that calculation process into the model's calculation network. Notice the point we made in Chapter 1 that even when a model is normative (using the above equation we solved for what pieces per hour should be to achieve minimum cost per piece), it still has the form of a network. In fact, if we diagram the above model, it will look very similar to the original what-if model minus the node for x (PiecesPerHour). x will become the dependent variable in this case, becoming a function of wear parameters and labor cost per hour, and its expression will be in Node 5 where CostPerPiece used to be! That model can also be considered a what-if model, answering the question what if the values of wear parameters and labor cost per hour were such and such? What will the value of x be?

To facilitate discussion of various NMOD concepts, we will use a more generalized and explicit evaluation approach for curve development. Though inefficient and imprecise, it can be applied in many situations as you will see shortly. We can also easily gather the values necessary to build the desired curve by using Trivial Search, which is shown in Problem 5 in the Examples section. If we are only interested in the minimum cost per piece rather than the whole curve, we can use the Golden Section Search explained in Chapter 19 (Reinforcing concepts through PrimerSig's feedback file) of this primer.

Execution of Network Type nodes