ORMSware Network-structured Modeler Modeling Examples

ORMSware modeling examples posted here are simplified versions of actual problems. Proprietary data have been changed where appropriate. If you plan to follow these examples closely it will be helpful to reflect on and map out first how you would solve these problems using tools with which you are familiar. Recall, however, that ORMSware is not available for purchase.

A key part of the ORMSware paradigm is the Customer-Surrogates/Probes/Thread-heads concept and the birth and death process (from Stochastic Processes and Discrete Event Simulation in Operations Research/Management Science/Decision Science). Modeling as well as programming are viewed in generalized terms of customers entering and exiting birth and death process systems. Customers are represented by surrogates/probes/thread-heads, etc., which travel simultaneously through queuing networks within the birth and death system. Execution of the program is therefore logically multithreaded.

At times the concept conveyed by "probe" is more communicative than "surrogate." You will see "probes," "surrogates," "entities" and "thread-heads" used interchangeably in the briefings here.

Click Problem heading or corresponding image for more information (diagrams, data, descriptions) on each problem.

This is a model for determining the best sequences of actions for replacing a machine in a production operation. Two versions of the general problem are presented. The first one is a trivial version involving just a few decision options over a planning horizon. It is solved using a trivial, mindless, explicit and exhaustive evaluation of all possible action sequences. The second one is a non-naive prescriptive if-what (or reverse what-if) approach.

Naive Version: This is the version you'll see by clicking the Problem 1 subheading above. Decision choices in this version involve buying a new or older model of the machine with options of keeping it or replacing it any given plan year with another new or older model, repeating this decision process over a desired planning horizon. Older models have lower purchase costs, but higher maintenance costs and lower trade-in values.

This version shows how easily alternative solution threads can be recorded and retrieved in NMOD. The reader will also see how the model can be easily expanded to accommodate more equipment age choices, price changes of new equipment over time, present value of alternatives, changeover costs, etc. Best sequences of actions over the time horizon are then calculated and sorted by exhaustive, explicit evaluation of all possible action sequences.

Non-Naive Version - dynamic programming implementation using ORMSware discrete event simulator: This version (being posted 8/27/2016) is more interesting. It is truly in the ORMSware spirit, using its discrete event simulation paradigm to handle the "curse of dimensionality" issue. It is described in a series of 5 videos. Click image below to watch them in a separate window:

Some of the concepts used in this example:

Automatic expansion of NMOD environment to accommodate the growing size of a problem
Use of Microsoft Excel tables in NMOD models
OR arcs (cause target nodes to fire as soon as flows along these arcs reach the nodes)
Transformation of surrogate/probe/execution thread-head properties as they traverse model's network
Use of Duration property of network objects and Event queue to order alternatives by cost
Trivial short path method to rank alternative solution paths
TravelNotes procedure to record decision-consequence path of each solution alternative
ShowTravelNotes procedure to retrieve decision-consequence path of each solution alternative
Extending a network object's content beyond what can be entered through Visio interface
Declaring model level analyst-defined variables
Start node
Normal node
Network node
Role property of network objects (grayed nodes and arcs with dashed lines are Support objects)
Use of Dummy/Support nodes and arcs (allows clarification of flows and precedences)
IF-THEN-ELSE construct
Cycles/recursion/iteration/DO construct

Problem 2: Fleet Migration/State Transition

This is a descriptive model for determining fleet migration of a rent-a-car operation, given the probability of where a customer is likely to drop off a vehicle picked up at one of its outlets.

The reader will be able to see how this simple model can be easily extended to formulate pricing strategies, perform tradeoff analyses to determine charges and discounts for improving competitiveness and profitability, develop cost-effective operational plans, etc.

Some of the concepts introduced in this example:

Parallel/multiple arcs between any given pair of nodes
AND arcs and AND arc multipliers
Changing AND arc multipliers programmatically
Convergence node (node with at least one AND arc terminating in it)
Incorporating analyst-defined variables and procedures at model level
Working with analyst-defined vectors/matrices/arrays
DO construct
Writing results to external files

Problem 3: Capacity Planning and Analysis

This is a quick-and-dirty deterministic model for sizing daily tax returns processing capacities of IRS Regional Centers. The objective of the model was to make a contract bid competitive by minimizing investment costs while meeting all required performance specs.

The reader will be able to see how the model can be extended to accommodate the probabilistic nature of of tax returns arrival rates and service (returns processing) rates, network architecture and performance for supporting returns processing, workload balancing among the centers, etc., all with the objective of reducing costs while meeting performance specs.

Some of the concepts introduced in this example:

Using NMOD's Optimization Module
Goal-seeking
Temporal arc -- a connection that comes into existence temporarily to connect a node or arc to another node or arc. Temporal arc disappears once the connection is complete.

NOTE: Details of this problem have been taken offline as the concepts covered are now present in updated versions of other examples available at this site.

This is a simplified, truncated version of a back-office operations tool which a small business uses to transform orders received over the Internet to packages to be shipped.

This example also demonstrates NMOD's hierarchical modeling capabilities. The reader will be able to see how the tool can be expanded to connect the business's order processing operations to financial performance analysis, inventory management, etc.

Problem 5: Trucking/Transportation Fleet Flow

This is a descriptive model for calculating total costs driven by fleet size of a dedicated trucking services operation.

We show how this descriptive (what-if) model is turned into a prescriptive (optimization/if-what) model for finding minimum cost fleet size by having the model respond to Fibonacci search stimuli from NMOD's Optimization Module.

The reader will also be able to see how the simple model presented here can be expanded to include maintenance operations, driver availability, etc. to improve financial and operational performance of a truck fleet dedicated to a customer; and, still, in spite of the increased complexity of the what-if model, be able to use the same Fibonacci search with no additional effort to find optimum fleet size.

Some of the concepts introduced in this example:

Optimization of an integer control/decision/... variable using Fibonacci search
Using Trivial Search to demonstrate to stakeholders validity of Fibonacci search results
Temporal arcs with Duration greater than zero
User-defined data structures/derived types
Tracking extrema of performance variables and values of related variables
Adding to built-in convergence logic
Using MergeSum function at Convergence nodes

Problem 6: Minimizing Transportation Costs from Distribution Centers to Stores

A retail chain in UK with 772 stores and 9 distribution centers (DCs) wanted a system for computing minimum-cost distribution of roughly 13 million cases of goods every week. Rather than exploring all [772 * 9 = 6948] links the company wanted the program to pick only 3 closest DCs to supply each store, limiting DCs-to-stores supply links to just 2316.

We first show you an algorithm attempted by an IT consultant bidding on the project (by explicitly and exhaustively evaluating all feasible allocations to pick the best distribution plan). Most people are likely to try such an approach, only to discover that there will not be enough time in their lifetime to get an answer to the problem.

We then we go on to show an Operations Research/Management Science (dynamic programming) formulation of the problem and the ease with which the solution was implemented with ORMSware. It produces a quick-and-dirty Initial Plan in a split-second and the Final Plan in a few seconds on a Windows 7 HP 2400 MHz notebook computer.

Some of the concepts introduced in this example:

More examples of creating and using derived types (data structures)
Using queues to sort items and hold entities (Store and Retrieve)
Procedures and functions available for getting status information about queues
More use signals and signal targets (temporal arcs/connections)
Using Events Queue to sequence entities according to cost factors
Dynamic memory allocation
Use of pointers

Operations management problems such as machine scheduling, vehicle routing, crew scheduling, tool path design, and numerous others, involve the issue of knowing how to systematically find all possible ways any given set of items or activities can be ordered/arranged/sequenced, even if all sequences may not be explicitly and exhaustively explored.

The focus of this example is not the sequences (permutations) generating algorithm developed with ORMSware or its expansion to solve an asymmetric traveling salesman problem (ATSP). Rather, the focus is the general process of getting to the final formulation of a model using typical ORMSware thinking.

If you are not familiar with existing permutation algorithms, we have provided a link to show you a programming language implementation of a permutations algorithm for comparison with the ORMSware solution.