1947 – George Dantzig develops pioneering linear optimization algorithm.

What is it?

Optimization is the determination of the ‘best possible’ set of decisions to be taken at any moment in time.

Operational decision-making problems involve making a set of choices that achieve the best possible outcome (often maximizing profit) while respecting a number of business-rules (e.g. customer requirements, demand fulfillment, etc.), known as constraints.

To find the ‘optimal’ course of action among all the possible decision combinations requires models with advanced algorithms. Without this state-of-the art mathematics, the sheer number of possibilities would render these types of problems intractable.

Optimization: Your decision-making intelligence engine.

For years, many of the world’s largest corporations have been using optimization models running on supercomputers to help optimize their operations and processes. New technology has leveled the playing-field, allowing any-sized organization to use optimization modeling to:

• Increase throughput and eliminate bottlenecks
• Develop intelligent and responsive pricing schemes
• Create ‘lowest-cost’ staff schedules and timetables
• Synchronize production scheduling
• Build risk-balanced asset portfolios
• Improve customer relationship management
• Plan floor space and allocate the right mix of product types
• Manage all aspects of the modern supply chain

• Bombardier FlexJet to reduce crew levels by more than 20%, while maintaining service levels above 90%.
• NBC to improve its advertising sales process with optimization-based systems, increasing revenues by $200 M between 1996 and 2000.
• Ford Motor Company to reduce annual prototyping costs by over $250 M and dramatically shorten the planning process.
• Canadian Pacific to optimize the routing of rail cars, reducing transit-times and cutting its cost base by $285 M.
• France Telecom to rapidly react to market changes by updating business rules on the fly, slashing the time required to implement new policies.
• DaimlerChrysler to improve purge rates by 10-20% and reduce inventory by $20 M.
• eBay to enhance the user experience of their site.

Consultation

• Co-client exploration of the decision-making problem at hand.
• The relevant optimization methodology (linear/non-linear programming, stochastic dynamic programming, marginal analysis, etc.) is determined.
• Data availability and requirements are assessed.

Modeling

• The decision-variables, objective function, constraints and their inter-relationships are represented by mathematical formulas.
• If appropriate, the math is coded into a software model, using powerful optimization modeling environments. This model is then solved by computers and the optimal solution determined.
• Alternatively, the mathematics may be further studied to determine an optimal policy to be followed under all, or a subset of, circumstances.

Analyses

• In linear programming models, sensitivity analyses can be performed to determine the stability of the optimal decisions.
• Studying the shadow prices can help ‘price’ constraints by determining the value of increasing resource levels.
• The model can be run with different criteria, to perform ‘what-if’ analyses.
• Various objective functions can be considered, representing different value judgments.
• Constraints can be added/removed as required to reflect changing realities or achieve an understanding of the limiting factors.

Solution Delivery

• The model can be solved internally and results delivered, or the optimization model can be embedded in custom-built software which interfaces with existing data-systems to constitute an end-to-end decision-making solution – all according to what best suits the client’s needs
• A detailed report explaining the structure of the optimization model and its underlying assumptions, as well as a user’s guide describing how to interact with the tool (if applicable) are always provided to ensure complete understanding and satisfaction.
• Training and support are available.

Late 1940s – John von Neumann conceives of the idea of simulation to study the effectiveness aircraft bombing.

What is it?

Simulation is the virtual modeling of complex real-world systems.

Many business processes and systems are so complex, with seemingly endless interdependencies and non-linearities, that they cannot be adequately represented using typical mathematical models.

Simulation is a computer-based tool which generates a virtual environment in which such intricate systems, and the associated uncertainty within them, can be fully modeled and better-understood, in order to make better decisions.

Using probability distributions to represent the random influences on a system, simulation models are executed for a large number of ‘realizations’. The results are then compiled to gain an overall picture of the expected system behavior. Statistics can be drawn from this data to form conclusions about the likelihood of particular outcomes under various starting conditions and assumptions. In this manner, simulation provides a window into uncertainty and a ‘sand-box’ in which one can try out ideas without disrupting live systems.

Don’t be overwhelmed by complexity – Gain insight with simulation

“The potential of simulation for business process modeling is beginning to be recognized by the business community.” Modern militaries around the world use simulation technology extensively to train soldiers, draft policies and make operational decisions. Increasingly, businesses are learning that simulation can be used in similar ways to improve the way they run their operations and make decisions. Simulation is being used to:

• Assess risk
• Develop strategy
• Test without impacting operations
• Experiment with ‘what-if’ scenarios
• Gain visibility
• Plan growth and capital expenditures
• Troubleshoot operational issues

• Peugeot Citroën to increase throughput with minimal capital investment, adding $130 M to its bottom line
• Visteon Chassis Systems to develop a decision-support system which helped increase productivity by 30%
• The US Department of Energy to analyze nuclear waste disposal and related policy options
• Canada Post to help optimize its parcel delivery network
• UPS to reduce aircraft turnaround time from hours to minutes
• Continental Airlines to improve staff resource allocation by 14%

Consultation

• Co-client exploration of the issues at stake and the goals to be achieved.
• Determination of the appropriate simulation technology and suitable level of abstraction
• Definition of the system boundaries.
• Consideration of data requirements and availability.

Modeling

• The structure of the system is codified into a simulation model
• Statistical distributions are fit to data in order to drive the randomness in the model
• The model is validated and incrementally improved until its behavior replicates that of the system under study.

Analyses

• The simulation is run for a large number of realizations to achieve an understanding of the system behavior over time.
• Initiating the model with different starting conditions, or changing variables of interest throughout a run (if appropriate), allows the user to perform scenario analysis, evaluate risk and study the effect of new policies.
• An analysis determines the distribution of the likelihood of outcomes and the sensitivity of the system to variations on particular inputs.

Solution Delivery

• Using customized and convenient input mechanisms, as well as reporting functionality based on the client’s needs, we deliver a complete end-to-end decision support tool.
• A detailed report explaining the structure of the simulation model and its underlying assumptions, as well as a user’s guide describing how to interact with the tool are always provided to ensure complete understanding and satisfaction.

“Firms should budget about one percent of their sales revenues for the forecasting effort.” – Scott Armstrong.

What is it?

Forecasting is the estimation of the value of variables at some future point in time.

Most of us use forecasting on a daily basis when we listen to weather forecasts. This information allows us to better plan our day and prepare for surprises. Business forecasts are even more important for organizations to help plan and manage their operations.

Business forecasting often uses historical data and is usually performed with the aid of computer software. Forecasting methods can be classified into several different categories: qualitative methods, regression methods, multiple equation methods, and time series methods. Although developing a rudimentary forecast is relatively straightforward, there can be substantial payoff to using (and combining) sophisticated techniques to generate accurate forecasts.

Plan better using advanced forecasting solutions.

Unpredictable demand is in many organizations, their most costly problem. Low forecast accuracy, or no forecast, often results in low service levels, frenzied schedules and poor performance. This costs the organization millions of dollars in safety stock, unneeded inventory, and lead to an unstable Supply Chain.

Companies that are 30% better at demand forecasting average*:

• 35% shorter order-to-cash cycle times
• 15% less inventory.
• 17% stronger perfect order fulfillment.
• 10% of the stockouts of their peers.

Typically, a 1% point improvement in demand forecast accuracy yields a 2% point improvement in perfect order fulfillment capability.

*Statistics quoted from “Consumer Products Industry Outlook: Profitable Growth Requires DDSN Strategies,” by Kara Romanow, AMR Research Report, August 2004. Copyright 2004 by AMR Research, Inc.

• DNATA, the largest airport terminal cargo operator in the Middle East, to forecast workloads and streamline productivity.
• Entergy Solutions to manage risk and forecast energy costs and demand in a fast-growing deregulated retail environment.
• Kirin Brewery Company of Japan to accurately forecast inventory levels.
• Reliant Energy, a Houston-based supplier of wholesale and retail natural gas and electricity around the world, to help the company meet customer demands reliably and at low cost.
• Salt River Project (SRP), the third-largest public power utility in the United States, to improve retail electricity rates using forecasting capabilities.
• Staples to calculate sales forecasts for nearly 1,100 existing stores and for the 5,000 potential real estate sites annually, using historical sales data and customer demographics.

Consultation

• Co-client exploration of the decision-making problem at hand.
• Determination of the relevant factors that may affect the forecast, such as weather, season, day, time, economy, trend.
• Assess data availability and requirements

Modeling

• Data is transformed to meet certain linearity constraints.
• The best forecasting method, or a set of them, are selected.
• The forecasting engine generates the forecast for the desired time frame.
• An inverse transformation is performed if required.

Analyses

• The forecast is tested for integrity and accuracy.
• The different forecasting methods are benchmarked by means of a variety of accuracy measures, such as MSE, MAD, MAPE, BIC or AIC, and often using a hold-out sample.
• The forecast may be performed using different initial assumptions.
• A confidence interval may be determined to not only obtain a mean value, but also the expected minimum and maximum — values crucial to best/worst case planning, which are too often ignored.

Solution Delivery

• The forecasted values are presented in both tabular and graphical form.
• The forecasting engine may be built into a custom software tool to repeatedly and flexibly perform organization-wide forecasts.
• The forecasting model is delivered to the client, accompanied by a detailed user guide describing how to interact with the tool and a technical document explaining the construction of the model.

1994 – John Nash is given the Nobel Prize for original work in Game Theory.

What is it?

Game Theory is the analysis of all possible decision-combinations taken by all participants involved in a strategic issue.

In many business situations multiple decision-makers (or “players”) with conflicting interests must choose an action that affects both the actions other players may take and the rewards for all parties involved.

Game Theory is a branch of mathematics that models such situations in order to determine the strategies decision-makers should adopt to best achieve their goals.

Due to the complexity of the interactions between players, other more traditional decision analyses are insufficient. Game Theory is precisely about making optimal decisions when facing dynamic opponents.

Stay ahead of the game – Anticipate and influence the actions and reactions of other parties.

Traditionally applied by governments and only the largest corporations, advances in computer technology have now leveled the playing field. Professionals today are employing Game Theory models and methodology for:

• FCC to perform $7B auctioning of broadcast frequencies & 3rd generation mobile licenses
• Homeland Security to analyze the risk of future terrorist attacks
• Hewlett-Packard to develop its framework for an automated Negotiation Support System
• IBM and Mars Inc. to save Freight Sales $70 million a year through a game-theory based procurement system
• Major League Baseball to perform salary negotiations
• US President George W. Bush Presidential Campaign Strategy Team to help win 2 elections
• Panama Canal Negotiations (1978) to unravel intractable diplomatic entrenchments

Consultation

• Co-client exploration and definition of issues and involved parties.
• Market/industry experts brought in if required.
• Co-client selection of scenario and player preference mappings.

Modeling

• Define the “scenario state-space” which lists all possible decision-combinations among the parties involved.
• Preferentially rank decision-combinations according to the goals of each decision-maker.

Analyses

Our powerful algorithms conduct and trace Path Analyses (tactics) from the status-quo (the strategic issue as it stands now) to Unilateral Improvements (competitive stance) or Mutually-Beneficial Resolutions (co-operative stance). This provides a step by step means of moving the strategic issue to a predetermined resolution.

• Equilibria Tests: for identifying the absorbing states (likely resolutions) in the game and the forces that sustain these. These decision-combinations are absorbing states from which no decision-makers would have a unilateral unsanctioned incentive to deviate from.
• Simulations: for iterative scenario/policy testing

Solution Delivery

To ensure full transparency and understanding of the model and its implications, we provide:

• Comprehensive reports detailing recommendations, with:
  • Prescriptive detail: to predict, anticipate and influence the decisions of the other parties.
  • Descriptive detail: for conflict resolution, dispute mediation and arbitration
• A dynamic real-time decision support system (DSS), if applicable

Business problems are as varied as they are complex. For us at Syllogix, this means never imposing a specific solution or service when it’s not exactly the right fit.

We strive to find and develop the precise modeling techniques that address the issues in your operational reality. This often involves leveraging or combining a variety of the mathematical techniques found in the Management Science toolkit, including those you may have already read about (Optimization, Simulation, Forecasting and Game Theory) but also others such as:

• Statistical Analyses Profile Matching
• Decision Analysis
• Data Mining
• Custom Algorithms
• Intelligent Spreadsheets
• Etc.

We can exploit virtually any existing mathematical or analytical framework to your organization’s benefit. In fact, with our staff of expert analysts and our partnerships with academic experts, Syllogix can even develop new mathematical theory if called upon to do so. It entirely depends upon the problems brought to us by our clients. Your needs drive our innovative solutions, not the other way around.

Syllogix distills complex business realities into the underlying mathematics, from which knowledge and understanding can be extracted and translated into value for your organization. Analyses and mathematical modeling are the powerful tools that allow us to deliver this value in a predictable, numbers-based and transparent way.

Unique needs require unique solutions. This is why, we at Syllogix provide customized software development to complement our models and end-to-end integration of our decision support tools to suit the enterprise solution needs of our clients.

Combining both in-house and partnered software development expertise, Syllogix regularly develops customized software solutions that:

• Improve your business processes
• Simplify complexity and provide intelligent reporting to improve your business decisions
• Provide real-time visibility and control over operations
• Optimize processes, production plans, scheduling
• Automate decision-making processes
• Integrate with your information systems
• Present user-friendly interfaces
• Simplify data entry and interaction with the model
• Report results in attractive, easy to understand charts and graphs

Powerful management science models are at the core of everything we do. Our custom software development offering is geared toward fully leveraging the power of these models and empowering managerial and executive insight with integrated decision support tools.

We build intelligent applications. They are driven by analytical models, tailor-designed to your unique needs, and will help you manage and gain control of your business in ways you thought not possible.

Management Science + Tailor-made Software = Smart, complete and customized solutions