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Formal Optimization Services: Engineering Optimal Decisions Under Industrial Complexity

We build executable decision systems grounded in formal mathematical methods: Mixed-Integer Programming (MIP), Decision Diagrams (DDs), Network Flow Models, and Dynamic Programming.

These are not spreadsheets or simulation toys. They are industrial-grade optimization engines that deliver provably optimal or near-optimal solutions to complex problems where intuition fails and trial-and-error is too expensive.

Core Service Offerings

Optimal Configuration Design via Mixed-Integer Programming (MIP)

A formally optimized system configuration ensures maximum business value under real-world constraints.

Challenge

Clients face dozens of technically feasible designs for new facilities or revamps, but lack rigorous methods to select the best one.

Method

Formulate as a Mixed-Integer Program (MIP) using CPLEX/Gurobi to optimize CAPEX, availability, maintenance burden, and EBITDA impact.

Tools & Frameworks

  • AspenTech Fidelis for RAM modeling
  • PDEL® for causal integration
  • CPLEX solver integrated within iDSS

Real-World Impact

Optimized the design of a major LNG compression train by evaluating over 348 configurations under constraints on redundancy, feed variability, and crew logistics.

Outcome:

Delivered proof of 98.7% optimality; unlocked $MM in EBITDA through superior system configuration.

Maintenance Scheduling Under Uncertainty Using Decision Diagrams (DDs)

A robust maintenance schedule integrates operational rules, resource limits, and risk exposure into a single executable plan.

Challenge

Large plants must coordinate hundreds of tasks across crews, spares, weather windows, and production commitments — a combinatorial challenge beyond manual planning.

Method

Apply Relaxed Decision Diagrams (R-DDs) to compactly represent feasible schedules, enforce logical constraints, and provide relaxation bounds on optimal performance.

Tools & Frameworks

  • Top-down compilation from dynamic programming models
  • Constraint propagation for feasibility validation
  • Integration with Fidelis failure data

Real-World Impact

Developed an optimized maintenance schedule for a large gas processing plant, eliminating infeasible sequences upfront and reducing downtime risk by 30%.

Outcome:

Generated a conflict-free plan aligned with real-world constraints — not theoretical assumptions.

Network Flow Optimization for Energy & Material Systems

An optimized flow network maximizes throughput while minimizing cost, energy use, and risk across interconnected assets.

Challenge

Gas pipelines, electrical microgrids, and steam systems suffer from inefficiencies due to suboptimal routing and load balancing.

Method

Model as Minimum-Cost Flow Problems to minimize pumping/fuel costs while maximizing delivery reliability and redundancy utilization.

Tools & Frameworks

  • DECA® for energy-mass-economic flow modeling
  • Dual variables to calculate shadow prices
  • Embedded within Digital Asset for real-time rerouting

Real-World Impact

Optimized power routing between grid, solar, battery, and diesel generators at a hybrid energy site, reducing fuel consumption by 22%.

Outcome:

Turned intermittent supply into reliable, low-cost operations.

Hybrid Decomposition Frameworks for Enterprise-Scale Problems

A decomposed optimization framework enables solution of enterprise-wide problems by coordinating subsystem-level decisions.

Challenge

Multi-site asset fleets or enterprise-wide decarbonization programs exceed solver capacity when modeled monolithically.

Method

Use Dantzig-Wolfe or Benders Decomposition to break problems into tractable subproblems solved iteratively, then recombine via master problem.

Tools & Frameworks

  • KIAME© framework to align execution levels
  • A7 Agile Value Tracking to monitor progress
  • Custom solvers in C++/Mathematica

Real-World Impact

Applied decomposition to optimize maintenance scheduling across a national hydropower fleet under shared resource constraints.

Outcome:

Solved what was previously considered intractable — without oversimplification.

Robust & Stochastic Optimization for Multi-Stage Investment Decisions

A multi-stage investment policy adapts to evolving risks and opportunities, preserving value across uncertain futures.

Challenge

Should we delay revamping? Upgrade modularly? Or replace entirely? Most firms rely on deterministic projections.

Method

Use Stochastic Dynamic Programming (DP) and Reinforcement Learning to simulate thousands of scenarios and prescribe adaptive investment strategies.

Tools & Frameworks

  • Fidelis for probabilistic forecasting
  • Bellman equations for policy iteration
  • PDEL® to link decisions to financial outcomes

Real-World Impact

Evaluated phased expansion pathways for a chemicals manufacturer under volatile feedstock prices and regulatory risk.

Outcome:

Prescribed an adaptive policy with 95% confidence of superior ROI over static alternatives.

Why Formal Methods Deliver Superior Value

Provable Optimality

Unlike heuristics or manual planning, formal optimization delivers mathematical proof that you've found the best solution — or quantifies exactly how close you are to optimal.

Constraint Enforcement

Physical limits, operational rules, safety requirements, and contractual obligations are encoded as hard constraints — guaranteeing feasibility before deployment.

Scalability to Complexity

Formal methods handle problems with thousands of variables and constraints that overwhelm spreadsheet analysis or simulation-based trial-and-error.

Adaptation to Uncertainty

Stochastic and robust optimization frameworks explicitly model uncertainty and prescribe adaptive strategies that preserve value across multiple scenarios.

This is engineering, not consulting. We co-architect systems where value is mathematically maximized, not guessed.

Engineering Value Resilience Through Formal Methods

At Knar, we walk beside mature organizations through complexity. Our engagements are not about delivering answers, but about co-architecting systems where technical reality meets financial performance, data becomes institutional knowledge, and decisions are made with traceability, not intuition.

Ready to move beyond guesswork?

Let's explore what optimal looks like for your next project.

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