ServicesStage 03 · Model03 / 11

Advanced Applied Mathematics

Turn complex problems into models that can be evaluated and solved

Optimisation progressmixed-integer · 12 pump stations
4073105138170iteration 039best feasiblelower bounditer 0 · best 163 · bound 55 · gap 66.3%iter 3 · best 139.1 · bound 65.7 · gap 52.7%iter 6 · best 125.5 · bound 73.9 · gap 41.1%iter 9 · best 116.6 · bound 80.1 · gap 31.3%iter 12 · best 110.8 · bound 84.9 · gap 23.4%iter 15 · best 110.0 · bound 88.5 · gap 19.6%iter 18 · best 104.6 · bound 91.2 · gap 12.8%iter 21 · best 103.0 · bound 93.3 · gap 9.4%iter 24 · best 101.9 · bound 94.9 · gap 6.9%iter 27 · best 101.3 · bound 96.1 · gap 5.1%iter 30 · best 103.8 · bound 97.1 · gap 6.5%iter 33 · best 100.5 · bound 97.8 · gap 2.8%iter 36 · best 100.4 · bound 98.3 · gap 2.0%iter 39 · best 100.2 · bound 98.7 · gap 1.5%
objective · cost indexiter 39 · gap 1.5%

Applied mathematics

MNC Analytics applies mathematical reasoning to problems involving uncertainty, constraints, interacting systems and competing objectives. We translate business and engineering questions into explicit models, then develop the computational methods needed to investigate them.

Our work supports decisions such as how to allocate resources, configure a process, estimate an unmeasured quantity or assess the consequences of a proposed change. Mathematical services can be commissioned independently or integrated into software, sensing and control systems.

What we offer

9

  1. 01

    Optimisation and operations research

    Develop models for scheduling, routing, resource allocation, production planning, inventory and network design using suitable linear, nonlinear, integer or multi-objective methods.

  2. 02

    Decision-making under uncertainty

    Apply stochastic and robust optimisation, scenario analysis and sensitivity studies to examine how decisions perform under different conditions.

  3. 03

    Statistical inference and experimental design

    Design sampling plans and experiments, estimate parameters and quantify uncertainty. Investigate causal effects where the study design and evidence support them.

  4. 04

    Dynamical systems

    Model the behaviour of mechanical, thermal, electrical and other time-dependent systems using differential equations and state-space representations.

  5. 05

    Numerical methods and scientific computing

    Develop computational solvers and simulation workflows, assessing convergence, stability and numerical error.

  6. 06

    Inverse problems and system identification

    Estimate hidden states, physical parameters or system characteristics from observations, while assessing the limits of what can be inferred.

  7. 07

    Probability and reliability modelling

    Analyse failure processes, queues, uncertain events and dependent risks using probabilistic models and simulation.

  8. 08

    Graph and network analysis

    Examine flows, connectivity, bottlenecks and resilience across interconnected systems.

  9. 09

    Reduced order and surrogate modelling

    Build efficient approximations of computationally expensive models for repeated analysis, rapid evaluation or operational use.

What this enables

A defensible basis for comparing alternatives, understanding trade-offs and selecting feasible actions. Outputs may include mathematical specifications, optimisation engines, numerical solvers, simulation models and uncertainty assessments.

Related work

All work
01Agriculture, water and environmental systemsSaudi Arabia

Optimising pump scheduling across a water transmission network

A hydraulic model and a mixed-integer optimiser schedule pumps against tariff periods and reservoir constraints, cutting energy cost while keeping storage within agreed limits.

  • -16%pumping energy cost
  • -38%pump starts per day
  • 0reservoir limit breaches in 9 months
Read more
Monthly pumping energy cost, indexed to baselineBaselineOptimised
020406080100M1M2M3M4M5M6M1 Baseline: 100 indexM1 Optimised: 96 indexM2 Baseline: 100 indexM2 Optimised: 90 indexM3 Baseline: 100 indexM3 Optimised: 86 indexM4 Baseline: 100 indexM4 Optimised: 84 indexM5 Baseline: 100 indexM5 Optimised: 83 indexM6 Baseline: 100 indexM6 Optimised: 84 index
indexM6 · 84 index
02Transport, logistics and supply networksSpain

Routing and scheduling for a regional distribution fleet

A vehicle routing optimiser with time windows, vehicle types and driver rules produces daily plans that planners adjust, reducing kilometres and overtime while keeping delivery windows.

  • -11%kilometres per delivery
  • -33%driver overtime hours
  • < 5 minto produce a daily plan for 38 vehicles
Read more
Kilometres per delivery by monthBeforeAfter
88.5099.501010.5M1M2M3M4M5M6M1 Before: 9.60 kmM2 Before: 9.80 kmM3 Before: 9.50 kmM4 Before: 9.90 kmM5 Before: 9.70 kmM6 Before: 9.60 kmM1 After: 9.10 kmM2 After: 8.80 kmM3 After: 8.60 kmM4 After: 8.60 kmM5 After: 8.50 kmM6 After: 8.60 km
kmM6 · 8.60 km
Next service · 04Advanced Electronics and Embedded Systems

Contact

Tell us about the problem you need to solve

You may have a defined project, an underperforming process or a technical question that needs investigation. We can help assess the challenge, identify the information required and define an appropriate next step.