Service overview
Single and multi-objective, metaheuristic, Bayesian and topology optimisation; decision models. This service is part of that division and is scoped individually around what you need to learn, decide or publish.
Operations research brings mathematical modelling to decisions about how to use limited resources: how to schedule jobs on machines, which maintenance tasks to do this month, how to route materials through a network, where to invest in infrastructure. The models range from linear and integer programmes that can be solved to proven optimality, to simulation models that explore systems too complex for equations, and multi-criteria methods that structure decisions with several goals.
The practical difficulty is representing the problem faithfully. A beautifully solved model of the wrong problem is useless. The service focuses on building models whose assumptions are explicit, whose data are traceable and whose results are tested for sensitivity to what is uncertain. It is applicable to research on production and maintenance planning, resource allocation and engineering investment decisions.
If you plan to publish the outcome, see manuscript & publication support, for example computational & simulation manuscripts or original research article writing.
What this service covers
Problems this service can address
- Complex allocation or scheduling decisions made by intuition
- Uncertainty in demand, cost or availability
- Multiple stakeholders with differing criteria
Methods and analytical approaches
- Linear, integer and nonlinear programming
- Discrete-event and Monte Carlo simulation
- Multi-criteria decision analysis
- Scenario and sensitivity analysis
Applications
- Production and maintenance scheduling
- Resource allocation
- Infrastructure investment prioritisation
Relevant engineering disciplines
Scope, inputs and deliverables
Scope of work
- Data audit and definition of the prediction or decision task
- Model development with structure-aware validation and baselines
- Evaluation, error analysis and uncertainty reporting
- Documentation sufficient for others to reproduce the work
- Feasibility check on: decision context and objectives
Typical inputs required from you
- Decision context and objectives
- Resource, cost and demand data
- Constraints
Deliverables
- Model formulation and solution
- Scenario comparison
- Recommendations with sensitivity discussion
Highly specialised requests are first checked for feasibility from this information. Please do not send confidential data through the public form; describe it first and agree secure transfer afterwards.
Project workflow and method
- 01Enquiry and requirement assessment
- 02Technical scoping and proposal
- 03Execution
- 04Quality review and delivery, with an agreed round of revisions
Read the full project workflow.
In depth: how the work is done
Mathematical programming
Linear programming models problems with linear relationships, solved efficiently even at large scale. Integer and mixed-integer programming add yes-or-no and discrete decisions, such as whether to open a facility or which machine processes which job; these are harder but often solvable with modern solvers. Nonlinear programming handles curved relationships. The formulation determines tractability, and reformulation can make a hard problem easy. We document the model so that it can be checked line by line.
Simulation: discrete-event and Monte Carlo
When systems have randomness, queues and interactions that resist analytical treatment, discrete-event simulation represents the flow of entities through processes with random durations and failures. Monte Carlo simulation propagates uncertainties through calculations. Both require input distributions fitted to data, verification that the model implements the intended logic, validation against observed system behaviour and enough replications to estimate performance with confidence intervals.
Multi-criteria decision analysis
Many engineering decisions involve criteria that are not commensurable: cost, risk, performance, environmental effects. Multi-criteria methods structure the problem by defining criteria, scoring alternatives and eliciting weights from stakeholders. Methods differ in their assumptions, and results can depend on them, so sensitivity of the ranking to weights and scores is tested. The method supports discussion; it does not replace judgement.
Scenario and sensitivity analysis
Models rest on uncertain data and assumptions. Scenario analysis tests plausible futures, and sensitivity analysis varies parameters to see which affect the decision. Robust decisions perform acceptably across scenarios, even if they are not optimal for the most likely one. Stochastic and robust optimisation formalise this when the decision must be made before uncertainty is resolved. We present results in a way that shows which assumptions deserve more investigation.
Implementation, data and validation
A model is validated by comparing its outputs with historical decisions or system behaviour and by review of its assumptions with those who know the system. Data sources and their quality are documented, since inputs such as processing times and costs often carry large uncertainty. Documentation allows others to update the model with new data. Where a recommendation is made, the report distinguishes what the model shows from judgement outside it.
Quality control and good practice
Quality-control approach
- Data are audited for quality, leakage and drift before modelling.
- Validation respects data structure (by specimen, machine or time) and includes simple baselines.
- Performance is reported with uncertainty and failure cases, not only headline scores.
- Model limits and the conditions under which it should not be trusted are documented.
Common pitfalls this service helps avoid
- Solving a simplified model of the wrong problem. Without consultation with practitioners, the model may omit constraints that determine feasibility.
- Using point estimates for uncertain inputs. Optimal solutions can be fragile if the data vary.
- Too few simulation replications. Insufficient runs give unreliable estimates of performance and rankings.
- Hidden weights in multi-criteria scoring. Unexamined weights can determine the result more than the alternatives do.
What good reporting looks like
An operations-research report states the decision problem and stakeholders, the model formulation with assumptions, the data and their sources, the solution methods and software, results with sensitivity and scenario analysis, validation against practice, recommendations with their conditions and the limitations. It makes the model available in a form others can inspect and update, and it distinguishes optimal solutions of the model from guarantees about the real system.
An illustrative scenario
Hypothetical example written for explanation. It is not a client case, a result or a testimonial.
Consider a research team scheduling preventive maintenance across a set of machines with limited crew time. A mixed-integer programme assigns tasks to weeks to minimise expected downtime subject to crew capacity. The first solution concentrates tasks in a way that fails when task durations vary, so a Monte Carlo simulation of the schedule shows the risk of overruns. A revised model includes slack, and the team reports both the planned cost and the probability of delay.
Questions to settle before you begin
- Who makes the decision, and what choices do they really have?
- Which constraints are physical and which are preferences?
- What data do I have, and how uncertain are they?
- Which uncertainty would change the recommendation?
- How will the model be validated against current practice?
Key terms
- Linear programme
- An optimisation problem with a linear objective and linear constraints.
- Integer programming
- Optimisation where some variables must take whole-number values.
- Discrete-event simulation
- A simulation that models systems as sequences of events in time.
- Multi-criteria decision analysis
- Methods for evaluating alternatives against several criteria.
- Robust optimisation
- Optimisation that seeks solutions performing well under uncertainty.
Working together on Engineering Optimisation & Decision Science projects
Optimisation engagements begin with formulation: objectives, decision variables, constraints and the model or experiment used to evaluate designs. Much of the value is created at this stage, because poorly posed problems give unusable optima. We ask for the evaluation model or data, bounds on variables, constraints and any manufacturing or operational limits. Algorithms are chosen to suit evaluation cost and problem structure, and results are checked against independent evaluations and robustness tests. Reports present trade-offs rather than a single answer where objectives conflict, and they state assumptions behind the model that an optimiser could exploit.
Frequently asked questions
Do you provide a decision tool for ongoing use?
Typically we deliver the model, results and documentation rather than a maintained software product.
What kinds of decisions can you model?
Scheduling, allocation, routing, inventory, maintenance and investment prioritisation are typical. Feasibility depends on data and problem size.
Do you need real data?
Yes, ideally. Where data are limited, assumptions are made explicit and tested for sensitivity.
Can you provide the model for my team to use?
Yes, within agreed licensing and software constraints, with documentation.
Does an optimal solution guarantee better results in practice?
No. It is optimal for the model. Real performance depends on how well the model represents the system and on implementation.
How is this service scoped and priced?
After your enquiry we review what you need, ask for missing information and send a written scope and quotation. Price depends on complexity, deliverables and timeline. See the project workflow.