Here is a concise guide on writing an optimization model. It is organized to

• Fit the natural flow of a technical interview discussion
• Serve as a practical reference when collaborating with business or production teams on real-world problems.

The structure combines ideas from software system design process and the AIMMS modeling handbook. See for reference:

• System Design Interview: A Step-By-Step Guide
• AIMMS Modeling Handbook

1. Understand the Problem #

0. Pause and think. (Let the other person know you are thinking.)

1. Gather requirements. Try re-stating the following in your own words:

   • Business Context: What is the real-world scenario — e.g., scheduling, routing, pricing?
   • Key Objectives: What exactly needs to be optimized — e.g., cost, profit, load?
   • Constraints: Are there regulatory constraints, capacity limits, budget constraints, etc.?

2. Ask clarifying questions and define scope. Consider:

   • Functionality. Specify the precise format of the input and output.
   • Time specification. Specify the precise time and order that events take place.
     • Does this happen in the beginning of the period? or at the end?
     • What is the frequency of execution?
   • What is each element / terminology in the business context? Ask for examples.
     • What is the realistic goal? Do we want approximation or exact solution?
   • What is the data availability?
   • Any edge cases?

Outcome:
A clear problem definition and scope.
Ensure all stakeholders share the same understanding.

2. Propose a Verbal Statement of the Model #

0. Call out the name of the model and method (if any).

1. Draft the Model in Plain Language, e.g., we aim to:

   • optimize [primary metric]
   • by choosing [key decisions]
   • subject to [key constraints]

2. Secure Buy-In from Stakeholders. Collect feedback on feasibility and correctness before proceeding to a deeper, more technical design.

Outcome:
Stakeholder alignment on the high-level objective and constraints.
Ensure no major requirement is overlooked.

3. Design Deep Dive: Model Elements #

To move from verbal understanding to a formal mathematical representation, define the following:

1. Notations
   1. Indices and sets. Examples:
      • $i \in \mathcal{I}$: set of products
      • $j \in \mathcal{J}$: set of warehouses
      • $t \in \mathcal{T}$: set of time periods
   2. Parameters and Data:
      • $C_{ij}$: unit shipping cost from $i$ to $j$
      • $D_{i}$: product $i$ demand
      • $M$: large constant for big-M constraints
   3. Decision Variables:
      • $x_{ij}$: units shipped from $i$ to $j$
      • $y_{j}$: 1 if warehouse $j$ is open, 0 otherwise
2. Constraints
   1. Balancing / linking constraints that tie decision variables together.
   2. Problem-specific constraints derived from business or domain logic.
   3. Variable type and bounds, e.g., binary, integer, non-negative, etc..
3. Objective Function

Outcome:
A clear optimization model.

4. Summary and Wrap-Up #

1. Mathematical statement: Combine the notations, objective, and constraints into a single cohesive,symbolic-indexed form.
2. Optional: vectorized / tensorized form: Re-express the model using matrix/vector notation for more compact representation and faster computation.
3. Implementation / Execution Plan
   • Software Tools: Decide on solver frameworks (e.g., Python + CVXPY + Gurobi, etc.).
   • Deployment: Integration with data pipelines, user interfaces, or scheduling systems.
   • Verification: Plan test cases (minimal representative examples, edge cases, stress tests).
4. Wrap Up
   • Summarize key trade-offs.
   • Revisit alignment with the business problem.
   • Outline next steps for iteration or scale-up (e.g., more constraints, refined objective).

Final Notes #

• Keep it Clear: Use simple terms when presenting to non-technical stakeholders.
• Start Small: Begin with a basic model, test it, then expand.
• Stay Focused: Keep checking if the model meets business needs as they change.