For a long time, production planning was seen as something "operational": organizing orders, allocating machines, fitting in shifts and ensuring that everything fit into the available capacity. However, the scenario has changed. Today, shorter lead times, a complex product mix, increasing customization, raw material restrictions and volatile costs mean that every sequencing decision has a direct impact on delivery times, margins and service levels.
When production planning is done empirically, production may work, but it often comes at a high price: excessive setups, overtime, misaligned stocks, recurring delays and bottlenecks that seem "mysterious". The good news is that many of these problems can be dealt with in a structured way, by looking at three central elements: sequencing, constraints and efficiency.
Sequencing goes beyond sorting
When we talk about production sequencing, we're talking about answering a simple and powerful question: "In what order should I produce what, in each resource, over how much time?".
In practice, this involves defining which order enters each machine or line first, determining when to start each activity considering setup, processing and transportation times; and coordinating the sequence between different resources.
In complex environments, the number of possible combinations increases very quickly. This is why sequencing is one of the classic problems of operations research: intuitive decisions, based only on "prioritizing urgent", almost always lead to hidden inefficiencies, such as:
- A lot of time wasted on unnecessary setups (poorly designed sequence);
- "Stalled" orders waiting for previous steps, creating queues and high WIP;
- Unbalanced use of resources (some machines idle and others always at their limit).
Mathematical sequencing models work precisely on this: finding a production order that respects constraints and reduces operating costs, completion times or average delays, depending on the company's objectives.
Restrictions and the reality that the plan needs to respect
If sequencing is ordering, constraints are the reality that prevents us from accomplishing what we want on paper. In a production planning problem, some typical constraints are:
- Machine and line capacity: hours available per shift, speed, scheduled stops;
- Manpower: number of operators, qualifications, working hours rules and shift changes;
- Availability of inputs and components: arrival dates, stock limits, minimum batches;
- Setup and changeover rules: time to change tool, mold, color, recipe, batch;
- Prohibited or preferential sequences: certain products cannot be produced one after the other, or there are more efficient sequences (by viscosity, color, thickness, etc.);
- Demands and delivery times: delivery dates, customer priorities, differentiated SLAs.
In practice, what differentiates a robust plan from a fragile one is precisely how these constraints are dealt with. If they are left "outside" the model (in manual exceptions, for example), the plan can look great until it meets the reality of the shop floor. When the constraints enter the mathematical model, they become part of the solution and not just a problem for the team to deal with later.
The result of well-structured decisions
Efficiency in production planning is not limited to "producing more with less", but doing what needs to be done with as little waste and deviation as possible, within the priorities of the business. This includes:
- Reduce setup times and unnecessary changes by grouping orders intelligently;
- Reduce intermediate stocks (WIP) without compromising the flow;
- Increase compliance with deadlines (OTD) and reduce chronic delays;
- Better load balancing between resources, avoiding islands of overload;
- Reducing the emergency overtime that has become the norm.
When sequencing and constraints are dealt with in an integrated manner, efficiency no longer depends solely on "heroes" in the programming and becomes the natural result of the decision-making process supported by mathematical models.
How mathematical models help orchestrate sequencing, constraints and efficiency
From a modeling point of view, production planning can be seen as a large puzzle with three layers:
1. What needs to be produced (orders, quantities, desired dates);
2. With what resources (machines, lines, shifts, teams, inputs);
3. Under what rules and priorities (objectives, constraints, business policies).
Mathematical models make it possible to translate all this into a logical structure, in which the algorithm searches for the best possible solution within the constraints. This makes it possible:
- Include setup costs, changeover times and delay penalties in the model;
- Set realistic capacity limits, taking into account schedules, downtime and maintenance;
- Define multiple objectives (e.g. minimize total delay while limiting setups);
- Run different scenarios: change priorities, capacity, demand or constraints and see how the plan changes.
Instead of generating a single "fixed" plan, the model becomes a scenario exploration tool, helping the team to understand trade-offs in a quantitative way and to choose the plan that best balances cost, service and operational viability.
The role of Linear Softwares Matemáticos in production planning
The leap in maturity comes when planning stops being just a manual adjustment of spreadsheets and starts to rely on specialized mathematical models, integrated with the ERP and other data sources. The team remains fundamental, but now with a more solid quantitative basis for making decisions, simulating alternatives and justifying choices to senior management.
Linear Softwares Matemáticos works precisely at this intersection between real production challenges and mathematical optimization models. Linear's solutions are based on operational data:
- Building production planning and sequencing models that respect shop floor constraints and maximize the use of resources;
- Integrate production planning with the rest of the supply chain, connecting factory decisions with stocks, purchasing and distribution;
- Run comparative scenarios (change of shifts, new lines, increase in demand, change in mix) before making structural decisions;
- Support recurring planning cycles (daily, weekly, monthly), with more consistent plans and less dependence on last-minute adjustments.
- In markets with pressured margins and demanding customers, meeting deadlines, stabilizing the flow and making good use of production resources can be the difference between winning and losing business
Want to find out how mathematical models can turn your production planning into a real competitive advantage? Contact Linear and take the next step in the efficiency of your operation.
