Today’s competition in many manufacturing industries is leading companies to expand their product portfolio, which combined with the advanced technology present in modern production sites, raises the need for efficient production planning. Often times, purchasing new production machinery is not an option because of the increase in fixed costs. Hence, efforts are being directed towards technology and efficiency improvement.

Even though each industry has its own specific characteristics, many share some of their processes, at least conceptually. This article aims at exploring some of them and at presenting how advanced analytics, and optimization in particular, can make a difference in efficiency.

The following figure shows some of the most common manufacturing processes and analytics problems that apply on each stage:

Figure 1. Manufacturing processes and analytics problem

A third important factor to be considered is the decision to be made. Be it strategic, tactical or operational, specific analyses and different techniques may apply.

## Annual budget planning

Every year, companies make an annual budget to help them plan for the upcoming year and make the necessary adjustments to cover expenses. For manufacturing companies, this means primarily determining the amount of raw materials or semi-finished products and energy needed to produce next year’s projected demand. It also aims at determining certain high-impact production processes and the production sites for each family of products, since these costs impact greatly on the overall annual expenditure as well.

Annual budgeting is especially difficult for manufacturing companies because of all the complex business and physical constraints that need to be taken into account in order to make a feasible production and distribution planning. The challenge lies in determining what to produce and when and where to produce it so that demand is satisfied while minimizing production and distribution costs and respecting business constraints such as desired regularity in energy consumption or client’s preferences in production sites; and physical constraints such as machinery capabilities or inventory capacity.

These complexities, together with the large amounts of data required to be processed, call for advanced analytical tools to proceed successfully in the decision-making process by:

• Providing feasible solutions in an automated and fast way
• Providing optimal production and distribution planning
• Providing visualization and analytical tools for a better understanding of solutions
• Providing simulation mechanisms

With these advanced tools, those responsible for decision making are capable of analyzing tons of possibilities in no time and get recommendations that would otherwise be out of their reach. The delivery of alternatives and recommendations in such a short space of time enables them to assess different scenarios, adjusting the decision making to the needs of their business, and ensuring the quality and effectiveness of these decisions.

## What decide has to offer

As mentioned above, many manufacturing industries share some of their processes. However, each industry has its own specificities, and very frequently even different companies of the same industry face different problems. In decide we have an extensive experience in developing tailor-made solutions that ensure 100% fit to our clients’ problems.

In the manufacturing sector, these solutions could help our clients address the following issues in the decision-making process:

• Overall impact of business unit decisions on the total performance of the production plants
• Impact of changes in inventory and supply on the financial performance
• Impact of breakdowns and poor operation on the plant operations
• Impact of plant improvements on performance of the plant and the company as a whole
• Impact of changes in process costs on overall cost of manufacturing

These issues are particularly relevant for annual budgeting, and some or all of them are also taken into account for strategic, tactical or operational decision making. It is important, though, to bear in mind that different decisions imply addressing different problems.

One of the key elements of the above-mentioned solutions is the objective or cost function. This function defines the client’s indicator/s to examine and determine whether a manufacturing planning is better than another one. It is typically defined as an aggregation of incurred costs such as production cost, supply cost, holding cost or unsatisfied demand related costs.

These costs can be given different priorities allowing the decision-maker to analyze multiple scenarios and gain a deeper insight of their business by understanding the impact of prioritizing one cost over the others on the company’s overall production and financial performance.

The figure below shows how this would be easily done on one of the software solutions developed at decide by just placing each point on de desired priority in the Optimization parameters menu:

Figure 2. Execution creation window

Visualization is critical when analyzing any kind of planning. Our solutions provide a wide range of visualizations that help better understand solutions. The following figure shows a cumulative graph with the different incurred costs measured by month:

Figure 3. Cumulative Cost Graph

By clicking on a specific cost on the right hand side menu, a closer visual analysis can be obtained of that specific cost/s. This way, from the figures shown below it can easily be derived that while some costs are very regular through time, others are very period-dependent.

Figure 4. Cumulative Cost Graph – Cost C

Figure 5. Cumulative Cost Graph – Cost D

Figure 6. Cumulative Cost Graph – Cost F

Some other interesting visualizations would be those of stock and energy use. It is very important provide interactive graphs so that decision-makers can understand results better.

Figure 7. Stock graph

Figure 8. Energy use graph

Finally, different scenarios can be compared to identify the consequences of changing costs, priorities or even business constraints. The figure below shows some of the possible comparisons (Setup costs, a specific family stock and energy use):

Figure 9. Scenario comparison

## Some technical aspects

Two of the technical challenges faced when modeling and solving these problems are described below.

### Delivery delays (backlog) and lost sales

Manufacturers need to satisfy demand within an agreed-upon time window. When not satisfied, clients are compensated somehow or, worst case scenario, the sale is lost, risking losing the client as well.

A simplified version of the relation among demand, delivery, backlog and lost sales is shown in the following figure, where the demand not satisfied in its requested period is considered backlog and the demand not satisfied within two consecutive periods starting in its requested period is considered lost sales:

Figure 10. Backlog and lost sales graph

Where:

• $\boldsymbol{DEM_{frt}}$  is the demand of product family f in client grouping region r in period t (input data)
• $\boldsymbol{trans_{fprt}}$ is the amount of product family f supplied from production plant p to client grouping region rin period t (decision variable)
• $\boldsymbol{backlog_{frt}}$ is the amount of product family ‘s demand in client grouping region r in period t not satisfied within that same period (decision variable)
• $\boldsymbol{lostSales_{frt}}$ is the amount of product family f ’s demand in client grouping region r in period t-1 not satisfied in period t (decision variable)

As can be noted, backlog definition is the piecewise-linear function shown below:

Note it is assumed in every period supply cannot exceed that period’s demand, plus backlog generated in the previous period.

For further details on piecewise-linear functions check out the following posts:

While most commercial optimization solvers have built-in implementations for this sort of functions, they are only implemented for piecewise-linear functions whose breakpoints are constants. In our case, the breakpoint is determined by the backlog from the previous period, which is a decision variable. This forces to model it in detail as follows.

Firstly, a new binary variable needs to be defined for every f, r, t:

The constraints below would force this new variable to be assigned to the expected value:

Finally, the two following constraints would define the first piece of the function:

And the two following ones would define the second piece:

### Setup ordering

Solving the whole problem with a MILP model proved to be virtually impossible for large datasets for being very time and memory consuming. Thus, the problem was divided in two phases.

In the first phase, setups for each production line and period of the planning horizon are selected without determining in which order they are set. This is solved with a MILP model. In the second phase, this order is determined using metaheuristic search methods.

This second-phase problem consists in determining a setup order for the setups selected in the first phase, satisfying the following requirements:

1. All setups have to be set within their period/s of activation.
2. Every setup has to be set once and only once within each of its periods of activation.
3. No setup of period n can precede a setup of period n-1.

Where the goal is to minimize the time spent in setup changes.

This allows for the following problem representation for each production line:

Figure 11. Setup ordering problem

Where each arc $\underset{s_{ij}s_{kl}}{\rightarrow}$ has a weight with a value equals to the time required to change from setup $s_{ij}$ to setup $s_{kl}$..

Note arcs between setups in period n and setups in period n+1 are one-way arcs, always from period n’s setups to period n+1’s setups to satisfy constraint (3) previously mentioned.

If a virtual setup $s_0$ is considered such that it is connected to:

• Every setup in period 1 with 0-weight, one-way arcs from $s_0$ to setups in period 1
• Every setup in the last period of the planning horizon with 0-weight, one-way arcs from setups in the last period to $s_0$

we have an asymmetric TSP problem with $s_0$ as origin node which can be solved using a metaheuristic search method such as Tabu Search or Simulated Annealing, either self-developed or using commercial or open source libraries.

## Conclusion

Growing competition in the manufacturing industry is forcing companies to look for increasingly sophisticated tools and strategies to optimize their global manufacturing enterprise from every perspective. Innovation is crucial to ensure their success. This article has presented how advanced analytics, in particular, can contribute to their success by supporting the decision-making process in annual budget planning.

In future articles, we will discuss how advanced analytics can support other processes and decisions in the manufacturing sector to ensure efficiency and help them succeed.

### 1 Comment

1. Alicia Pottinger says:

You really make it appear so easy with your presentation but
I in finding this topic to be actually one thing that I think
I might never understand. It sort of feels too complex and
very large for me. I’m looking ahead for your next put up,
I’ll try to get the hang of it!