Capacity is “the volume of output that a system is able to achieve in a specific period of time” (Yang, 2001). When talking about capacity, probably the first thing that comes to mind is productive capacity. However, capability is a much broader and more encompassing term. In this article, we will approach the subject with a focus on capacity decisions in logistics applications: How many conference ramps should be built in the expansion of a distribution center? What size should the finished products storage tanks of a petrochemical company be to support the operation in five years? What impact could new technologies have on the future operation? These are some questions that must be answered for the elaboration of a strategic capacity planning.
It is important to emphasize that, many times, due importance is not given to the issue of capacity in companies. Thus, executives can find themselves in situations in which they realize that investments should have already been made and that they will not be able to meet the demand due to lack of capacity.
The criticality of capacity planning increases with the time required to implement an expansion. If an operation's capacity can be expanded in a few days, a plan for the next five years may seem unnecessary. However, if projects require months or years to be executed, strategic capacity planning is essential.
When deciding what level of capacity to maintain over time, an organization must assess the trade-off between too little and too much. In a scenario of lack of capacity, the company does not completely meet the demand, and may lose customers due to the poor level of service, making room for the advancement of competitors. On the other hand, excess capacity leads to idle resources, incurring opportunity costs, or to forced strategies to increase demand, such as, for example, price reductions.
Thus, we encounter a problem very similar to the problem of defining product safety stocks. The literature provides some methodologies for defining the so-called capacity buffers, which, similarly to safety stocks, aim to guarantee a certain level of service, given the existing variability. Hayes and Wheelwright (1984), for example, discuss a methodology for defining this capacity cushion, which should reflect the magnitude of the relationship:
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In the formula, Cs represents the cost of missing (short) and Cx represents the cost of excess (excess). However, this approach has some weaknesses. Defining these parameters accurately is something extremely difficult, if we observe that the cost of excess can, for example, vary depending on the amount of capacity to be installed; and the cost of non-attendance can include components that are difficult to quantify, such as, for example, the lost margin of future sales due to loss of customers and damage to the organization's image and reputation.
Despite this, it is important to emphasize that the relationship captures the type of existing trade-off, which can help guide the decision, even if the value itself is not used mathematically to define the mattress. Depending on this trade-off, the capacity expansion plan can be driven by one of the policies described below.
Policy A: Avoid absence
If the cost of lack is greater than the cost of excess, the organization should tend towards a policy of maintaining a relatively large capacity cushion and, thus, guaranteeing a low probability of not meeting demand. In these cases, one should, at the extreme, opt for the expansion behavior illustrated in Graph 1.
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The lack of storage capacity in a continuous production process, such as in the petrochemical sector, can lead to a plant stoppage. In this case, the cost of lack of capacity is represented by the loss of margin caused by the stoppage, which is clearly greater than the cost of excess.
Policy B: Follow the forecast
If the cost of shortage is similar to the cost of excess, the expansion plan must ensure that the probability of occurrence of lack of capacity is similar to the occurrence of excess. Thus, this policy suggests that the organization try to adapt the productive capacity to the demand forecast. Graph 2 represents the behavior of capacity against demand over time.
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Policy C: Avoid excess
If the cost of excess is greater than the cost of lack of capacity, the company must maintain a “negative” cushion, in order to ensure that the probability of occurrence of a shortage is greater than the probability of excess. This policy leads to a high resource utilization rate, consequently generating a greater return on investments than the other two already presented. However, attention should be paid to the fact that its adoption can also lead to a deterioration of the organization's image and positioning in the market. The capacity expansion behavior related to this policy is illustrated in graph 3.
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However, it is important to emphasize that strategic capacity planning must be aligned with the organization's business strategy. Since it is extremely difficult to calculate exactly what the ideal size of the capacity cushion is, the organization must pay attention to other strategic factors that generate and suffer consequences arising from capacity decisions – when to expand, how much to expand – when defining strategic planning.
A capacity expansion can be used as a demand trigger, making it grow faster when compared to a scenario without expansion, or as a tool to intimidate the competition, mainly smaller players. For example, an increase in a company's resources, so that it can be present and take its products to a certain region at a lower price, can stimulate demand, which would not happen if such a decision had not been taken.
However, the capacity of a system is directly related to the quantity and characteristics of the available resources. And the total capacity of a system can hardly be defined by just one resource. Typically, a set of different resources is required to make up a system's capability. Therefore, the Strategic Capacity Planning must define the quantity of each of the necessary resources over time based on assumptions and future forecasts.
For this, the decision maker needs to understand how the resources are related, how each one of them can impact the others, how the quantity and efficiency of each one of them can change the total capacity and how the system reacts under certain conditions that do not exist today. , but may come true in the future. Having this basis for decision-making is not at all simple, since a capacity strategy is based on a series of assumptions and long-term forecasts about the market (demand), technology and competitive behavior, the main ones being:
- The forecast of growth and estimation of demand variability;
- Efficiency, availability and costs of building and operating the resources;
- The behavior of other players and suppliers.
Obviously, all these predictions and assumptions are strictly necessary, and by definition they carry with them a high degree of uncertainty that needs to be adequately considered.
THE UNCERTAINTIES
Dealing with uncertainties in a consistent way in an organization is not a trivial task. Working with unique and average values in this type of environment often leads to misinterpretations and, consequently, to wrong management decisions. At the same time, considering these uncertainties in analyzes and evaluations through statistics such as percentiles, standard deviation or covariance is also not very simple. In the case of Capacity Planning it is no different. In addition to future demand, which is one of the main input data for a capacity study, uncertainties are also present in other parameters, such as, for example, the types of resources available, the efficiency of these resources or their availability.
The present degree of uncertainty is directly proportional to the planning horizon, that is, for long-term capacity analyzes, the uncertainty contained in future demand estimates is greater when compared to the uncertainty related to demand forecasts carried out to feed capacity capacity analyses. short term. In addition, estimating other factors such as the behavior of competitors and suppliers in the long term is an extremely difficult task.
Incorporating present uncertainties, or at least the main ones, is very important for long-term capacity planning, since it can significantly change the decision taken and, consequently, the investments needed to implement the expansion plan.
There are some methods that can be used in a capability analysis study, such as analytical modeling, stochastic programming and simulation. However, the complexity generated by the uncertainties present in several interdependent variables generally seriously hinders the adoption of an analytical or programming methodology to solve the problem. Thus, it will be detailed how the simulation can be applied in a capability analysis study.
INTRODUCTION TO SIMULATION AND PRACTICAL APPLICATION
According to Saliby (1999), “…simulation consists of the process of building a model that replicates the functioning of a real or idealized system (still to be built) and conducting computational experiments with this model, with the aim of better understanding the problem under study, testing different alternatives for its operation and thus proposing better ways of operating it.” This definition makes it clear how simulation can be used as a tool for a capability analysis study. The model must represent the logistic system or sub-system to be studied, considering the existing relationships between resources and activities, being close enough to the real operation, in order to guarantee robust and reliable results.
To achieve this goal, it is highly recommended to follow the methodology diagramed in Figure 1.
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Step 1: Information gathering
In this step, the simulation analyst must obtain all the necessary information for a clear understanding of the system to be modeled and the objectives that must be achieved. It is important to clearly define the scope and keep in mind which questions need to be answered by the model.
Step 2: Conceptual and Data Modeling
In data modeling, after collection, these need to be treated in order to identify possible flaws and inconsistencies that may impact the quality of the final result – the maxim garbage in, garbage out applies. After treatment, the data must be used in order to define the probability distributions that will represent the uncertainties and other random phenomena in the model.
Furthermore, at this stage conceptual modeling is also carried out, which consists of defining the logic of the model and its representation so that all people involved in the process can understand it. It is at this stage that, for example, service priorities, flow of materials, resources involved and their relationships with activities, among others, are defined. It can be said that this is the most important step in the development of a simulation model.
Step 3: Mathematical Modeling
In it, the conceptual model is converted into a computational model through the use of some programming language or some simulation software. It is important to point out that current simulation software allows a high level of customization, using a graphical interface and leading to a reduction in model implementation time. Thus, a simulation analyst will hardly need to resort to a specific programming language.
Step 4: Model validation
After building the computational mathematical model, it needs to be compared to the conceptual model in order to assess whether the previously defined logic was faithfully implemented. Then, the model must be run and some results generated in order to verify if it is an accurate representation of reality. This is usually done by entering historical data for a given period and comparing the model's output with what actually happened in the operation over that period.
It is important to mention that, depending on the results obtained, the need to return to previous steps may be identified. This is because the model may return erroneous results due to problems in understanding the system, conceptual modeling, input data or computational implementation.
Step 5: Analysis of results
Only after validation can the model be used to carry out the experiments. In this stage, several rounds are carried out depending on the scenarios and variations to be evaluated. It is important to emphasize that the simulation alone does not answer which would be the best alternative, but how a system behaves given a certain configuration. It can be said that simulation is a what-if? technique, that is, “what happens if…” and not a technique that returns an optimal result, such as optimization. Thus, the experiment plan of a capacity analysis model must be designed to study different demand scenarios, assess the impact of changes in competition or suppliers, and, mainly, verify different configurations of resources.
Once built, a simulation model should have the following structure:
- input parameters
- Mathematical logic
- output data
Take as an example the model developed by Braskem – UNIB together with CEL – Center for Studies in Logistics, and presented at the XII International Logistics Forum (2006) to support the preparation of its Strategic Capacity Planning. This model covers several subsystems of different finished products, the raw material subsystem and the relationship of these subsystems with ports. Figure 2 illustrates these subsystems and their relationships.
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Given the complexity of the complete model, let's take just one subsystem, that of Product Z, represented by Figure 3.
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The illustrated subsystem presents four groups of entities. The first is made up of domestic market customers who are served directly from the plant through pipelines. The second group consists of the Braskem plant, which is responsible for producing and storing the finished product. The third represents the port of Aratu, which is connected to the plant by a pipeline and is used for berthing and loading ships that supply the foreign market and other customers in the domestic market via cabotage.
Operation in this subsystem depends on a certain set of features. The plant has two storage tanks, necessary because, naturally, there is no synchronization between continuous production and demand. The pipelines are resources of great importance, as they define the capacity to supply customers 1, 2, 3 and 4 and to transfer to the port of Aratu. The port tank has the role of storing the product while the ships are awaited. Lastly, port berths restrict the maximum number of ships that can be berthed and loaded at the same time.
All resources need to be parameterized in the model. The pipelines must have their capacities entered. The plant and port tanks must also have their storage capacities defined. Of course, the number of berths must also be added. In addition to these, other input parameters are necessary: the demand of each of the customers served by the pipeline; the plant's production rate; the frequency of arrival of vessels and their loading rate.
Some of these parameters were modeled in a deterministic way (single values), such as the pumping capacity in the pipelines, the storage capacity in the tanks, the production rate and the number of berths. Others, due to their variability and uncertainties, were modeled using probability distributions, such as the arrival of ships and the demand of customers served by pipeline.
The mathematical logic of the model must represent the logic of flows and decisions of the real operation. This logic is represented by the diagram in Figure 4.
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As the diagram suggests, two flows can be considered: ships and products. The flow of ships begins with the arrival of the vessels and their forwarding to the mooring queue. Mooring takes place under two conditions: availability of berth and product in the port tank. Berthed, the ship is then loaded and proceeds to its destination.
The product flow starts in production. If there is a request to send it to customers served by pipeline, pumping is activated and the product is transferred to the customers' tanks. If not, check whether there is storage space in the plant tank. If so, the product is pumped into this tank. If the tank is already 100% full, the plant stops. The port tank is replenished whenever it has capacity and there is product in the plant tank.
The main output data of the capacity analysis model are those related to the use of resources and the level of service. In the exemplified model, to evaluate the use of resources, three statistics were used: average use, 90th percentile of use and percentage of time that use was above 90%. The joint analysis of these statistics allows concluding whether a given resource is under- or over-dimensioned.
As mentioned earlier, the simulation does not return an optimal result, but rather how the system behaves given certain conditions. Concluding that a feature is poorly dimensioned leads to a next run of the model, changing the parameters of this feature and reanalyzing the output data. Chart 1 shows some results of a model run.
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It can be seen, for example, that Tank 1 of the plant seems to be under-dimensioned, because, despite presenting an average use of 72%, the 90th percentile reaches 96% and in one fifth of the time the tank level is above 90% capacity. In this operation, undersized tanks can lead to the need to stop the plant and, consequently, to prohibitive costs. This situation illustrates well the case in which the cost of lack of capacity is greater than the cost of excess capacity. To evaluate what will be the adequate capacity of the tank, the model must be run again a few times, with different values of capacity of tank 1, greater than the first value.
In addition to data on the use of resources such as tanks and pipelines, the study of the use of the port's berths was also extremely important. The availability of berths has a direct impact on the queue of vessels in the port. Longer queues lead to longer service times and higher demurrage costs (fine for delay in berthing and releasing the ship). Thus, the model was also designed to return data regarding the use of the port and the queue of ships.
Constructed considering the main uncertainties, variability and interdependencies of the current and future operation, the model developed by Braskem-UNIB together with CEL allowed the study of different scenarios and the sizing of the main logistical resources involved. Thus, the Strategic Capacity Planning was prepared for a ten-year horizon, defining the actions to be taken over time, as well as the necessary investments.
CONCLUSION
The process of preparing a Strategic Capacity Planning brings several challenges to organizations. One of the biggest is how to deal with the uncertainties arising from the forecasts and estimates needed for planning. The adequate treatment of these uncertainties is extremely important to guarantee the quality of the decisions taken.
This article shows how computer simulation can be used as a tool in a capability analysis study. A simulation model allows certain actions to be tested and their effects analyzed without actually taking them in reality.
Although the process of building a mathematical model is not a simple task, requiring trained professionals and the involvement of several people within the organization, it is certainly paid for by the richness of the analyzes that can be carried out and by the basis and security of the conclusions that will feed the planning. strategic capacity of the company.
BIBLIOGRAPHY
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