THEORY OF RESTRICTIONS: MAIN CONCEPTS AND PRACTICAL APPLICATION

The Theory of Constraints, also called TOC (Theory of Constraints) is a relatively recent development in the practical aspect of taking several organizational decisions in which there are constraints. OCD was first described by Dr. Eliyahu Goldratt in his book, The Goal.

A constraint is anything on a company that impedes or limits its movement toward its goals. It is clear that the application of TOC requires an appropriate definition of the objectives to be achieved. For most companies, the main objective is present profit and its sustainability in the future. There are two basic types of constraints: physical and non-physical. Physical constraints are most often related to resources: machines, equipment, vehicles, installations, systems, etc. Non-physical constraints can be the demand for a product, a corporate procedure, or even a mental paradigm in addressing a problem.

In an industrial company, TOC involves three performance indicators that make it possible to assess whether the set of operations is moving towards the objectives (profit):

• Profitability: is the rate at which the company builds its profit through the marketing of its products. In essence, the profitability of a product could be approximated by the contribution margin (sales price – variable cost of raw materials). Labor costs and other fixed costs are considered as part of operating expenses.
• Operating expenses: all the money spent by the company in converting its inventories into contribution margin.
• Inventories: all the money held by the company in things that can or could be traded. Inventories include not only conventional items (raw materials, work-in-process and finished products), but also buildings, land, vehicles, equipment. It is not included in inventories, therefore, the value of labor added to work-in-process inventories.

It is noticed that TOC has a very strong connection with managerial accounting, specifically with the contribution margin costing approach. It is clear that the use of generally accepted principles in financial accounting or for legal purposes can lead to suboptimal decisions, basically due to the need to allocate and apportion all fixed costs to cost centers, which, eventually, can be constraints. Another four performance indicators can be calculated from Profitability, Operating Expenses and Inventories:

Net margin = profitability - operating expenses

Return on Investment (RSI) = (profitability – operating expenses) / inventory

Productivity = profitability / operating expenses

Turnover = profitability / inventories

The slight difference of these indicators, specifically the Giro and the RSI, should be observed when transposing the principles of financial accounting to managerial accounting. For example, in financial accounting, Turnover is defined as sales/inventory.

Application and Implementation

TOC has been applied at three different decision-making levels: production management, in solving problems related to bottlenecks, programming and inventory reduction; profitability analysis, leading to the shift from cost-based decisions to decisions based on continuous improvement of operations that affect profitability; and, process management, in identifying organizational factors, which are not necessarily resources, that prevent companies from achieving their goals.

There are five steps for applying the TOC.

• Identify the system constraint. In an industrial company, the restriction can be the available time or the capacity of a machine, a department or a workstation. For service or high-tech companies, the constraint can be the available time of the most capable employees.
• Calculate the profitability per unit of resource consumed in the constraint. This value is obtained by dividing the profitability or unit contribution margin by the resource consumption of the constraint to produce a product. The key to maximizing profit is to focus on producing and marketing the products with the highest profitability per unit of resource consumed in the constraint.
• Subordinate the system to the constraint. Resources and stocks must be managed in order to provide exactly what is needed to achieve the objectives defined for the constraint. This step may imply the idleness of resources that are not restrictions. Usually the system is subject to restriction through a method of programming and production control called Drum-Buffer-Rope or DBR.
• Break or lift system constraint. Through continuous improvement of operations, capacity acquisition or fluctuations in demand, for example, the system constraint can be broken or lifted so that this constraint ceases to be. A new physical or non-physical, internal or external constraint will take over the role of the previous constraint.
• Identify the new system constraint if the constraint is broken.

It should be noted, however, that implementing TOC may require a substantial change in the way the company operates. For example, suppose that, in a company, producing and marketing the product with the lowest unit price and highest demand maximizes profit (objective). If the company compensates its sales force on a commission basis as a percentage of revenue, there may be an implicit incentive to sell the more expensive products. This scenario would demand a new sales force remuneration policy.

Drum-Pulse-Rope (DBR)

DBR is the production programming and control method that allows you to subordinate the system to the constraint. Its objective is to ensure maximum utilization of the constraint to meet demand. The Drum is the detailed constraint schedule, with the items to be produced, their quantities, start and end times. Demand is the starting point for determining the Drum.

Non-constraint features must pace the constraint. This is why restriction programming is called Drum, for “determining the rhythm of the whole troop”. Resources that are not constraints must be managed so that the constraint is not missing items, otherwise the objective will be threatened. Since non-constraint resources have greater capacity than demand, they do not need to be scheduled. The DBR method signals for the release of the necessary items to feed the Drum and for the resources that are not restrictions to process this quantity as quickly as possible.

Due to the uncertainties, a hedge must be created for the release of items some time before their processing in the restriction. This protection is called a Buffer, and in TOC, the Buffer is measured in units of time, not item quantities. The duration of the Buffer is influenced by the speed of other non-constraint resources and by the response time variance of operations. The greater the variance, the greater the duration of the Buffer. The higher the speed of the other resources, the smaller the Buffer.

Generally speaking, the Buffer is created to protect programming. It is an anticipation of the moment of release of the items in order to guarantee the fulfillment of the production schedule. There can be three types of lung in OCD:

• Constraint Buffer – aims to protect the Drum with the early release of items to the constraint.
• Shipping Buffer – Constraint is not the only element with programs to watch. The loading of finished products must also be protected with a buffer, in order to ensure the reliability of deadlines for customers.
• Assembly Buffer – when items that have been processed by the constraint must be assembled with items that have not passed the constraint, another buffer needs to be created. In this case, all parts that passed through the restriction must be used to form the finished product and in this way, no “non-restriction” items must be missing.

Not all industrial enterprises need all three types of buffer. This decision depends on the type of process and the location of the restriction. If there is a physical constraint associated with a resource, there will be at least 2 buffers, the constraint buffer and the loading buffer. The Assembly Buffer is needed if there is an operation that combines items that were with others that were not processed by constraints. All items fall into two alternatives:

• The items that are processed by the restriction will have two lungs in their flow: the Restriction and the Shipment.
• Items that are assembled with other items that are processed by the constraint will have two lungs in their flow: Assembly and Shipping.

Taking the Drum as the starting point and subtracting the Buffer from the Restriction it is possible to determine the instant of release of the items. Corda ensures that the exact amount of items that will be processed by the restriction will be released. In other words, through Corda it is ensured that all resources will operate at the same pace as the constraint, without increasing the levels of in-process inventory.

The application of the DBR method for subordination of the system to the constraint, must observe other additional steps, in addition to the five steps mentioned in the previous section:

• Represent the Drum in a Gantt chart, that is, the detailed schedule of the constraint over time;
• Decide on the proper size of the Constraint, Assembly and Loading buffers for each product;
• Subtract the Buffer from the Constraint at the beginning of the operation from the corresponding constraint, represented in the Gantt chart, to determine the instant of release of the items in order to support the Drum.
• Subtract the Assembly Buffer from the end of the corresponding constraint operation to determine the release of items to support assembly of items that were not processed by the constraint with items that were processed by the constraint.
• Add the Loading Buffer to the end of the corresponding constraint operation to determine the product loading date, if production is for stock. If the production is counter-order, the Loading Buffer must be subtracted from the delivery date to determine the instant of release of the items.
• Develop a schedule for the production of items at divergent points, that is, an operation where two or more products can be manufactured from the same common item based on constraint, loading and assembly schedules.

The following section exemplifies the adoption of the TOC steps and the DBR method in a fictitious company that manufactures two products.

Practical Application

A company manufactures two products, Y and Z which are processed in four departments, A, B, C and D. Product Y requires three types of materials: M1, M2 and M4. Product Z requires two types of materials, M2 and M3. In Figure 1, the logical product structures are represented. The combination of the list of materials or items (bill of materials) of a product with the route of operations (or workstations, or departments) traversed by the items that make up this product (part routings) forms the logic of the product structure .

Figure 1 - Logic of product structures

NOTE: The coordinates, defined by Greek letters and Arabic numerals define an operation within the logic of the product structure. For example, α is the operation performed in department A to process raw material M1. Subsequently, the processed item is sent to department C to perform operation β1.

The manufacturing requirements for each product are summarized in Table 1:

Each department has 2400 minutes of available capacity per week. The operating expenses of this hypothetical company are $30000 per week. Based on current demand, the company is able to sell 100 units of product Y and 50 units of product Z per week. The selling prices are $450 for product Y and $500 for product Z. All four materials are available in sufficient quantities. The necessary manpower is also available.

The approach that is presented below is particularly useful when there are only two products and there is only one active constraint in addition to demand. However, the linear programming approach becomes necessary in more complex situations, with multiple products and several active constraints in addition to demand.

The first step is to determine the constraint of the system. For this, the total time needs of each department to meet the current weekly demand of Y and Z must be calculated, as indicated in Table 2, and confronted with the available capacity.

As each department has an available capacity of 2400 minutes per week, department B is the constraint because it does not have enough capacity to attend weekly to 100 units of Y and 50 units of Z.

The second step initially depends on determining the profitability or the unitary contribution margin for each product. This is needed to determine how to manage the constraint in order to maximize profit. Unit profitability is given in Table 3.

Table 3 provides the necessary elements to complete the second step and determine the profitability per unit of resource consumed in the constraint to manufacture the product. This calculation is indicated in Table 4.

The third step consists of subordinating the system to the constraint. In this practical application, profit maximization involves manufacturing the largest possible number of units with the highest profitability per unit of resource consumed in the constraint. To meet demand, the company would have to produce 100 units of Y. This would consume (100 units)(15 minutes) = 1500 minutes of B's ​​available capacity and leave 2400 – 1500 = 900 minutes per week to manufacture 30 units of Z, i.e. 900 minutes / 30 minutes per unit = 30 units.

Figure 2 graphically illustrates the approach taken to determine production batch sizes. To build this graph, the constraints that delimit the space of feasible solutions must be initially determined. In this company, the constraints are the current demand for the two products (Y = 100 and Z = 50) and the trade-off of department B's resource consumption per unit produced (15Y + 30Z = 2400). Observing this trade-off and ignoring current demands, department B could produce 160 units of Y (2400/15) and no units of Z, or 80 units of Z (2400/30) and none of Y or any combination of Y and Z totaling 2400 minutes per week. This combination is represented by the line connecting these points in Figure 2.

Figure 2 – Graphical representation of restrictions

The solution that maximizes the contribution margin must be found at the vertices that delimit the space of feasible solutions. The contribution margin is given by the equation 235Y + 300Z. Table 5 presents the results for the contribution margin equation as a function of these vertices.

Finally, weekly profit can be calculated by incorporating operating expenses. Weekly profit = $32500 – 30000 = $2500. Once the constraint has been identified and the production mix defined, a Gantt chart detailing the Drum (constraint schedule, ie department B) must be constructed. Several schedules are feasible and, for simplification purposes, it is assumed that there are no uncertainties in the system and that the customer has not established deadlines for receipt, so that all buffers (restriction, assembly and loading) are equal to zero. Also assuming set up times equal to zero in department B, batches equal to the daily demand can be produced without creating a new restriction. In this case, it would be 20 units of Y (100/5) and 6 units of Z (30/5) for 480 minute shifts (2400/5). The Gantt chart for the Drum is shown in Figure 3, in addition to the instants for releasing and receiving items in the operations carried out in each department. It is noticed that the utilization rate of the restriction is 100%, while the utilization in the other departments is lower than the maximum limit, alternating periods of idleness with occupation.

Figure 3 - Possible production program for a Tambor shift

CONCLUSION 

TOC is a philosophy for production planning, anchored in linear programming techniques, in which the constraints would determine the performance (profitability) of the system. The operationalization of planning by TOC in a production program occurs through the DBR method. By DBR, the whole system is subordinated to the programming of the restriction (Drum), the different buffers are incorporated to protect the drum from system uncertainties and the strings ensure the release of exact amounts.

The object of analysis by TOC and DBR is the logic of the structure of the products, that is, the combination of the list of materials with the route of operations (or workstations) covered by the items that make up these products. In MRP (Materials Requirements Planning), on the contrary, the object of analysis for formulating production planning and programming is the list of materials and their time lag, in order to ensure the execution of the MPS (Master Production Program) at from a sales forecast.

Given that it is not possible to state, a priori, the superiority of TOC over MRP or any other policy for production planning and scheduling, the choice of a given policy depends substantially on how easy and direct the association between raw materials is. , work-in-process and net requirements with finished goods scheduling. Silver, Pike and Peterson argue that there is a direct connection between the position in the product-process matrix and the ease of this association. In this case, as shown in Figure 4, the TOC would be, for example, more suitable for job shop situations with several main products.

Figure 4 – The impact of the product-process matrix on the choice of production planning and scheduling policy

Description:

TOC – Theory of Constraints

MRP – Material Requirements Planning

JIT – Just in Time

PFS - Process Flow Scheduling

BIBLIOGRAPHY

Anonymous, “What is the theory of constraints and how does it compare to lean thinking?” in www.qmi.ans.au (accessed on 17/12/2003).

Corbett, T., 2003, “Drum-Buffer-Rope” in www.corbett.pro.br (accessed on 17/12/2003).

Silver, E., Pyke, D., Peterson, R., 2002, Inventory Management and Production Planning and Scheduling, 3rd Edition, New York: Wiley & Sons.

Sytsma, S., 2003, “The Theory of Constraints – Making Process Decisions Under Conditions of Limited Resources, Capacities or Demand” in www.sytsma.com.