Question

Production Management #3
Explain the meaning of capacity planning. Identify and explain the different classifications of capacity planning. Enumerate and discuss the different factors affecting capacity planning. Please elaborate.

Production Management #4

Discuss the relevance of Linear Programming. Enumerate the properties of linear programming and steps for graphical method and simplex method.

Answer 1

Capacity Planning:

Demand fluctuates every time. Understanding the demand of the market and producing accordingly is when capacity planning come into play. It is the process of determining the capacity of production needed by an organization to meet changing demands for the products.

Capacity planning is a strategic procedure as it involves the utilization of capital intensive resources like plant, machinery, labor etc.

Types of Capacity Planning:

Based on the timeline capacity planning is classified into three types. They are;

• Long Range
• Medium Range
• Short Range

Long Range: It is the capacity planning which is done for a long term like for the complete life of the organization (defining the production capacity of the company to the industry). It depends on various factors like design capacity, production capacity, sustainable capacity, and effective capacity.

• Design Capacity implies maximum output by an equipment manufacturer under ideal working condition. For example, the design capacity of a sewage treatment plant is measured in liters/day.
• Production Capacity is the maximum output possible from equipment under normal working conditions.
• Sustainable Capacity is the maximum production level achievable in realistic work condition and consideration normal machine breakdown, maintenance etc
• Effective Capacity is the optimum production level when roles are assigned in an efficient way with normal work schedules, normal machine breakdown, maintenance, etc.

Medium Range: The capacity planning undertaken by the organization for 2 or 3 years of a time frame is called medium range capacity planning.

Short Range: The daily, weekly and monthly timeframe capacity planning is referred to as short term capacity planning.

The ultimate goal of capacity planning is to meet the current and future level of the requirement at a minimal wastage.

Factors affecting Capacity Planning:

Past Data: Past data is an important factor in capacity planning. The trends can be identified in the past demand of particular product types and the capacity planning can be done accordingly which helps in producing accurately.

Type of Project: A company might have different business models, from consulting to contingency fees. Multiple projects create a complex forecasting environment, but with the right tools, it’s easy to turn data into insights and see which project types in the pipeline are more likely to come to fruition.

Location: It can have a big impact on what the personnel plan looks like and should be considered early in the forecasting process.

Production facility (layout, design, and location), product line or matrix, production technology, human capital (job design, compensation), operational structure (scheduling, quality assurance) and external structure ( policy, safety regulations).

Linear Programming: It is an essential technique used for optimum utilization of resources mostly applicable to operations research. The resources are always limited. But every resource has various alternative uses. Every manager wants to maximize profit or minimize the cost of production. The linear programming technique is used for selecting the best possible strategy from a number of alternatives.

Characteristics of Linear Programming:

To solve a linear programming problem, the following are necessary:

• Objective function
• Constraints
• Non-negativity
• Linearity
• Finiteness

Objective function: A clearly defined objective which can be stated in a quantitative way. Generally, the objective in a business problem is either a profit maximization or cost minimization.

Constraints: The limitations regarding resources should be stated in the mathematical form.

Non-negativity: The value of variables must be zero or positive and not negative. In production, the manager can decide about any particular product number in positive or minimum zero, not the negative.

Linearity: Linear means there should be a proportional relationship between two or more variable, i.e., the degree of variables should be maximum one.

Finiteness: The number of inputs and outputs need to be finite. If there are infinite factors, a feasible solution is not possible.

Assumptions:

• The objective function should be optimized (profit maximization(>=0) or cost minimization(<=0))
• The prices of input and output are constant.
• The constraints should be in quantitative terms.
• Objective function and constraints are linear.

Graphical Method of LP:

The business problems involving two variables can be easily solved by drawing the graph for various constraints. Following are the steps in the graphical solution of the linear programming problem.

• Formulate LPP by writing the objective function and the constraints.
• Constraints are changed into equalities.
• Plot the constraints on the graph.
• Identify the feasible region and ascertain their coordinates.
• Test which point is most profitable.

Simplex Method of LP:

Any linear programming problem involving two variables can be easily solved with the help of graphical method as it is easier to deal with the two-dimensional graph. All the corner points of the feasible area are tested for optimal solution by putting the corner points in the objective function.

But if the number of variables increases from two, it becomes very difficult to solve the problem by drawing its graph as the problem becomes too complex. The simplex method is the mathematical treatment of the graphical method. Here also various corner points of the feasible area are tested for optimality.

Steps for the Simplex Method:

• A standard form is the baseline format for all linear programs before solving for the optimal solution and must be a maximization problem.
• Slack variables are additional variables that are introduced into the linear constraints of a linear program to transform them from inequality constraints to equality constraints. If the model is in standard form, the slack variables will always have a +1 coefficient. Slack variables are needed in the constraints to transform them into solvable equalities with one definite answer.
• A Simplex tableau is used to perform row operations on the linear programming model as well as to check a solution for optimality. The tableau consists of the coefficient corresponding to the linear constraint variables and the coefficients of the objective function.
• Once the tableau has been completed, the model can be checked for an optimal solution. The optimal solution of a maximization linear programming model are the values assigned to the variables in the objective function to give the largest zeta value. The optimal solution would exist on the corner points of the graph of the entire model. To check optimality using the tableau, all values in the last row must contain values greater than or equal to zero. If a value is less than zero, it means that the variable has not reached its optimal value. As seen in the previous tableau, three negative values exist in the bottom row indicating that this solution is not optimal.

Advantages of LP:

• LP makes logical thinking and provides better insight into business problems.
• A manager can select the best solution with the help of LP by evaluating the cost and profit of various alternatives.
• LP provides an information base for optimum alloca­tion of scarce resources.
• LP assists in making adjustments according to changing conditions.
• LP helps in solving multi-dimensional problems.

Limitations of LP:

• This technique could not solve the problems in which variables cannot be stated quantitatively.
• In some cases, the results of the LP give a confusing and misleading picture.
• LP technique cannot solve the business problems of non-linear nature.
• The factor of uncertainty is not considered in this technique.
• This technique is highly mathematical and complicated.
• If the numbers of variables or constraints involved in LP problems are quite large, then using costly electronic computers become essential, which can be operated, only by trained personnel.