Question

Explain the meaning of the following terms: constraints, decision variables, feasible region and objective function. Explain their relevance to product mix decisions.

Answer 1

Solution

1. Explain the meaning of Constraints, Decision Variables, Feasible Region and Objective Function.

a) Constraints

The word Constraints means 'Something that limits or restricts someone or something': control that limits or restricts someone's action or behaviour.In the field of accounting, when reporting the financial statement of a company, accounting constraints (also known as constraints of accounting) are boundaries, limitations or guidelines. These constraints may allows for variations to the accounting standard. Types of cconstraints include objectivity,costs and benefits, materiality, consistency, industiral practices, timeliness and conservatism etc. These constraints deals with issues such as requiring evidence, balancing the costs and benefits of providing financial information, deciding the precision of a report remaining consistent within a report and from year to year, following the practices of an industry, reporting in a timely manner and not overstating profit and assets.

The definition of constraint is something that imposes a limit or restriction or that prevents something from occuring. A Constraint is also known as bottleneck or choke point. It is anything that prevents the organization from achieving its goals.

Theory of Constraints

The theory of constraints proposes that improvement efforts of the company should always be focused on the limiting factor because all other efforts elsewhere in the business will be rendered useless unless such constraint is managed well. The goal therefore of management is to properly identify and manage the constraint.

b) Decision Variables

A Decision Variable is a quantity that the decision maker controls. For example, in an optimization model for labour scheduling, the number of nurses to employ during the morning shift in an emergency room may be a decision variable.

Decision variables describes the quantities that the decision makers would like to determine. They are the unknown of a mathematical progaramming model. Typically we will determine their optimum values with in an optimization method. In a general model decision varaibles are given algebraic designation such as x1, x2, x3......xn.

c) Feasible Region

The Feasible Region is the set of all points whose coordinates satisfy the constraints of a problems. In mathematical optimization, a feasible region , feasible set, search space or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problems constraints, potentially including inequalities, equalities and integer constraints.

In the theory of linear programming, a basic feasile solution is a solution with a minimal set of non-zero variables. When no feasible solution exists there is no feasible region.

d) Objective Function

The objective function is where you specify the goal you are trying to achieve. The goal can either be to maximize or minimize the value of the objective function. Linear programming is an optimization technique for a system of linear constraints and linear objective function. The Objective function defines the quantity to be optimized , and the goal of linear programming is to fin the values of the variables that maximize or minimize the objective function.

2. Explain the relevance of constraints, decision variables, feasible region and objective function in product mix decisions

Introduction

Product mix also known as product assortment or product portfolio refers to the complete set of products or services offered by a firm. A product mix consists of product lines which are associated items that consumer tends to use together or think of as similar products or services.

Product mix decision refers to the decisions regarding adding a new or eliminating any existing product from the product mix, adding a new product line, lengthening any existing line or bringing new variants of a brand to expand the business and to increase the profitability.

a) Relevance of Constraints in Product Mix Decision

The constraints include maximum amount of each product or service demanded, minimum amount of product or service policy will allow and maximum amount of resources available.These are important for Product Mix Decision.

The quality of the Theory of constraint based approach to generate good or even optimal solutions is assessed with very different results, particularly when compared with other product mix decision tools. In Theory of Constraint the goal is to choose product line on the basis of constraints elapsed time throughput. Throughput is a rate in which the systems creates money or the target unit by using and selling it and is obtained through the following relation.

TU = P-TVC

TU = Each Product Unit throughput

P = Sale Price

TVC = Total variable cost

It means that in constraints, the priority is allocated to products having more throughput and they consume the minimum production time of constraints.Thus, the amount of throughput in a minute is the criteria for product manufacturing prioritization.

In order to select product mix through Theory of constraints based creativity the following steps should be taken.

1) Recognize the system constraints by calculating the necessary capacity in each source to manufacture all products. Constraints or bottleneck is source which market wants to increase in capacity.

2) Making decisions for how to utilize the system constraints by

a) Calculating Contribution Margin Ratio for each product in the form of sales price minus raw material costs.

b) Calculating Contribution Margin Ratio to product under manufacture in bottleneck source.

c) In order to decrease the contribution margin or Bottleneck ratio for products, make the BottleNeck Capacity eaual to Bottleneck final capacity limit.

d) Product planning for manufacturing all products which do not need to process time in bottleneck, free product in order to decrease their Contribution Margin Ratio.

Thus Theory of constraints based creativity for selecting the best product mix in all cases.

b) Relevance of Decision Variables in Product Mix Decision

The first step when formulating a product mix model is to identify and give names to the decision variables.Decision Variables are the element of the model that the decision maker controls and those values determine the solution of the product mix model.It include how much to produce and market of each product or service for the planning period.

c) Relevance of Feasible Region in Product Mix Decision

Feasible Region is the set of points that satisfies all constraints of linear programming. The region that is bound by the constraints is called the feasible region.It represents the possible values of the variables that satisfy all of the constraints.

e) Relevance of Objective Function in Product mix Decision

Objective function include to select the mix of products or services that results in maximum profits for the planning period. The objective function is a function that defines some quantity that should be minimized or maximized. The arguments of the objective function are the same variables that are used in the constraints. In order for linear programming rechniques to work, the objective function should be linear.

Conclusion

So we conclude that Objective function, Decision variable and Constraints and Feasible region is the important part of the Product mix decision.