Steps of Problem Solving

Contents

Introduction 3

Steps of problem solving 3

Step 1: Define the problem 3

Step 2: Define the variables 3

Step 3: Formulate the objective function 4

Step 4: Define the constraints 4

Methods of solving LP problems 4

Microsoft Excel Solver 4

References 9

Appendix 10

Answer Report 10

Sensitivity Report 10

Limits Report 11

Introduction

Decision makers are often faced with the problem of allocating limited resources between competing demands in order to maximize output, revenue, service level, etc., or to minimize costs. This kind of problem arises, for example, in production planning, feedstock blending, investment portfolio management and staff scheduling. Decisions are often made in a relatively simplistic way as the complexities involved overwhelm traditional tools of analysis. This necessitates the use of managerial judgement or rules of thumb. Linear programming (LP) offers a holistic, decision support tool which takes account of all of the complexities to calculate an overall best or optimum solution. LP type problems can be solved in a number of ways. Spreadsheet packages make it very simple to construct "What if?" (Caine & Parker, 1996).

For these types of problems LP, perhaps the best known of all management science techniques, often provides the only technique available to obtain an optimum solution for a number of variables within a set of constraints. Additionally, LP can provide extensive "What if?" analysis which can greatly enhance decision making effectiveness (Caine & Parker, 1996).

Steps of problem solving

It is necessary to first formulate the problem in an algebraic format. This formulation follows four steps:

Step 1: Define the problem

The first step with any problem situation is to define in words the purpose of the investigation for example in this case the problem is determining the optimal number of aqua-Spas and Hydro-Luxes to produce in order to maximize profits.

Step 2: Define the variables

At this stage the decision makers need to decide which variables are under their control and are likely to influence the solution to the problem. In this case, there are just two controllable variables, number