Introduction to Management Science

Introduction 

The key areas entailed are body of knowledge problem solving and decision making, quantitative analysis, models of cost, revenue and profit and quantitative methods in practice. The body of knowledge involves quantitative analysis approaches in decision making. There are seven steps used in problem solving whereby the first five are the decision making process. They are: defining the problem, determining collective other explanations, determination of the process involved in evaluation of other ways, evaluating options and choosing between the alternatives which is the making of a decision. 

The decision making process is basically made up of two parts: structuring of the problem and analyzing the problem. The analysis phase involves qualitative analysis, which depends on the experience and judgment, and quantitative analysis which depend on the analysis of the data and quantitative facts linked to the problem. In model development, there are three models: iconic models, mathematical models and analog models. Quantitative analysis is more complex as it involves development of mathematical expressions describing the constraints, objectives and other associations that exist in the problem. Small tests are done in order to know whether the model in question can be used in full-scale. This is called model testing and validation. There are also management science techniques that focus on taking various approaches in problem-solving. Among this include Linear Programming. 

Introduction to Linear Programming 

In this section, it involves linear programming issues, problem designation, graphical solution procedure and other optimal solutions. Also, the section will include simple limiotations of the issues and cases that are believed to be so special. Linear programming therefore involves selection of a particular problem and what brought about the problem. However, linear programming problems have restraints limiting the extent of tracking the objectives. Therefore, a feasible solution is one that contents the constraints of the problem. 

Conversion of a problem’s verbal statement to a mathematical statement is called modeling or problem formulation. There are guidelines for linear programming model formulation such as understanding the problem entirely, describing the objective and each constraint among others. Extreme points are vertices of the feasible region and it is where the problems affecting the program and the optimal solution can be found. A feasible section for n Linear Program problem that is two-variable can either be a single point, a polygon, unbounded areas or nonexistent. The special cases include when an LP problem’s solution is made indefinitely large and without violating any constraint. 

Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM) 

The application of PERT is essential in handling uncertain activity times. On the other hand, Critical Path Method is used in industrial projects. However, both are used in to schedule, plan, and control a large variety of projects. Project managers depend on this methods to determine the duration it will take to complete the project, the schedule for various project activities, operations that vital and those that should be completed exactly as dictated in the schedule. A project network is made to model the activities’ precedence. The network is made up of nodes, arcs and a critical path each of these has its meaning. The overall project completion time is presumed to assume a normal distribution with a mean equal to a sum of all the variances along the critical path. 

Inventory Models 

There are several inventory models that include Economic Order Quality and Economic Production Lot Size Model. Other inventory models are inventory model with planned shortages and Quality Models. This section primarily answers the question of the quantities that should be ordered whenever one an order is required. The aim is to limit the total variable cost over certain duration. EOQ is the most basic model over all the other deterministic inventory. In this model, the ordering costs and the annual holding cost are equal. The assumptions include that demand is known and that it occurs at rate that is constant and, the order quantity (Q) is the same for every order. The best formula for calculating the optimal order quality is Q * = 2DCo/ C h 

The Economic Production Lot Size Model on the other hand is usually a difference of the EOQ Model. One of the differences is that unlike in the EOQ, in the Economic Production Lot Size Model, replacement order is not accepted in a single lump sum. In this model, the assumption made states that demand is always at persistent degree of items per day or D items per Day, and that the purchase cost per every unit is constant (Anderson et al., 2015). In the EOQ with Planned Shortages Model, shortages happen till a prearranged backorder amount is achieved, whereby the replacement order get to. The variable costs include the backorder, ordering and holding. The assumptions in this model include that demand happens at rate that is constant of D items per year. 

The EOQ together with Quantity Discounts is suitable anywhere the supplier provides a purchase cost at a lower price when a product is ordered in bigger quantities. The assumptions in this model include that demand happens at a rate that is constant of D items per year. 

Reference 

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2015).  An introduction to management science: quantitative approaches to decision making . Cengage learning.