Optimization Essay ⋆ Business Essay Examples ⋆ EssayEmpire

Optimization is the study of organizational problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. In mathematics, optimization is called mathematical programming. This type of programming is not computer programming, though computers are used extensively to solve complex optimization problems.

Practically, optimization is a process, technique, or methodology to make a decision, system, or design as perfect, functional, and effective as possible under the given circumstances.

Over time, optimization has developed into a field of study in recognition of the fact that several disparate disciplines present situations in which commonalities in terms of mathematical elements can be identified. Based on these commonalities, optimization problems can be formulated and resolved by the use of a unified set of ideas available in the field of optimization.

Optimization forms part of a larger repertoire of techniques in the field of operations research or management science that includes probability theory, queuing theory, games theory, decision analysis, and simulation. Operations research (in the United States) or operational research (in the United Kingdom) is an interdisciplinary branch of applied mathematics that deals with optimization of the performance of a system.

A typical situation requiring the application of optimization involves the manager of a business call center who faces a problem such as the following. A client service group has 50 call center staff members. On an average, each executive handles 800 calls per work session. For each staff member added to the group, the call-handling capacity per executive drops by 10 calls. The manager wonders how many staff members should be added to the existing group so that the total call-handling capacity of the group is maximized. The solution to this problem requires the technique of optimization. (The solution is to add 15 staff members to have a call-handling capacity of 42,250 calls per session. Adding fewer or more than 15 staff members would reduce the total number of calls handled.)

The optimization problem involves three elements: the objective function, a set of variables, and a set of constraints. The objective function is the variable that is to be optimized. The set of variables affects the value of the objective function. The set of constraints prevents the variables from taking on certain values that are not admissible. In the problem above, the objective function is the total call-handling capacity of the client group at the business call center. The set of variables is the number of staff members and the number of calls per session. The set of constraints is the limitations set on the variables—the number of staff members or calls cannot be negative, for example.

Applications

Optimization finds applications in a wide range of disciplines that include biology, business, economics, engineering, and information technology. The basic idea of optimization applications is that situations have common elements that could be expressed mathematically in terms of a model. This model brings together several variables that can be used to solve optimization problems. The complexity of the model depends on the number and variety of variables involved in the problem being resolved. Thus, linear programming could be used to solve simple optimization problems.

A simple problem in linear programming is one in which it is necessary to find the maximum (or minimum) value of a simple function subject to certain constraints, as illustrated in the call center example earlier in this article. More complex techniques include nonlinear programming, integer programming, and stochastic programming.

Applications of optimization in organizations have increased greatly after the availability of computers to solve optimization problems with several variables. Optimization can be applied in many situations in business organizations. Application areas include airline optimization, finance and economics, marketing, production and logistics, scheduling, supply-chain management, telecommunications, transportation, and yield management.

International Applications

Myriad areas are available for application of optimization in international business, too. Optimization methods enable international businesses to increase their responsiveness to changing global market forces while minimizing their cost. Areas of applications in the international context include material allocation; transportation logistics; workforce and production planning; and efficient management of inventories, customers, risk, compliance, pricing, and marketing.

A multinational corporation could face a situation in human resource management in which it needs to match highly skilled and multicultural employees to available job positions, using a method that is scalable so that it can handle large pools of jobs and resources in a dynamic market. The approach could use constraint programming, for example, to manage the complex constraints encountered in the field and reach near-optimal assignments that take into account all resources and positions in the job pool. The constraints, which are applied at both the individual and team levels, concern job role, skill level, geographical location, languages, and many other factors.

In international organizations, marketing optimization can deal with the typical problem of multichannel marketing event optimization. An increasing number of firms use multiple channels—such as e-mail, call centers, and direct mail—to contact customers with marketing events. The determination of an optimal set of marketing events to present to an individual customer, given a set of marketing events by channel, a set of individuals, some additional constraints, and the concepts of saturation and cannibalization can be a useful application of optimization.

Optimization has certain limitations, such as facing difficulties with the specification of the objective function, unrealistic linearity, lack of feedback, and lack of dynamics. Often, organizations that want to deploy optimization tools face the challenge of the relatively high cost of such tools.

Bibliography:

Urmila Diwekar, Introduction to Applied Optimization (Springer-Verlag, 2008);
Christodoulos Floudas and P. M. Pardalos, eds., Encyclopedia of Optimization (Springer, 2008);
A. J. Nicholson, Optimization in Industry (Aldine Transaction, 2007);
Stephen Powell and Kenneth R. Baker, Management Science: The Art of Modeling With Spreadsheets (John Wiley & Sons, 2007).

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