Mathematical Programmingin Practice5In management science, as in most sciences, there is a natural interplay between theory andpractice. Theoryprovides tools for applied work and suggests viable approaches to problem solving, whereas practice addsfocus to the theory by suggesting areas for theoretical development in its continual quest for problem-solvingcapabilities. It is impossible, then, to understand fully either theory or practice in isolation. Rather, they needto be considered as continually interacting with one another.Having established linear programming as a foundation for mathematical programming theory, we noware in a position to appreciate certain aspects of implementing mathematical programming models. In thenext three chapters, we address several issues of mathematical-programming applications, starting with ageneral discussion and followed by specific applications. By necessity, at this point, the emphasis is on linearprogramming; however, most of our comments apply equally to other areas of mathematical programming,and we hope they will provide a useful perspective from which to view forthcoming developments in the text.This chapter begins by presenting two frameworks that characterize the decision-making process. Theseframeworks suggest how modeling approaches to problem solving have evolved; specify those types ofproblems for which mathematical programming has had most impact; and indicate how other techniquescan be integrated with mathematical-programming models. The remainder of the chapter concentrates onmathematical programming itself in terms of problem formulation and implementation, including the role ofthe computer. Finally, an example is presented to illustrate much of the material.5.1 THE DECISION-MAKING PROCESSSince management science basically aims to improve the quality of decision-making by providing managerswithabetterunderstanding of the consequences of their decisions, it is important to spend sometimereflectingupon the nature of the decision-making process and evaluating the role that quantitative methods, especiallymathematical programming, can play in increasing managerial effectiveness.There are several ways to categorize the decisions faced by managers. We would like to discuss twoframeworks, in particular, since they have proved to be extremely helpful in generating better insights intothe decision-making process, and in defining the characteristics that a sound decision-support system shouldpossess. Moreover, each framework leads to new perceptions concerning model formulation and the role ofmathematical programming.175176 Mathematical Programming in Practice 5.1Anthony’s Framework: Strategic, Tactical, and Operational DecisionsThefirstoftheseframeworkswasproposedbyRobertN. Anthony.∗Heclassified decisions in three categories:strategic planning, tactical planning, and operations control. Let us briefly comment on the characteristics ofeach of these categories and review their implications for a model-based approach to support managementdecisions.The examples given to illustrate specific decisions belonging to each category are based primarily onthe production and distribution activities of a manufacturing firm. This is done simply for consistency andconvenience; the suggested framework is certainly appropriate for dealing with broader kinds of decisions.a) Strategic PlanningStrategic planning is concerned mainly with establishing managerial policies and with developing the neces-sary resources the enterprise needs to satisfy its external requirements in a manner consistent with its specificgoals. Examples of strategic decisions are major capital investments in new production capacity and expan-sions of existing capacity, merger and divestiture decisions, determination of location and size of new plantsand distribution facilities, development and introduction of new products, and issuing of bonds and stocks tosecure financial resources.These decisions are extremely important because, to a great extent, they are responsible for maintainingthe competitive capabilities of the firm, determining its rate of growth, and eventually defining its successor failure. An essential characteristic of these strategic decisions is that they have long-lasting effects, thusmandating long planning horizons in their analysis. This, in turn, requires the consideration of uncertaintiesand risk attitudes in the decision-making process. Moreover, strategic decisions are resolved at fairly highmanagerial levels, and are affected by information that is both external and internal to the firm. Thus, anyform of rational analysis of these decisions necessarily has a very broad scope, requiring information to beprocessed in a very aggregate form so that all the dimensions of the problem can be included and so that topmanagers are not distracted by unnecessary operational details.b) Tactical PlanningOnce the physical facilities have been decided upon, the basic problem to be resolved is the effective alloca-tion of resources (e.g., production, storage, and distribution capacities; work-force availabilities; marketing,financial, and managerial resources) to satisfy demand and technologicalrequirements, taking into accountthe costs and revenues associated with the operation of the resources available to the firm. When we aredealing with several plants, many distribution centers, and regional and local warehouses, having productsthat require complex multistage fabrication and assembly processes, and serving broad market areas affectedby strong randomness and seasonalities in their demand patterns, these decisions are far from simple. Theyusually involve the consideration of a medium-range time horizon divided into several periods, and requiresignificant aggregation of the information to be processed. Typical decisions to be made within this con-text are utilization of regular and overtime work force, allocation of aggregate capacity resources to productfamilies, definition of distribution channels, selection of transportation and transshipment alternatives, andallocation of advertising and promotional budgets.c) Operations ControlAfter making an aggregate allocation of the resources of the firm, it is necessary to deal with the day-to-dayoperational and scheduling decisions. This requires the complete disaggregation of the information generatedat higher levels into the details consistent with the managerial procedures followed in daily activities. Typicaldecisions at