Operations Planning

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Introduction and Purpose

1.1 Operations Planning

Within the broad field of business administration, the area of business op-

erations encompasses the activities required to produce goods and services

and bring them to markets and customers. Executing the associated produc-

tion and distribution activities requires material inputs as well as physical and

organizational infrastructure. Physical infrastructure is comprised of the facil-

ities (e.g., factories, warehouses, retail stores) and equipment (e.g., production

and material handling equipment, inter-facility transportation vehicles) neces-

sary to transform material inputs into production outputs that provide value

to customers. Organizational infrastructure consists of the human resources

required to ensure the execution of operations activities, as well as the func-

tional responsibilities and relationships among the organization’s members.

Execution of operations activities requires planning in addition to infras-

tructure and materials. At some point, the establishment of every existing

factory, warehouse, and retail outlet was planned. This plan began with the

identification of the need for the facility, its defined mission, and a charac-

terization of the scope of interaction with other facilities and organizations

required to accomplish the planned mission. Similarly, the broad responsibili-

ties and functions of each organizational member were, at some point, planned

and defined. Such infrastructure and organizational plans often require initial

investments and are put in place for a relatively long time horizon (e.g., five

years or more). These long-range planning activities fall within the domain of

strategic planning, and they serve as a basis for achieving an organization’s

set of long-term, strategic goals (e.g., to provide a particular class of products

or services to a particular set of markets).

After establishing the infrastructure required to implement a strategy, the

medium-range scope of activities performed at facilities and the interactions

between facilities and their outputs require planning as well. Such plans in-

clude establishing targeted quarterly workforce levels, required material in-

puts, production outputs, and material and finished goods inventory levels at

each facility over a one- or two-year horizon, for example. These medium-range

plans are critical for determining operating capital requirements, contractual

arrangements for material supplies and distribution services, and projected

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2 Operations Planning: Mixed Integer Optimization Models

earnings for a firm, for example. Planning for these medium-range activities

is often referred to as tactical planning.

Reaching markets with products and services requires daily operations

activities, including the production of actual goods and the movement of goods

between locations. On any given day (or in any given week or month), for

example, the workers in a facility need to process a set of activities in order

to meet some desired output by the end of the day (or the end of the week or

month). That is, given a set of requirements for production output, a sequence

in which these requirements will be processed must be determined. Such work

sequencing decisions typically impact the economic performance of a facility as

well as the facility’s ability to meet customer expectations. These short-range

work sequencing decisions fall within the domain of operations planning.

Each of these planning categories falls within an overall planning hierar-

chy, wherein the decisions made at higher levels of the hierarchy constrain the

available decisions at lower levels. Strategic planning serves as the top level in

this hierarchy, tactical planning as the middle level, and operations planning

as the lowest level. The intent of this conceptual hierarchy is to decompose

the entire scope of planning activities into a set of manageable decisions, be-

cause the amount of information required and the complexity involved often

preclude simultaneously considering decisions at each level of the hierarchy.

In order to mitigate the possible negative impacts of decomposing decisions

into such a hierarchy, decisions at higher levels often use rough-cut or aggre-

gated estimates of the required activity levels at lower levels in the hierarchy.

For example, when planning the construction of a facility (a strategic plan-

ning decision), the facility’s capacity level may be determined based on the

projected maximum annual demand the facility is intended to satisfy. This

projected maximum annual demand is a function of the aggregate anticipated

requirements over a medium-range planning horizon (e.g., one year), which

are, in turn, aggregated estimates of the requirements during the short-term

(e.g., weekly). Planning at each level of the hierarchy requires a systematic,

methodological approach in order to ensure that the plans are consistent at

all levels and allow an organization to effectively execute its strategy.

1.2 Mixed Integer Optimization

Problems arising over the last century in the production and distribution of

goods and services have led to numerous mathematical modeling and sci-

entific approaches for operations planning decisions. Development of these

approaches was accelerated following the conception of Linear Programming

(LP) by George B. Dantzig in 1947 (see [36] for a history of the advent of LP

as told by Dantzig himself) and the ensuing development of the field of oper-

ations research. The broader field of mathematical programming generalizes