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
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

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