2
1 Motivation
of view, it is possible to determine an “optimal solution” based solely on the
walking distances and traffic densities. Other possible objectives include reducing
congestion, facilitating communication, and increasing safety (Heragu 2008).
An assignment is said to be optimal if it provides a total distance travelled that
is no greater than the total distance travelled for the other feasible assignments,
i.e., assignments that satisfy all the requirements of area and shape. The purpose
of a facility layout algorithm is to compute such an optimal layout for a given
instance of the problem or, alternatively, to provide a competitive layout, ideally
with a guarantee that it is close to optimality.
In this book we limit our attention to approaches based on mathematical
optimization. We consider both exact methods and heuristics (sometimes called
matheuristics) that make use of mathematical optimization approximations and/or
relaxations. Specifically, we consider models based on mixed-integer linear
optimization (MILO), often referred to as mixed-integer programming or MIP,
semidefinite optimization (SDO), also called semidefinite programming or SDP, and
nonlinear optimization, also called nonlinear programming or NLP. We assume that
the reader is familiar with the basics of building mathematical optimization models,
as presented, for example, in Williams (2013).
The use of mathematical optimization models for layout dates back at least to the
seminal paper of Koopmans and Beckmann (1957), which introduced the famous
quadratic assignment problem (see Sect. 5.1). Research into the application of these
models to layout problems has thus been carried out for more than 60 years and
continues on both the theoretical and applied fronts.
References
Heragu SS (2008) Facilities design. CRC Press
Koopmans TC, Beckmann M (1957) Assignment problems and the location of economic activities.
Econometrica 25(1):53–76
Simmons DM (1969) One-dimensional space-allocation algorithm: An ordering algorithm. Operations Research 17(5):812–826
Williams HP (2013) Model building in mathematical programming. Wiley
1 Motivation
of view, it is possible to determine an “optimal solution” based solely on the
walking distances and traffic densities. Other possible objectives include reducing
congestion, facilitating communication, and increasing safety (Heragu 2008).
An assignment is said to be optimal if it provides a total distance travelled that
is no greater than the total distance travelled for the other feasible assignments,
i.e., assignments that satisfy all the requirements of area and shape. The purpose
of a facility layout algorithm is to compute such an optimal layout for a given
instance of the problem or, alternatively, to provide a competitive layout, ideally
with a guarantee that it is close to optimality.
In this book we limit our attention to approaches based on mathematical
optimization. We consider both exact methods and heuristics (sometimes called
matheuristics) that make use of mathematical optimization approximations and/or
relaxations. Specifically, we consider models based on mixed-integer linear
optimization (MILO), often referred to as mixed-integer programming or MIP,
semidefinite optimization (SDO), also called semidefinite programming or SDP, and
nonlinear optimization, also called nonlinear programming or NLP. We assume that
the reader is familiar with the basics of building mathematical optimization models,
as presented, for example, in Williams (2013).
The use of mathematical optimization models for layout dates back at least to the
seminal paper of Koopmans and Beckmann (1957), which introduced the famous
quadratic assignment problem (see Sect. 5.1). Research into the application of these
models to layout problems has thus been carried out for more than 60 years and
continues on both the theoretical and applied fronts.
References
Heragu SS (2008) Facilities design. CRC Press
Koopmans TC, Beckmann M (1957) Assignment problems and the location of economic activities.
Econometrica 25(1):53–76
Simmons DM (1969) One-dimensional space-allocation algorithm: An ordering algorithm. Operations Research 17(5):812–826
Williams HP (2013) Model building in mathematical programming. Wiley