Generalized allocation problem in building design part I: formulation

Abstract

Problems of efficient internal design can often be formulated as a constrained optimization programme with (at least some) discrete variables and a linear, or quadratic, objective function, depending on the nature of the underlying measure. In this first part (of a two-part paper) we present detailed considerations of the problem with a linear objective function, offering five mathematical programming formulations. In the context of one small and one medium-sized example we examine the ‘scale’ of these formulations and comment on their practicability. A few remarks are offered on the quadratic problem. Implementation details of some of the formulations are the subject of another paper.