Designing Difficult Office Space Allocation Problem Instances with Mathematical Programming
Office space allocation (OSA) refers to the assignment of room space to a set of entities (people, machines, roles, etc.), with the goal of optimising the space utilisation while satisfying a set of additional constraints. In this paper, a mathematical programming approach is developed to model and generate test instances for this difficult and important combinatorial optimisation problem. Systematic experimentation is then carried out to study the difficulty of the generated test instances when the parameters for adjusting space misuse (overuse and underuse) and constraint violations are subject to variation. The results show that the difficulty of solving OSA problem instances can be greatly affected by the value of these parameters.
A statistical model is established to estimate the effects of the geometric and nongeometric errors on the quality of the operation for various operating speeds. Furthermore, a stochasitc optimization problem is formulated to obtain the optimal operating speed for a given accuracy in the robotic operations. To demonstrate this approach, the experiments on a PUMA 560 robot are used as an example.