Chemical plant layout via graph partitioning

Srinivasan Jayakumar, Purdue University

Abstract

A graph theoretic decomposition scheme is proposed for the determination of the optimal layout of equipment in single and multifloor chemical plants, given a network of processing units, their size parameters, species flows, and equipment location restrictions. The layout problem is decomposed into two steps--segregation of units into groups and location of units in each group separately. Equipment segregation is a bottleneck in this scheme since it treats a much larger problem than the second, which involves solving several smaller problems. Consequently the bulk of the work is focussed on this problem. For the second step, a graph planarity based analysis is described and a solution scheme proposed. Grouping of units on a single floor arises due to the occurrence of corridors, aisles or other boundaries. A heuristic procedure of pairwise interchanges with the objective of minimizing inter-unit flow related costs, utilizing gain matrices and one-step look-ahead schemes is developed to solve the graph partitioning problem for single floor equipment partitioning. This procedure gives globally optimal solutions in attractive computation times to all examples studied for which optimal solutions were obtainable by exhaustive enumeration. Problems with up to hundred units have been solved. In multifloor structures, direction (upward, downward, horizontal) dependence of flow costs is incorporated in the heuristic procedure by introducing three cost values for every inter-unit flow. Results for problems equally distributing units on floors without consideration of unit sizes, are likewise encouraging. In addition, an Integer Non-Linear Program (scINLP) formulation of this problem is exactly linearized to a Mixed Integer Linear Program. Continuous relaxations of this problem are solved by Lagrangean relaxation and subgradient optimization to yield tight lower bounds. An scINLP formulation for the problem of equipment segregation on multiple floors with realistic property constraints such as space availability and load bearing capacity of each floor is linearized by the same technique. The lower bounding scheme is modified appropriately and is shown also to yield tight bounds. Exact solutions obtained by a depth-first branch-and-bound scheme further illustrate the tightness of the linearization by generating a very small number of nodes.

Degree

Ph.D.

Advisors

Reklaitis, Purdue University.

Subject Area

Chemical engineering

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