A Dynamic Programming Approach to Solve the Facility Layout Problem for Reconfigurable Manufacturing

Preparing manufacturing systems to deal with disruptions caused by unexpected factors such as COVID-19 is critical to remain in today’s competitive market. Reconfigurable manufacturing systems (RMS) which are characterized by being rapid and cost-effective in response to market changes, are a good alternative to cope with such unexpected events. From the layout point of view, in an RMS, the layout of facilities needs to be changeable and able to be redesigned easily. Dynamic facility layout problem (DFLP) is a good approach to develop layouts that are capable to be changed and redesigned. Dynamic programming (DP) has been known as one of the effective methods to deal with DFLP. To optimize DFLP by DP, the set of possible layouts for every single period which is called the state-space is given to DP and the best multi-period layout is found. Since the number of possible layouts increases rapidly with the increase in the number of facilities, considering all these layouts encounters two major difficulties, memory requirements and computer time requirements. This paper proposes a method that has two main phases. In the first phase, the set of layouts to be considered in each period are determined using a heuristic approach. These layouts are the states in the DP approach where the periods constituted the decomposition stages. The recursive formulation of DP is solved in the second phase using a hybridized metaheuristic approach. The proposed approach restricts the DP to a good subset of the state-space. A genetic algorithm is applied to search for the best subset of layouts where each chromosome represents one subset of layouts. This subset is given to DP to be solved and the result is considered as the fitness of the chromosome. By the evolution of the chromosomes, the best subset of layouts that leads to the best multi-period layout plan is found. The proposed approach is evaluated against DP benchmarks in the literature. Computational results show that the proposed approach is able to provide more efficient solutions, especially for large-sized problems.

A Hybrid Method Integrating a Discrete Differential Evolution Algorithm with Tabu Search Algorithm for the Quadratic Assignment Problem: A New Approach for Locating Hospital Departments

The facility layout problem (FLP) is a very important class of NP-hard problems in operations research that deals with the optimal assignment of facilities to minimize transportation costs. The quadratic assignment problem (QAP) can model the FLP effectively. One of the FLPs is the hospital facility layout problem that aims to place comprehensive clinics, laboratories, and radiology units within predefined boundaries in a way that minimizes the cost of movement of patients and healthcare personnel. We are going to develop a hybrid method based on discrete differential evolution (DDE) algorithm for solving the QAP. In the existing DDE algorithms, certain issues such as premature convergence, stagnation, and exploitation mechanism have not been properly addressed. In this study, we first aim to discover the issues that make the current problem worse and to identify the best solution to the problem, and then we propose to develop a hybrid algorithm (HDDETS) by combining the DDE and tabu search (TS) algorithms to enhance the exploitation mechanism in the DDE algorithm. Then, the performance of the proposed HDDETS algorithm is evaluated by implementing on the benchmark instances from the QAPLIB website and by comparing with DDE and TS algorithms on the benchmark instances. It is found that the HDDETS algorithm has better performance than both the DDE and TS algorithms where the HDDETS has obtained 42 optimal and best-known solutions from 56 instances, while the DDE and TS algorithms have obtained 15 and 18 optimal and best-known solutions out of 56 instances, respectively. Finally, we propose to apply the proposed algorithm to find the optimal distributions of the advisory clinics inside the Azadi Hospital in Iraq that minimizes the total travel distance for patients when they move among these clinics. Our application shows that the proposed algorithm could find the best distribution of the hospital’s rooms, which are modeled as a QAP, with reduced total distance traveled by the patients.

Algorithmenbasierte Fabrikplanung

Rechnergestützte Optimierungsverfahren unterstützen Entscheidungen der innerbetrieblichen Layoutplanung. Beim Facility Layout Problem (FLP) wird die bestmögliche Position von Maschinen und Anlagen in einem Fabrikgelände bestimmt. In diesem Beitrag wird gezeigt, wie die Lösung des FLP dazu beitragen kann, das Fabriklayout der SMC Deutschland GmbH für eine geplante Erweiterung zu optimieren. Zum Einsatz kamen dabei genetische Algorithmen. Die Lösung des FLP wurde mit dem aktuellen Planungsstand im Unternehmen verglichen. Dabei wurde festgestellt, dass bei Anwendung des FLP bis zu 14 Prozent bessere Zielfunktionswerte erreicht werden.