The single row layout problem (SRLP) is a specially structured instance of the classical facility layout problem, especially used in flexible manufacturing systems. The SRLP consists of finding the most efficient arrangement of a given number of machines along one side of the material handling path with the purpose of minimising the total weighted sum of distances among all machine pairs. To reflect real manufacturing situations, a minimum space (so-called clearances) between machines may be required by observing technological constraints, safety considerations and regulations. This thesis intends to outline the different concepts of clearances used in literature and analyse their effects on modelling and solution approaches for the SRLP. In particular the special characteristics of sequence-dependent, asymmetric clearances are discussed and finally extended to large size clearances (machine-spanning clearances). For this, adjusted and novel model formulations and solution approaches are presented. Furthermore, a comprehensive survey of articles published in this research area since 2000 is provided which identify recent developments and emerging trends in SRLP.

The single-row facility layout problem (SRFLP) is concerned with finding the optimal linear placement of n departments with different lengths in a straight line. It is typically achieved by minimizing the cost associated with the interactions between the departments. The semidefinite programming (SDP) relaxation model that incorporates cutting planes proposed recently by Anjos, Kennings, and Vannelli (AKV) was considered a breakthrough in the field. This thesis presents a new SDP model AKV' and compares the two relaxations. The AKV' is largely based on the previous model, but it reduces the number of linear constraints from O(n³) to O(n²). Therefore, it reduces the computing time at the expense of a slightly weaker lower bound. However, AKV' is observed to pay off as the instance size increases. By examining the gap for both the AKV and AKV' relaxations, we notice that both relaxations generate very small gaps at the root node, which demonstrates the effectiveness of the relaxations. Six different strategies are presented to separate the cutting planes for the medium-sized SRFLP. In combination with the two SDP relaxations, we compare the six strategies using three instances of different characteristics. An overall best strategy is deduced from the computational results, but the best choice of relaxations and the best number of cuts added at each iteration changes depending on the characteristics of the instances. Two new cutting plane strategies are proposed for large instances. This allows the solution to optimality of new instances with 36 departments, which is higher than previously published results in literature. We also briefly point out how the computing time can vary greatly between different sets of data of the same size due to the characteristics of the department lengths.

The single-row facility layout problem (SRFLP) is concerned with finding the optimal linear placement of n departments with different lengths in a straight line. It is typically achieved by minimizing the cost associated with the interactions between the departments. The semidefinite programming (SDP) relaxation model that incorporates cutting planes proposed recently by Anjos, Kennings, and Vannelli (AKV) was considered a breakthrough in the field. This thesis presents a new SDP model AKV' and compares the two relaxations. The AKV' is largely based on the previous model, but it reduces the number of linear constraints from O(n³) to O(n²). Therefore, it reduces the computing time at the expense of a slightly weaker lower bound. However, AKV' is observed to pay off as the instance size increases. By examining the gap for both the AKV and AKV' relaxations, we notice that both relaxations generate very small gaps at the root node, which demonstrates the effectiveness of the relaxations. Six different strategies are presented to separate the cutting planes for the medium-sized SRFLP. In combination with the two SDP relaxations, we compare the six strategies using three instances of different characteristics. An overall best strategy is deduced from the computational results, but the best choice of relaxations and the best number of cuts added at each iteration changes depending on the characteristics of the instances. Two new cutting plane strategies are proposed for large instances. This allows the solution to optimality of new instances with 36 departments, which is higher than previously published results in literature. We also briefly point out how the computing time can vary greatly between different sets of data of the same size due to the characteristics of the department lengths.

The present work studies the relationship between target and sidewall surfaces of a multirow, narrow impingement channel at various jet heights with one impingement hole per row. Temperature sensitive paint and constant flux heaters are used to gather heat transfer data on the target and side walls. Jet-to-target distance is set to 1, 2, 3, 5, 7 and 9 jet diameters. The channel width is 4 jet diameters and the jet stream wise spacing is 5 jet diameters. All cases were run at Reynolds numbers ranging from 5,000 to 30,000. Pressure data is also gathered and used to calculate the channel mass flux profiles, used to better understand the flow characteristics of the impingement channel. While target plate heat transfer profiles have been thoroughly studied in the literature, side wall data has only recently begun to be studied. The present work shows the significant impact the side walls provide to the overall heat transfer capabilities of the impingement channel. It was shown that the side walls provide a significant amount of heat transfer to the channel. A channel height of three diameters was found to be the optimum height in order to achieve the largest heat transfer rates out of all channels.

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