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In reality, the machines may interrupt because of the nature of deterioration of the machines. Thus, it is inevitable to perform maintenance alongside production planning. The preventive maintenance is a schedule of strategic operations that are performed prior to the failure occurring, to retain the system operating at the preferred level of consistency. Thus, preventive maintenance plays a significant role in flow shop scheduling models. With its practical significance, this study addresses a practical three-machine n jobs flow shop-scheduling problem (FSSP) in which machine specific preventive maintenance, where each machine is given with a maintenance schedule is considered. In addition, a practical ordered precedence constraint in which some set of jobs has to process in the specified order irrespective of their processing times is also considered. The problem’s goal is to establish the optimal job sequence and preventive maintenance such that the overall cost of tardiness and preventive maintenance is as minimum as possible. An efficient heuristic approach is designed to tackle the present model, resulting in total cost savings. A comparative analysis is not conducted due to absence of studies on the current problem in the literature. However, Computational experiments are carried out on some test instances and results are reported. The reported results may be useful for future studies.

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Abstract. The k-cardinality degree constrained clustered minimum spanning tree problem (k-DCCMST) aims to determine a k-node (out of n nodes) spanning tree of minimum weight defined on a complete weighted undirected graph, where the node set is partitioned into set of clusters such that except the root node, the degree of other nodes in the resultant spanning tree does not exceed the predefined degree limit. The k-DCCMST model has significant applications in the context of designing of networks and is then formulated as a zero-one integer linear program. To solve this problem optimally, an exact Lexi-search algorithm (LSA) is developed. The developed LSA is subjected in Matlab, tested on some benchmark as well as randomly generated test instances and computational results are reported. Numerical experimental results demonstrate the efficiency of proposed LSA on dense graphs.

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