Mathematical analysis on production control in manufacturing units under disaster and repair with compulsory vacation

The single server queuing system with optional second service and compulsory vacation that is subjected to disaster is considered in which an arriving customer is provided with the first essential service. The study focuses on optimizing production schedules to minimize cost. An arriving customer can request a second optional service with some probability. After the completion of services, the server takes a compulsory vacation. Disaster occurs independently only when the server is busy rendering the first essential service, in which case it removes all the customers from the system. The repair period is initiated, followed by the disaster. The system is analysed using the supplementary variable technique to establish the probability generating functions of a queue size and various performance measures of the model. The special cases and numerical results of the prescribed model are established. These findings provide a thoughtful insights for a effective production management practices offering guidance for manufacturing decision makers under adverse conditions.