A time-shared machine repair problem with mixed spares under N-policy

Subject Areas : Mathematical Optimization

Madhu  Jain ¹ (Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247 667, Uttarakhand, India)
Chandra  Shekhar ² (Department of Mathematics, Birla Institute of Technology and Science, Pilani, 333 031, Rajasthan, India)
Shalini  Shukla ³ (Department of Mathematics, D.A.V. (PG) College, Dehra Dun, 248 001, Uttarakhand, India)

Received: 2020-10-04 Accepted : 2020-10-04 Published : 2016-06-01

Keywords: Markov chain . Machine repair . Mixed spares . Time sharing . Threshold policy . Additional repairman . Queue length,

Abstract :

The present investigation deals with a machine repair problem consisting of cold and warm standby machines. The machines are subject to breakdown and are repaired by the permanent repairman operating under N-policy. There is provision of one additional removable repairman who is called upon when the work load of failed machines crosses a certain threshold level and is removed as soon as the work load again ceases to that level. Both repairmen recover the failed machines by following the time sharing concept which means that the repairmen share their repair job simultaneously among all the failed machines that have joined the system for repair. Markovian model has been developed by considering the queue dependent rates and solved analytically using the recursive technique. Various performance indices are derived which are further used to obtain the cost function. By taking illustration, numerical simulation and sensitivity analysis have been provided.