Detection model for a suitable waiting list with maximising the discount effort reward search under the quality control process

The economic benefits of the company are increased by improving the quality of its services. At the same time, the customers aimed to get the service with minimum cost. In this paper, we provide a detection model which satisfies these purposes. The customer chooses the suitable engineering consultancy company from independent companies. Each company has a Markovian waiting list of customers with size N. The customer arrives to the waiting list with Poisson process and its service time has an exponential distribution. Under the quality control process and some concepts like balking and reneging of each waiting list, we provide the optimal decision to consider the suitable company. We consider the searching effort is bounded by a random variable with a known probability distribution. After applying the discount effort reward search function, we solve a difficult stochastic optimisation problem to get the maximum values of the service rate, discount effort reward and the minimum value of the detection cost. A case study is provided to get these optimal values and the optimum performance measures which give the optimal expected profit.