Multiobjective undiscounted Markov renewal program and its application to a tool replacement problem in an FMS

This paper deals with a multiobjective undiscounted Markov renewal program with expectation and variance criteria. The problem is formulated as a multiobjective nonlinear programming problem. An algorithm based on the satisficing trade-off method is proposed for finding a stationary satisfactory Markov policy. In the proposed algorithm, a decision-maker need not have high degree of judgment and is easy to take the balance of expectation and variance criteria. The tool replacement problem for a machining center (MC) in a flexible manufacturing system (FMS) is one of the basic problems in a tool management system. The proposed algorithm is applied to the tool replacement problem with expectation and variance criteria. Numerical examples show that the algorithm finds stationary satisfactory Markov policies in a few iterations and that the variance can be considerably reduced with a small sacrifice of the expectation.