Time value of delays in unreliable production systems with mixed uncertainties of fuzziness and randomness

This paper proposes a parametric programming approach to address the notion of the time value of delays in the presence of mixed (random and fuzzy) uncertainties that result from unreliable systems. To consider different types of delay time values, the system states are appropriately and carefully identified and defined, and a cost-based fuzzy decision model that incorporates several unreliability factors is constructed. Then, the proposed model is transformed into a pair of nonlinear programs parameterized by the possibility level α to identify the lower and upper bounds on the minimal total cost per unit time at α and thus construct the membership function. To provide analytical expressions, a special case with analytical results is also presented. In contrast to existing studies, the results derived from the proposed solution procedure conserve the fuzziness of the input information, representing a significant difference from the crisp results obtained using approaches based on probability theory. The results indicate that the proposed approach can provide more precise information to managers and improve decision-making in practical system design.