A mathematical framework for estimating prototyping cost considering transition of quality states under Markovian setting

PurposeThis research aims to aid product development managers to estimate the expected cost associated with the development of cost-intensive physical prototypes considering transitions associated with pertinent states of quality of the prototype and corresponding decision policies under the Markovian setting.Design/methodology/approachThe authors evolve two types of optimization-based mathematical models under both deterministic and randomized policies. Under the deterministic policy, the product development managers take certain decisions such as “Do nothing,” “Overhaul,” or “Replace” corresponding to different quality states of prototype such as “Good as new,” “Functional with minor deterioration,” “Functional with major deterioration” and “Non-functional.” Under the randomized policy, the product development managers ascertain the probability distribution associated with these decisions corresponding to various states of quality. In both types of mathematical models, i.e. related to deterministic and randomized settings, minimization of the expected cost of the prototype remains the objective function.FindingsEmploying an illustrative case of the operator cabin from the construction equipment domain, the authors ascertain that randomized policy provides us with better decision interventions such that the expected cost of the prototype remains lower than that associated with the deterministic policy. The authors also ascertain the steady-state probabilities associated with a prototype remaining in a particular quality state. These findings have implications for product development budget, time to market, product quality, etc.Originality/valueThe authors’ work contributes toward the development of optimization-driven mathematical models that can encapsulate the nuances related to the uncertainty of transition of quality states of a prototype, decision policies at each quality state of the prototype while considering such facets for all constituent subsystems of the prototype. As opposed to a typical prescriptive study, their study captures the inherent uncertainties associated with states of quality in the context of prototype testing, etc.