Modelling of an imprecise production inventory problem with interval-valued demand and semi-Type-2 interval-valued inventory costs: Its optimality via parametric optimization technique

In real-life production inventory systems, decision-makers often struggle to estimate demand rates, production rates, and inventory costs because of market volatility, limited historical data, and unstable economic conditions. While traditional interval-based models have some usefulness, they do not properly address uncertainty in cost estimates. This study proposes a new production inventory model that includes interval-valued production rates, interval-valued demand that depends on both time and selling price, and semi-Type-2 interval-valued inventory costs for ordering, holding, and production. The semi-Type-2 interval method keeps one boundary fixed and lets the other vary, more accurately reflecting cost uncertainties caused by inflation, supply chain disruptions, and market fluctuations. The model uses interval differential equations and parametric interval mathematics. To study the optimal policy of the proposed model, we derive the parametric form of the semi-Type-2 intervals and an optimization technique for the semi-Type-2 interval-valued average profit function. Three numerical examples show how to determine the optimal policies. A sensitivity analysis is performed to show the effects of known system parameters on the optimal policy. The numerical results show that allowing the flexible upper bound of cost estimates can improve decision-making and increase profitability in production inventory systems.