Abstract
ABSTRACT Advance payment for replenishment and the lifetime of an item are the most vital issues in the business sector. With the consideration of these issues, the formulation of a non-deterministic inventory model in the interval environment is of great importance. In this work, two different non-deterministic inventory models are formulated along with a variable holding cost, variable demand, and advertisement frequency under an advance payment policy in the interval environment. In the first inventory model, a no-shortage situation is discussed, whereas in the second model, a stock-out scenario is adopted by partially backordering during modelling. The modelling framework for both problems is accomplished based on interval differential equations. The interval optimization problems related to both models are obtained utilizing parametric approach and interval mathematics. Then, using interval order relations and different types of quantum particle swarm optimization, both interval optimization problems are solved. By means of two examples, the authentication of both models is examined and the benefits of the proposed approach are demonstrated. The impact of deviations of various parameters on optimality is studied graphically through the performance of sensitivity analyses, and the work is concluded by providing potential management insights and future scopes.
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