The orthodox way of tile printing results in mulish production. To tame this, digital inkjet printing technology was imposed. In this article, a mathematical prototype is designed exclusively for the tile printing wing. The various plants coming under printing are correlated to the proposed prototype. The article throws light on the functioning of the prototype. The prototype turns up subservient to bulk service queue models with two types of vacations. The prototype is resolved under the supplementary variable technique. The prototype with peculiar conditions is proved to be the existing model. Anticipated line distance, awaited active duration, awaited standby time, and expected idle period were computed. Thus, the total average cost is acquired for diverse vacation values. The main intention of the pattern is to downside the total average cost.

The primary intention of this article is to study numerical solutions of differential equation with interval Type-2 Fuzzy Number (T2FN) as the initial condition. The differential equation is first redrafted in the parametric form; then, it is restructured into three systems of linear differential equations. Each system includes two concurrent linear differential equations with respective initial conditions. The classical 4 th order Runge-Kutta method is developed for the above derived systems. The ability of the method is corroborated by illustrating problems.

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