For a single item, a production inventory model is created. Demand is affected by the amount of inventory on hand and the cost of production. Shortages are permitted and completely booked. The period between making a choice and starting production is known as "preparation time," and it is expected to be crisp or imprecise. The cost of setup is determined by the amount of time it takes to prepare. Using closest interval approximation, the fuzzy preparation time is reduced to a crisp interval preparation time, and the reduced problem is turned to a multi-objective optimization problem using interval arithmetic. For a single- objective crisp model, a mathematical analysis was performed (Model-I). Both crisp (Model- I) and fuzzy (Model-II) models have been numerically shown. Model-I is solved using the generalised reduced gradient approach, whereas Model-II is done using the Global Criteria Method. Some Model-I parameters have been subjected to sensitivity assessments.