In real-world markets, demand is influenced by various parameters. Many researchers have recently been interested in integrated production and marketing planning strategies in inventory models where demand is dependent on a variety of parameters, such as price and/or marketing expenditure. Quite possibly of the main element that impacts request in genuine business sectors is the nature of administrations gave to clients of an item, however stock models have not considered this. Conversely, genuine stock frameworks' expense boundaries and different boundaries, like value, promoting, and administration flexibility to request, are dubious and questionable. Consequently, the idea of fuzziness can be used to control this uncertainty. This paper proposes a novel fuzzy inventory model for profit maximization in the face of shortages. When calculating demand as a power function, all factors like price, marketing, and service costs are taken into consideration. Unit cost is also calculated using order quantity as a power function. Due to the fuzziness of the proposed model's operating environment and expected outcomes, a fuzzy decision must be made to satisfy the decision criteria. Geometric programming and fuzzy optimization are used to formulate and solve the proposed model in order to approximate the results' membership functions. Following the presentation of a numerical example of the model, a case study is provided to evaluate and verify the results of the model.
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