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Estimating market demand for a product is essential to business growth; yet, it is exceedingly difficult. This article considers various demand patterns for a single product in a three-echelon supply chain where a single supplier, a single manufacturer and a single retailer are involved. A robust inspection process is considered at the manufacturer's end to deliver a high-quality product to the retailer. The backorder strategy is incorporated to enhance the company's trust and reputation among consumers. The major idea of this research is to analyze the nature of the product's demand in three distinct situations, as well as the benefits of implementing the backorder technique. Three cases are analyzed on the basis of different demand patterns, in which the demand rate is assumed to be constant (i.e., deterministic), price-dependent and fuzzy in the first, second and third cases, respectively. To verify this model, numerical examples are tested independently with identical information for each case and owing to the complexity of the objective function; a genetic algorithm is employed to obtain the best solution. Finally, sensitivity analysis, managerial insights and conclusions, including the future directions, are provided. [ABSTRACT FROM AUTHOR]