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In recent decades, changes in people’s lifestyles and occupations have led to new food consumption patterns around the world, with a notable growth in the demand for ready meals and meat products. Accordingly, the food industry has tried to transform the global food culture by promoting its more profitable products to become able to set a higher price for meat. Considering the short lifetime of products in perishable food supply chains, inventory decisions are considered crucial. In addition, the demand for perishable food products is greatly affected by their freshness. In this paper, we develop a multi-objective mixed-integer non-linear programming model for a four-level sustainable supply chain (SC) of a perishable product with price-dependent demand and deterioration rates. The SC consists of suppliers, a production center (PC), distribution centers (DCs), and retailers. We aim to ascertain the optimal pricing policy and cycle length to maximize profit, achieve specific social objectives, and minimize the total cost and adverse environmental impacts. The proposed model determines the deterioration rate of each product according to its expiration date, the optimal location of supply-side facilities, and the flow rate between the facilities based on the selected mode of delivery. The products are delivered to the retailers by a mechanized transportation system either directly from the PC or indirectly through the DCs. Finally, an actual case study is provided to demonstrate the applicability of the model and our theoretical results under real-world conditions. We solve the case study by a preemptive fuzzy goal programming method and perform several sensitivity analyses on the results. By performing simultaneous sensitivity analyses on the demand and expiration dates, the optimal values of the problem’s parameters are determined. The optimal values help decision-makers make optimal decisions regarding the selling price of products and replenishment times. The model is applicable to supply chains of any perishable items with expiration dates.