This paper studies the influence of different picking policies in a stock of perishable items on the quantity of waste, the degree of freshness of the stored products and the profit. We consider a push-pull supply chain with three echelons (an agricultural producer, a manufacturer and a retailer), in which the quantity ordered from the upstream supplier is determined using a forecast based on a simple exponential smoothing of historical sales data of perishable products. To meet a stochastic demand that is symmetrically distributed around a given average, the stock of this perishable product must be sufficient without exceeding the expiration dates to avoid any waste. If the demand exceeds the available stocks, the manufacturer can resort to external suppliers on a spot market to deliver the products very quickly. We developed a simulation model to compare three picking policies (FIFO: first-in-first-out, LIFO: last-in-first-out and RDM: random picking policy) and their performance in terms of the average age of stored goods, the quantity of waste and the profit. A counterintuitive result showed that under certain conditions, the LIFO policy led to better performance than the FIFO policy, a result we proved mathematically. We then simulated different scenarios by varying product depreciation and margin rates. When margins decrease linearly with product age, the FIFO policy is the least competitive. In the case of normally distributed demand, LIFO is the most efficient picking policy, whereas in the case of uniform demand, the RDM policy performs better. We also studied the sensitivity of the model to the parameters of the demand function and the smoothing coefficients used to forecast the quantities of perishable products to be supplied. Finally, we applied our model to some specific features of the poultry and meat industry and simulated a policy of preventive production reduction.