We consider a problem where a firm produces a variety of fresh products to supply two markets: an export market and a local market. A public transportation service is utilized to deliver the products to the export market, which is cheap, but its schedule is often disrupted severely. Each time this happens, the firm faces the following questions. (i) For a product that has been finished and is waiting for delivery to the export market, should it continue to wait, at an increasing risk of decay, and when should the waiting be terminated and the product be put to the local market? (ii) For a product that has not been finished, should its processing be postponed, so as to reduce the loss from decay after its completion? (iii) What is the best sequence to process the remaining products, according to the information available? We develop, in this study, a model to address these and other related questions. We find optimal policies that minimize the total expected loss in both the make-to-order and make-to-stock production systems, respectively. For each finished product, we reveal relationships among the desirable waiting time, the price at the local market, and the decaying cost. For unfinished products, we find the optimal start times and processing sequence. Numerical experiments are also conducted to evaluate the optimal policies.