Unlike the great importance of differences between market types, the investigation of them is almost neglected in the fresh agricultural product supply chain (FAPSC). In this respect, this study aims to find proper answers for two questions, which FAPSC’s members face: 1) which market (daily or bourse) is economical for trading items? 2) How to adopt a strategy (decentralized or coordinated) to control the waste by FAPSC members while the members’ profit remains at a satisfactory level? Accordingly, the daily and bourse markets under a farmer-retailer Stackelberg game are studied in the first model. Afterward, a mathematical coordination model using a novel two-part tariff contract is developed between farmer and retailer in the market, which has been optimally determined in the first model. A data set from a real-world application is examined to validate the proposed models. The results demonstrate that the profit of both the farmer and retailer under the bourse market is more than the daily market. Moreover, the coordinated strategy increases the retailer’s profit as well as its order quantity, the farmer’s freshness-keeping investment as well as its profit, and the entire FAPSC’s profit compared to the decentralized strategy. The quantity of wasted products and the retail price under the coordinated strategy is lower than that under the decentralized strategy. Accordingly, related decision-makers are advised to make the two-part tariff contract under a coordinated strategy to reduce wasted products without posing a risk to their profit. The sensitivity analysis implies that by increasing the demand uncertainty and shipping cost, the coordinated strategy is more efficient in improving the FAPSC profit and controlling the quantity waste rather than the decentralized strategy.