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This paper presents a joint economic lot-sizing problem under stochastic demand for a vendor-buyer system by synchronizing ordering and production cycles. The buyer manages its inventory periodically using a periodic review policy. The average demand and the buyer's ordering cost are assumed to be fuzzy. The vendor's production process is imperfect and the buyer's inspection process is also imperfect. The vendor has opportunity to make an investment to reduce the setup cost. Since it is often difficult to calculate the shortage cost in inventory model, a service-level constraint corresponding to the buyer is considered in the mathematical model. The objective of the model is to simultaneously optimize the review period, production rate, setup cost, and the number of deliveries, such that minimize the joint total cost. We suggest an iterative procedure to find the optimal values of decision variables. A numerical example and a sensitivity analysis are given to show the application of the model and to investigate the effect of the changes in key parameters on the behavior of the proposed model.

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