Abstract
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.
Highlights
During the last decades, the research concerning with joint inventory problem has received a great deal of attention
We develop a single-vendor–single-buyer model with stochastic demand, imperfect production process and periodic review policy
The above literature review shows that a stochastic vendor–buyer inventory model has been extensively discussed in the past, but none has analyzed the impact of incorporating fuzzy annual demand, fuzzy ordering cost, imperfect production process, inspection errors, and adjustable production rate simultaneously
Summary
The research concerning with joint inventory problem has received a great deal of attention. The essence of the research was to coordinate and collaborate the parties in supply chain system by synchronizing production and inventory decisions in order to reduce the total cost. Lin (2010) was the first who considered a stochastic periodic review vendor–buyer model under imperfect production process and backorder price discount. A few researchers, including Jha and Shanker (2009, 2013) have used a service-level constraint to replace the shortage cost which implies that the shortage level per cycle is bounded These models assumed that the production process is always perfect. We develop a single-vendor–single-buyer model with stochastic demand, imperfect production process and periodic review policy. We study the impact of the changes in service-level constraint on model’s behavior, especially when there are imperfect items and inspection errors. A numerical example and a sensitivity analysis are presented to show the application of the model and to study the changes in key parameters on model’s behavior
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