multi objective ordering planning for multi buyers deteriorating items

this paper is a research on the ordering planning of a supply chain with one supplier, multi buyer and multi deteriorating items. items have fixed life time and expire dates. the ordering period is taken as variable and must be computed the proposed models. the problem is studied via two different approaches the first is the joint replenishment, based on the hwang and chew's model [3] and with some new assumptions. in the case that the life time is less than the ordering period, the cost of deterioration is considered in the model. the second approach is cooperative planning. in this approach transportation cost, inventory and shortage costs are considered in the proposed model. the models are studied for both single and multi period cases. the purpose of the models is an investigation about the influence of expire date on ordering periods' lengths. the proposed models can compute these lengths and also the amounts of orders.