عنوان مقاله [English]
Recently, different inventory models have been widely used in production and sales. However, some assumptions of these models do not provide the possibility of their use in practice. Therefore, it seems necessary to put aside these assumptions and expand the existing models. The most popular of these models is the classical economic order quantity (EOQ) that appears in every basic textbook covering inventory management. A key assumption of the basic EOQ model is that the demand is certain, so shortage is not permitted. While, in the real world, usually, demand is probabilistic, so, there is the possibility of encountering shortages. In some real life situations, there is a part of demand that cannot be satisfied from the current inventory, leaving the system in stock out. In these systems, two situations are mainly considered: all customers wait until the arrival of the next order (complete back order case) or all customers leave the system (lost sales case). However, in practical, some customers are able to wait for the next order to satisfy their demands during the stock out period, while others do not wish to, or cannot wait, and they have to fill their demands from other sources. This situation is modeled by consideration of partial backlogging in the formulation of the mathematical model. Therefore, In general, three approaches, including backorder, lost sales and partial backlogging, are considered when faced with shortage. In backorder
models, the answer to all demands is commitment, in lost sales, there is no commitment to demand, and, in partial backlogging, a portion of the demand is backlogged. In partial backlogging, some customers are willing to wait for delivery, others are not. A common characteristic of this model is the assumption that the percentage of orders arriving during the shortage period that will be backordered is exogenously determined. Either these customers will cancel their orders or the supplier will have to fill them within the normal delivery time by using more expensive supply methods. Another major problem in traditional inventory models is restrictions in real world constraints, such as budget constraint, space constraint, number of orders constraint, service level
constraint and etc. This applies more particularly to shortage models. Work on inventory control models, especially continuous models, pays little attention to constraints.
In this survey, a multi product continuous review inventory model with capacity warehouse constraints, budget, and minimum service level in partial backlogging, in order to obtain the quantity order and reorder point to achieve minimum total annual cost, is minimized. Lagrangian relaxation and a hybrid heuristic algorithm based on Hadly-Whithin for small size problems, and a simulated annealing (SA) algorithm for large scale problems is used. Since the release Lagrange method is an exact method, to evaluate solutions obtained from the simulated annealing algorithm can be used. Comparison of the results obtained from the Lagrange method and the SA algorithm shows that the SA algorithm is credible and has suitable efficiency.