In this paper, an inventory model for two-stage supply chain is investigated. A supply chain with single vendor and single buyer is considered. We assume that shortage as a backorder is allowed for the buyer and the vendor makes the production set up every time the buyer places an order and supplies on a LOT for LOT basis. With these assumptions, the joint economic LOT size model is introduced and the minimum joint total relevant cost and optimal order quantity and optimal shortage quantity are obtained for both the buyer and the vendor at the same time. Numerical example is given and then Sensitivity analysis is performed to study the effects of changes in the parameters on optimum joint total relevant cost and optimal order quantity and optimal shortage quantity.

In this paper, a two-stage stochastic capacitated LOT-sizing problem with random demand, and service level constraints under static and static-dynamic uncertainty strategies is introduced. A static strategy determines the setup period and LOT sizing at the beginning of planning period, whereas a static-dynamic strategy allows the LOT size to be adjusted during the planning period. A new model formulation of the demand differential adjustment policy in a multi-stage production system is proposed. LOT-sizing adjustments depend on the difference in demand between actual and expected demand. To quantify the economics of our uncertainty strategy for multi-level LOT size the problems, the number of test instances with different parameter settings is evaluated. Computational experiments show that the additional costs of semifinished products, and the lack of storage capacity in the downstream processes reduce the potential for cost savings via multi-volume reform. Also a robust model is developed and as the robust model under study is NP-hard, it solved by a hybrid heuristic using the proposed stochastic model, a robust model is developed, which is solved by a hybrid heuristic algorithm based on Lagrangian relaxation and Bender’s decomposition algorithms. To evaluate the convergence rate and solution quality, the method is applied to some random test instances generated in the literature. The computational results indicate that the proposed method is capable of efficiently solving the model.

The Materials Requirements Planning (MRP) method that is applied in production planning and management has some weaknesses. One of its weaknesses is that the time in MRP method is discrete, and is considered as time period. Hence we are not able to order our requirements at irregular time moments or periods. In this paper, a new form of MRP is introduced that is named Continuous Materials Requirements Planning (CMRP) approach. We discuss the disadvantages of Discrete MRP (DMRP) approach and analyze? the conditions, applications and the manner of applying CMRP approach in our problems.

Although LOT streaming scheduling is an active research field, LOT streaming flexible flow lines problems have received far less attention than classical flow shops. This paper deals with scheduling jobs in LOT streaming flexible flow line problems. The paper mathematically formulates the problem by a mixed integer linear programming model. This model solves small instances to optimality. Moreover, a novel artificial bee colony optimization is developed. This algorithm utilizes five effective mechanisms to solve the problem. To evaluate the algorithm, it is compared with adaptation of four available algorithms. The statistical analyses showed that the proposed algorithm significantly outperformed the other tested algorithms.