In most industrial applications, determining production quantities are one of the most key decision making. In this paper, an integer mathematical programming model for lot-sizing problem with considering set-up time, safety stock, shortage cost, and different production manners, is presented.The objective is to minimize summation of production, set up, holding, and shortage costs. To solve the model, a forward Dynamic programming (DP) approach is presented and compared with classical backward DP method.Finally, different numerical illustrations with different dimension are generated. The statistical analysis on computational results showed that the proposed DP approach is more applicable than the classical DP in terms of computational time.

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.

This paper considers the problem of a vendor-buyer integrated production-inventory model. The vendor manufactures the item at a finite rate and delivers the final goods at a lot-for-lot shipment policy to the buyer. We relax the assumption of uniform demand in the hitherto existing joint economic lot sizing models and analyze the problem where the end customer demand is price-sensitive. The relation between demand and price is considered to be linear. The model proposed, based on the integrated expected total relevant profits of both buyer and vendor, finds out the optimal values of order quantity and mark-up percentage, using an analytical approach. Some numerical examples are also used to analyze the effect of the price-sensitivity of demand on the improvements in joint total profit over individually derived policies.

In this paper, the multi-level lot sizing problem which is used to determine the production lot sizes in industrial environments, has been investigated. A new problem which we refer to it as “multi-level lot sizing problem with deterioration inventory and disposal costs” is introduced. The aim of multi-level lot sizing problem is to determine the production quantity of production periods for each product in each level, such the the total cost containing production costs, holding costs and setup costs to be minimized. In the proposed model, the deterioration property of the inventory is assumed. Furthermore, disposal costs that represents the costs for removing the perishable inventories from the storage environments, is combined with the generalized model in order to make the model closer to reality. The aim of the new problem, are determining the production quantity of production periods for each product in each level, and determining the periods in which the perishable inventory to be disposed. Therefore, the disposal costs is considered in the objective function of the problem. Two meta heuristic algorithms consist of genetic algorithm and simulated annealing algorithm is used to solve the proposed problem. In order to compare the performance of the proposed algorithms with existing methods in the literature, instance problems are created, and the results are analyzed.

Carbon emissions related to energy consumptions from the manufacturing industry have become a substantial part of environmental burdens. This study presents carbon emission constraint into the economic lot scheduling problem to reduce carbon emissions. The aim of this research to satisfy customer demand for various items over the planning horizon, with an objective to minimize total costs, includes setup, production, rework and holding costs. In this problem, it is assumed that the production process is defective, and during the process some of the goods are produced with undesirable quality. Defective products can be sold using a rework process. This proposed model has been proven to be a nonlinear convex programming problem. Hence, the optimal solution of this proposed model can be obtained using the derivative method. Finally, a hypothetical example is solved to demonstrate the performance of the proposed exact solution algorithm.