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.

In this paper, a simultaneous lead time quotation and lot sizing problem in an assembly system is investigated. We address a production system with a product that has deterministic demand over a T-period planning horizon and is produced in lots because of the economy of scale. If a lot is completed before the demand period, inventory carrying cost is incurred. On shortages, a lead time is quoted to customers and a lead time quotation cost is incurred. Finally, if the order is delivered later than its due date period, a tardiness cost is charged. The components supply lead time is stochastic, which follows a discrete distribution. The problem is to decide on the lot size of products and components, supply and production starting periods and the due date of lots (to be quoted to customers) so that relevant costs are minimized. The objective function is the sum of the production, inventory carrying, lead time quotation and tardiness costs. We develop a genetic algorithm to solve the proposed model. An experimental framework is set up to test the efficiency of the proposed method, which turns out to rate high, both in terms of cost effectiveness and execution speed.

This paper addresses a new mixed integer nonlinear and linear mathematical programming economic lot sizing and scheduling problem in distributed permutation flow shop problem with number of identical factories and machines. Different products must be distributed between the factories and then assignment of products to factories and sequencing of the products assigned to each factory has to be derived. The objective is to minimize the sum of setup costs, work-in-process inventory costs and finished products inventory costs per unit of time. Since the proposed model is NP-hard, an efficient Water Cycle Algorithm is proposed to solve the model. To justify proposed WCA, Monarch Butterfly Optimization (MBO), Genetic Algorithm (GA) and combination of GA and simplex are utilized. In order to determine the best value of algorithms parameters that result in a better solution, a fine-tuning procedure according to Response Surface Methodology is executed.

Considering its application, stochastic lot sizing is a significant subject in production planning. Also the concept of service level is more applicable than shortage cost from managers’ viewpoint. In this paper, the stochastic multi period multi item capacitated lot sizing problem has been investigated considering service level constraint. First, the single item model has been developed considering service level and with no capacity constraint and then, it has been solved using dynamic programming algorithm and the optimal solution has been derived. Then the model has been generalized to multi item problem with capacity constraint. The stochastic multi period multi item capacitated lot sizing problem is NP-Hard, hence the model could not be solved by exact optimization approaches. Therefore, simulated annealing method has been applied for solving the problem. Finally, in order to evaluate the efficiency of the model, low level criterion has been used.