In this paper, a new period-based approach is proposed for modeling a capacitated inventory system, operating under an (S,T) policy with backlog. The system experiences stochastic discrete demand and lead time. By using the proposed method, a mathematical model is developed. The model can accurately estimate the inventory system measures of performance: the expected inventory on-hands and over-storage amount. Through a simulation experiment, the new model is compared with two other models, which are developed by using a widely used mean-based approach. The comparison is conducted based on a case study data set. The results demonstrate that the period-based model is superior to the mean-based models with respect to capturing the behaviors of the inventory system. Therefore, better inventory policy parameters can be obtained by employing the new model.

In this paper, we consider a two-echelon supply chain in which one warehouse provides a single product to N retailers, using integer-ratio policies. Deterministic version of the problem has been widely studied. However, this assumption can lead to inaccurate and ineffective decisions. In this research, we tackle the stochastic version of two-echelon inventory system by designing an extension of a well-known heuristic. This research considers customer demands as following a normal density function. A set of 240 random instances was generated and used in evaluating both the deterministic and stochastic solution approaches. Due to the nature of the objective function, evaluation was carried out via Monte Carlo simulation. For variable demand settings, computational experiments shows that: i) the use of average demand to define the inventory policy implies an underestimation of the total cost and ii) the newly proposed method offers cost savings.

Cell formation and layout design are two important steps for the implementation of the production systems. The existing models majorly have focused on the cell formation issue and the layout design of machines, but have paid little attention to the placement of cells in dynamic environment. In addition, in most of the available papers, binary variables have been used for cell formation, and other information such as volume of production, operation sequences and production costs have played unimportant roles in the structure of the existing models. In this paper, a nonlinear program-ming model under potentially dynamic conditions is proposed which minimizes the cost associated with the difference between the estimated demands from its expected value. The other purpose of the proposed model includes minimization of the total costs of inter/intra cellular movements of elements (forward and backward movements), the existence of exceptional elements, intercellular displacement of machines and cellular reconfiguration and operational costs and constant cost of machineries. The problem is solved via GAMS and a Genetic Algorithm (GA) is employed to solve the large sized problems and the results are analyzed.

The product-mix planning and the lot size decisions are some of the most fundamental research themes for the operations research community. The fact that markets have become more unpredictable has increaed the importance of these issues, rapidly. Currently, directors need to work with product-mix planning and lot size decision models by introducing stochastic variables related to the demands, lead times, etc. However, some real mathematical models involving stochastic variables are not capable of obtaining good solutions within short commuting times. Several heuristics and metaheuristics have been developed to deal with lot decisions problems, in order to obtain high quality results within short commuting times. Nevertheless, the search for an efficient model by considering product mix and deal size with stochastic demand is a prominent research area. This paper aims to develop a general model for the product-mix, and lot size decision within a stochastic demand environment, by introducing the Economic Value Added (EVA) as the objective function of a product portfolio selection. The proposed stochastic model has been solved by using a Sample Average Approximation (SAA) scheme. The proposed model obtains high quality results within acceptable computing times.

We study the question of how to ideally divide total profits among supply chain members, especially in a stochastic demand market. The Shapley value is used as the methodology solution to divide profits in a supply chain. To illustrate the Shapley value solution and procedures, a two-echelon supply chain consisting of one supplier and two heterogeneous retailers is examined. The goal is to figure out ideal transfer prices for products delivered among supply chain members. These transfer prices will achieve the suggested profit allocations among three companies.

In this paper, a new multi-item inventory system is considered with random demand and random lead time including working capital and space constraints with three decision variables: order quantity, safety factor and backorder rate. The demand rate during lead time is stochastic with unknown distribution function and known mean and variance. Random constraints are transformed to crisp constraints with using the chance-constrained method. The Minimax distribution free procedure has been used to lead proposed model to the optimal solution. The shortage is allowed and the backlogging rate is dependent on the expected shortage quantity at the end of cycle. Two numerical examples are presented to illustrate the proposed solution method.