In this paper, the problem of lot sizing for the case of a single item is considered along with supplier selection in a two-stage supply chain. The suppliers are able to offer quantity discounts, which can be either all-unit or incremental discount policies. A mathematical modeling formulation for the proposed problem is presented and a dynamic programming methodology is provided to solve it. Computational experiments are performed in order to examine the accuracy and the performance of the proposed method in terms of running time. The preliminary results indicate that the proposed algorithm is capable of providing optimal solutions within low computational times, high accuracy solutions.

The present study focused on the Taguchi experimental design technique of Friction Stir Welds of dissimilar aluminum alloys (AA2024-T6 and AA6351-T6) for tensile properties. Effect of process parameters, rotational speed, Traverse speed and axial force, on tensile strength was evaluated. Optimized welding conditions for maximize tensile strength were estimated in order to improve the productivity, weld quality. Non-linear regression mathematical model was developed to correlate the process parameters to tensile strength. The results were verified by conducting the confirmation tests at identified optimum conditions.

This study develops an integrated production inventory model from the perspectives of vendor, supplier and buyer. The demand rate is time dependent for the vendor and supplier and buyer assumes the stock dependent demand rate. As per the demand, supplier uses two warehouses (rented and owned) for the storage of excess quantities. Shortages are allowed at the buyer’s part only and the unfulfilled demand is partially backlogged. The effect of imperfect production processes on lot sizing is also considered. This complete model is studied under the effect of inflation. The objective is to minimize the total cost for the system. A solution procedure is developed to find a near optimal solution for the model. A numerical example along with sensitivity analysis is given to illustrate the model.

We study a location-inventory problem in a three level supply chain network under uncertainty, which leads to risk. The (r,Q) inventory control policy is applied for this problem. Besides, uncertainty exists in different parameters such as procurement, transportation costs, supply, demand and the capacity of different facilities (due to disaster, man-made events and etc). We present a robust optimization model, which concurrently specifies: locations of distribution centers to be opened, inventory control parameters (r,Q), and allocation of supply chain components. The model is formulated as a multi-objective mixed-integer nonlinear programming in order to minimize the expected total cost of such a supply chain network comprising location, procurement, transportation, holding, ordering, and shortage costs. Moreover, we develop an effective solution approach on the basis of multi-objective particle swarm optimization for solving the proposed model. Eventually, computational results of different examples of the problem and sensitivity analysis are exhibited to show the model and algorithm & apos; s feasibility and efficiency.

Although supply chains disruptions rarely occur, their negative effects are prolonged and severe. In this paper, we propose a reliable capacitated supply chain network design (RSCND) model by considering random disruptions in both distribution centers and suppliers. The proposed model determines the optimal location of distribution centers (DC) with the highest reliability, the best plan to assign customers to opened DCs and assigns opened DCs to suitable suppliers with lowest transportation cost. In this study, random disruption occurs at the location, capacity of the distribution centers (DCs) and suppliers. It is assumed that a disrupted DC and a disrupted supplier may lose a portion of their capacities, and the rest of the disrupted DC & apos; s demand can be supplied by other DCs. In addition, we consider shortage in DCs, which can occur in either normal or disruption conditions and DCs, can support each other in such circumstances. Unlike other studies in the extent of literature, we use new approach to model the reliability of DCs; we consider a range of reliability instead of using binary variables. In order to solve the proposed model for real-world instances, a Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is applied. Preliminary results of testing the proposed model of this paper on several problems with different sizes provide seem to be promising.

The hub location problem involves a network of origins and destinations over which transportation takes place. There are many studies associated with finding the location of hub nodes and the allocation of demand nodes to these located hub nodes to transfer the only one kind of commodity under one level of service. However, in this study, carrying different commodity types from origin to destination under various levels of services (e.g. price, punctuality, reliability or transit time) is studied. Quality of services experienced by users such as speed, convenience, comfort and security of transportation facilities and services is considered as the level of service. In each system, different kinds of commodities with various levels of services can be transmitted. The appropriate level of service that a commodity can be transmitted through is chosen by customer preferences and the specification of the commodity. So, a mixed integer programming formulation for single allocation hub covering location problem, which is based on the idea of transferring multi commodity flows under multi levels of service is presented. These two are applied concepts, multi-commodity and multi-level of service, which make the model & apos; s assumptions closer to the real world problems. In addition, a differential evolution algorithm is designed to find near-optimal solutions. The obtained solutions using differential evolution (DE) algorithm (upper bound), where its parameters are tuned by response surface methodology, are compared with exact solutions and computed lower bounds by linear relaxation technique to prove the efficiency of proposed DE algorithm.

Recovery of used products has steadily become interesting issue for research due to economic reasons and growing environmental or legislative concern. This paper presents a closed-loop logistics network design based on reverse logistics models. A mixed integer linear programming model is implemented to integrate logistics network design in order to prevent the sub-optimality caused by the separate design of the forward and reverse networks. The study presents a single product and multi-stage logistics network problem for the new and return products not only to determine subsets of logistics centers to be opened, but also to determine transportation strategy, which satisfies demand imposed by facilities and minimizes fixed opening and total shipping costs. Since the deterministic estimation of some parameters such as demand and rate of return of used products in closed loop logistics models is impractical, an uncertain programming is proposed. In this case, we assume there are several economic conditions with predefined probabilities calculated from historical data. Then by means of expert & apos; s opinion, a fuzzy variable is offered as customer & apos; s demand under each economic condition. In addition, demand and rate of return of products for each customer zone is presented by fuzzy-random variables, similarly. Therefore, a fuzzy-random programming is used and a priority-based genetic algorithm is proposed to solve large-scale problems.

This study determines the optimal investment portfolio in Tehran Stock Exchange (TSE) industries. For this purpose, a conditional capital asset pricing model (CAPM) with time-varying covariance, according to a Multivariate GARCH approach has been formulated. According to this conditional CAPM, the conditional variance-covariance matrix and mean of returns are calculated for some industries. By using the Mean-Value at Risk portfolio selection model, the optimum proportion is detected. Results showed that the Pharmaceutical Industry, Financial Group and Cement Industry have the most quotas in portfolio since they maintain the minimum variance and maximum return among all other industries.

In this research, three variance ratio tests: the standard variance ratio test, the wild bootstrap multiple variance ratio test, and the non-parametric rank scores test are adopted to test the random walk hypothesis (RWH) of stock markets in Middle East and North Africa (MENA) region using most recent data from January 2010 to September 2012. The empirical results obtained by all three econometric tests show that the RWH is strongly rejected for Kuwait, Tunisia, and Morocco. However, the standard variance ratio test and the wild bootstrap multiple variance ratio test reject the null hypothesis of random walk in Jordan and KSA, while non-parametric rank scores test do not. We may conclude that Jordan and KSA stock market are weak efficient. In sum, the empirical results suggest that return series in Kuwait, Tunisia, and Morocco are predictable. In other words, predictable patterns that can be exploited in these markets still exit. Therefore, investors may make profits in such less efficient markets.

The purpose of these comments is to serve as a revision to the article by Khan, Jaber, & Bonney [2011, An economic order quantity (EOQ) for items with imperfect quality and inspection errors, International Journal of Production Economics, 133: 113–118]. This commenting paper first suggests that the revenue function derived in Khan et al. (2011) is unrealistic, and then offers revisions to complement the shortcomings.