Increasing the number of disasters around the world will decrease the performance of the supply chain. The decision makers should design resilience supply chain network which could encounter with disruptions. This paper develops an integrated resilience model of supplier selection and order allocation. Resiliency measures including quality, delivery, technology, continuity, environmental competences are explored for determining the Resilience Weight of suppliers. Fuzzy DEMATEL and ANP methods are applied to find overall performance of each supplier. Then, the developed mathematical model maximizes overall performance of suppliers while minimizes total cost of network. The proposed mathematical model helps the decision makers to select supplier and allocate the optimum order quantities by considering shortage. Since the disruptive incidents are inevitable events in real world problems, the impact of disruptions on suppliers, manufactures and retailers has been considered in the proposed model. Inherent uncertainties of parameters are taken into account to increase the compatibility of the approach with realistic environments. To tackle the uncertainty and multi-objectiveness of the proposed model, interval Method and TH aggregation function is adapted. The proposed model is validated through application to a real case study in a furniture company. Results demonstrate the usefulness and applicability of the proposed model.

Supplier selection, order allocation and production planning are important and challenging decisions in supply chain management. There are many studies on mentioned topics separately. In this paper, a multi-objective mathematical model is proposed to optimize a sustainable supplier selection problem with order allocation and production planning simultaneously. This study considers a multi-supplier, multi-product, multi-item and multi-period supply chain. The designed mathematical model seeks to maximize total profit and minimize unsatisfied demand and total risk along with enforcing sustainability criteria in selecting suppliers. Supplier selection is a virtual process in every manufacturing company. On the other hand, this research considers all the important aspects of this problem. Therefore, the proposed framework can be implemented in many different companies like electronic, food, chemical industry. The proposed model is solved utilizing two metaheuristic algorithms including NSGA II and MOPSO. Moreover, algorithms are tuned utilizing Taguchi analysis. Furthermore, ten sample problems are generated and results are compared to identify the best algorithm for the proposed model.

In this study, an inventory management model based on a Markov decision process (MDP) framework is developed for a finite planning horizon with discrete time periods. The primary objective of the model is to minimize the total inventory management costs by determining the optimal order quantities and their allocation to suppliers. Ordering costs are modeled as random variables, while In this paper, an inventory management model based on the Markov Decision Process (MDP) framework is developed for a finite horizon and discrete time periods. The primary objective of this model is to minimize the total inventory management costs by determining the optimal order quantities and their allocation to suppliers. Ordering costs are modeled as stochastic variables, while holding costs are represented as linear functions. Utilizing a backward dynamic programming approach, optimal policies have been derived to minimize costs associated with ordering and holding inventory.To evaluate the model, a case study was conducted in a manufacturing company that sources polypropylene raw material from two suppliers. The results indicate that optimal order allocation can significantly reduce the overall supply chain costs by the end of the planning horizon. This cost reduction stems from the optimization of order quantities and the appropriate selection of suppliers based on the policies provided by the model. The proposed model, by incorporating uncertainty in ordering costs, demonstrates applicability in real-world settings. It offers effective tools for improving decision-making and cost reduction in supply chain management and can serve as a practical approach for manufacturing firms with multiple suppliers.

The supplier selection and order allocation are two key strategic decisions in purchasing problem. The review presented in this paper focuses on the supplier selection problems (SSP) and order allocation from year 2000 to 2017 in which a new structure and classification of the existing research streams and the different MCDM methods and mathematical models used for SSP will be presented. The review was examined in three aspects: the summaries of the existing evidence concerning the problems, the identification of gaps in the current research to help determine where further investigation might be needed and positioning new research activities.

Objective: The Supply chain plays a key role in adapting the organization to variable conditions and an uncertain future. The selection of appropriate suppliers can significantly increase the competitiveness and ability of a business in the market. One of the essential factors in supply chain optimization is controlling and managing inventory cost. This paper aims to simultaneously optimize supplier selection and order allocation while considering inventory control using a fractional programming approach.  Methodology: The methodology integrates quantitative analytical techniques in a multi-phase approach. First, the most frequent supplier selection criteria are identified with a literature review. The Delphi method was used to select the supplier selection criteria. In the next step, fuzzy Shannon entropy determines criterion weights. Then, fuzzy EDAS calculates supplier performance scores. Finally, fractional programming facilitates supplier selection and order allocation. Results: The most frequent supplier selection criteria were extracted from the literature review. In the Delphi technique, experts ultimately agreed on six key criteria: price, quality, delivery, flexibility, responsiveness, and financial stability. The results of the Shannon entropy analysis indicate that flexibility, with a weight of 0. 20, holds the highest relative importance among the criteria. The suppliers score obtained from the fuzzy EDAS method is used as one of the parameters of the mathematical model. Conclusion: The proposed hybrid MADM approach and mathematical model have been validated using empirical data obtained from Sirjan Steel Company. The result shows that the hybrid MADM approach and fractional programming have high accuracy in selecting the best supplier.

In this paper, a delay - difference second - order proportionally - fair rate allocation algorithm has been proposed. As conventional proportionally - fair rate allocation algorithms deploy some form of scaled gradient ascent iterative algorithm for converging to user optimal rates, using fast second - order algorithms, such as Jacobi or approximate Newton methods, can be considered as natural and good candidates for increasing the convergence speed of the rate allocation algorithms, Stability analysis, related to scaled gradient ascent algorithms, in the presence of propagation delays, has been performed by some researchers, such as R. Johari et al., in Cambridge, In the current paper, the stability conditions of a second - order Jacobi method in the presence of propagation delays, with the simplifying premise of equality between all the users_ propagation delays, is derived mathematically_ Simulation results show that even in the general case of different propagation delays, stability is maintained.

Intelligent agents are considered as significant means towards realizing the semantic web vision. On the Semantic Web, integrating ontologies and rules enables software agents to interoperate between them, however, this leads to a problem, that no studies have focused on effective distributed reasoning for integrating ontologies and rules in multiple knowledge-bases. The methods that have been presented for distributed reasoning not only get a lot of times and memory, but also do not lead to a complete and sound reasoning. In this paper, to solve this problem, we present a distributed reasoning system that deals with the representation of the knowledge-base of order sorted logic. This logic is able to describe the hierarchy of predicates and inheritance of expressions that there are in our natural language. To have a distributed reasoning, our proposed method uses the expansion of rigid and valid-non-rigid properties between knowledge-bases. Furthermore, with considering time and the situation of properties for reasoning, the non-rigid properties have not been ignored, in fact, in their valid time and situation, they are used. With this method, we achieve a complete reasoning and, moreover, the extracted knowledge is completely considered in the knowledge-bases and we have a distributed reasoning with high efficiency and sound without missing any information.

Performance of a supply chain highly depends on its suppliers and therefore, appropriate selection of them is of great importance. This paper presents an integrated model of an MCDM method and a mathematical programming in order to select suppliers and determine lot sizes in the supply chain. It proposed framework comprises two main sub-models; the qualitative sub-model seeks to evaluate the suppliers by means of Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Then, in the quantitative sub-model, a mixed integer nonlinear program is proposed in order to determine the optimal orders allocated to each supplier. Fuzzy multi-objective method (TH) is used to tackle complexity of the model. The most notable features of the proposed model is considering different quality levels and related defective rates as well as partial supplier switch. Finally, to demonstrate applicability of the proposed model and superiority of the developed algorithm, several example problems are generated and have been solved.