In Industry 4.0, a network of enterprises and factories is constructed collaboratively and dynamically according to the cyber physical system (CPS) paradigm. It is necessary to build smart supply chains according to this concept. A network of component enterprises in a supply chain would be modeled as a virtual supply chain in the cyber world. From the viewpoint of Industry 4.0, virtualizing a supply chain is the foundation for constructing a CPS for a supply chain. The virtualization of a supply chain makes it easier for companies to study their integrating and expanding opportunities. By using this CPS, comprehensive and autonomous optimization of the supply chain can be achieved. This virtual supply chain can be used to simulate the planning phase with negotiation, as well as the production phase. In this paper, instead of specific mathematical modeling for each supply chain, a general configuration method of a virtual supply chain is proposed. The configuration method of a supply chain model is proposed as a virtual supply chain using enterprise e-catalogues. A virtual supply chain is constructed as a multi-agent system, which is connections of software agents that are automatically created from each selected enterprise model in the e-catalogues. Three types of component enterprise models are provided: manufacturer model, part/material supplier model, and retailer model. Modeling templates for these three types of enterprises are prepared, and each template is a nominal model in terms of enterprise’s behavior. Specific component-enterprise models are prepared by filling the appropriate template. Each component enterprise agent is implemented using the enterprise model selected from the catalogues. Manufacturer, retailer, and supplier e-catalogues, as well as an automatic construction system of a virtual supply chain, are implemented. Methods for developing templates for the manufacturer, retailer and supplier were provided, and the construction system for specific enterprise models (as e-catalogues) is implemented as a trial.

The paper aims to study a multi-period maximal covering location problem with the configuration of different types of facilities, as an extension of the classical maximal covering location problem (MCLP). The proposed model can have applications such as locating disaster relief facilities, hospitals, and chain supermarkets. The facilities are supposed to be comprised of various units, called the modules. The modules have different sizes and can transfer between facilities during the planning horizon according to demand variation. Both the facilities and modules are capacitated as a real-life fact. To solve the problem, two upper bounds—(LR1) and (LR2)—and Lagrangian decomposition (LD) are developed. Two lower bounds are computed from feasible solutions obtained from (LR1), (LR2), and (LD) and a novel heuristic algorithm. The results demonstrate that the LD method combined with the lower bound obtained from the developed heuristic method (LD-HLB) shows better performance and is preferred to solve both small- and large-scale problems in terms of bound tightness and efficiency especially for solving large-scale problems. The upper bounds and lower bounds generated by the solution procedures can be used as the profit approximation by the managerial executives in their decision-making process.

This paper presents an extension of the covering location problem as a hybrid covering model that utilizes the set covering and maximal covering location problems. The developed model is a multi-period model that considers strategic and tactical planning decisions. Hybrid covering location problem (HCLP) determines the location of the capacitated facilities by using dynamic set covering location problem as strategic decisions and assigns the constructive units of facilities and allocates the demand points by using dynamic modular capacitated maximal covering location problem as tactical decisions. One of the applications of the proposed model is locating first aid centers in humanitarian logistic services that have been addressed by studying a threat case study in Japan. In addition to validating the developed model, it has been compared to other possible combined problems, and several randomly generated examples have been solved. The results of the case study and model validation tests approve that the main hybrid developed model (HCLP) is capable of providing better coverage percentage compared to conventional covering models and other hybrid variants.

In this article, a dynamic maximal hub location covering problem for a freight transportation system is studied, in which the model has the possibility of having expansion scenarios for future according to the forecasts of increasing demands. Two expansion scenarios are to add up the number of hubs in the network and to add up more carriers. As the markets are involved in the pricing procedure, the model is a bi-level problem which needs more effort to deal with, for which in this work two reformulations based on Karush-Kuhn-Tucker conditions and duality theory are utilized to reformulate the bi-level problem to a single-level one. To solve the model efficiently, a decomposition method is applied and numerical examples are solved to verify the accuracy of the proposed model.

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