This paper presents an exact model for the multi-mode resource-constrained project scheduling problem with generalized precedence relations in which the minimal or maximal time lags between a pair of activities may vary depending on the chosen modes. All resources considered are renewable. The objective is to determine a mode and a start time for each activity so that all constraints are obeyed and the project duration is minimized. Project scheduling of this type occurs in many fields, for instance, construction industries. The proposed model has been inspired by the rectangle packing problems. In spite of the fact that it needs a feasible solution to start for conventional models, the new model has no need for a feasible solution to start. Computational results with a set of 60 test problems have been reported and the efficiency of the proposed model has been analyzed.

Purpose One of the most important issues in supply chain (SC) management is the identification and management of the risk involved in it. The purpose of this paper is to propose a comprehensive model of supply chain risk management (SCRM) in the product life cycle (PLC) and the operational process cycle (OPC). To decrease the risks in a fuzzy environment, the model considers the organizational performance factors (OPF) and the risk operational practices (ROP). Design/methodology/approach Fuzzy analytic hierarchy process is used to determine the weights of the relationships between the PLC, OPC and OPF in the hierarchical structure of the decision problem. In addition, the fuzzy technique for order preference by similarity to ideal solution is employed to recognize the priority of ROPs in dealing with the performance factors. The integrated framework is evaluated using the case study of an automotive company in Iran. Findings The results demonstrated that the proposed model can be used to formulate an appropriate method for prioritizing defined alternatives to decrease risk and improve the organizational performance in SCRM under fuzzy conditions. Research limitations/implications A major limitation of the study is that a few of the selected criteria for risk assessment are focused only on economic factors. Another limitation of the current study is related to the PLC, OPC and OPF being based on the work of Xia and Chen (2011). Practical implications The current study identified the more important stage in the PLC. More significant process in each stage of the PLC and weightier risk factors in each process of the OPC were determined. Some strategies for reducing risk in each stage of the PLC were presented. The best alternatives for reducing risks in SC were indicated. Originality/value It is worth mentioning that previous studies have not applied multiple criteria and alternatives to decrease the risks involved in the PLC and OPC parts of the SC under fuzzy conditions. However, it should be stated that some academics have used these techniques separately, in other specialized areas of the SC.

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