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To form a smart production system, the effect of energy and machines’ failure rate plays an important role. The main issue is to make a smart production system for complex products that the system may produce several defective items during a long-run production process with an unusual amount of energy consumption. The aim of the model is to obtain the optimum amount of smart lot, the production rate, and the failure rate under the effect of energy. This study contains a multi-item economic imperfect production lot size energy model considering a failure rate as a system design variable under a budget and a space constraint. The model assumes an inspection cost to ensure product’s quality under perfect energy consumption. Failure rate and smart production rate dependent development cost under energy consumption are considered, i.e., lower values of failure rate give higher values of development cost and vice versa under the effect of proper utilization of energy. The manufacturing system moves from in-control state to out-of-control state at a random time. The theory of nonlinear optimization (Kuhn–Tucker method) is employed to solve the model. There is a lemma to obtain the global optimal solution for the model. Two numerical examples, graphical representations, and sensitivity analysis of key parameters are given to illustrate the model.

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Modern supply chains are vulnerable to high impact, low probability disruption risks. A supply chain usually operates in such a network of entities where the resilience of one supplier is critical to overall supply chain resilience. Therefore, resilient planning is a key strategic requirement in supplier selection decisions for a competitive supply chain. The aim of this research is to develop quantitative resilient criteria for supplier selection and order allocation in a fuzzy environment. To serve the purpose, a possibilistic fuzzy multi-objective approach was proposed and an interactive fuzzy optimization solution methodology was developed. Using the proposed approach, organizations can tradeoff between cost and resilience in supply networks. The approach is illustrated using a supply chain case from a garments manufacturing company.

Conservation of natural resources in order to protect the environment, support the economy, and offer a better life to living beings has become an urgent need of modern business so that future generations can survive within available resources and in a healthy environment. Recycling of used products plays an important role in the conservation of natural resources and the development of sustainable business for deteriorating products because the number of these items increases with time, which creates economic loss and environmental pollution. This paper considers the production and cycle time as decision variables to design a forward and reverse supply chain system that produces two different types of products, which are subject to deterioration. Rate of deterioration is time-varying and depends on the maximum lifetime of products. Used products of a forward supply chain are collected and treated as raw materials in a reverse supply chain to produce other products. The system involves three types of inventory stocks, i.e., product 1, 2, and returned inventory. The objective of this research is to minimize total cost per unit time for two types of systems, one in which products of both the supply chains deteriorate and the second in which the products of the first supply chain deteriorate. Kuhn−Tucker method is employed to solve the model and a solution algorithm is proposed to obtain optimal solution. Application of the model is supported with numerical examples and sensitivity analysis. Some managerial insights are provided to help managers while applying the proposed models in real situations. Results of numerical experiments suggest for deteriorating products to plan short replenishment cycles of inventory.

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The paper represents a variation of the national income determination model with discrete and continuous process in fuzzy environment, a significant implication in economics planning, by means of fuzzy assumptions. This model is re-recognized and deliberated with fuzzy numbers to estimate its uncertain parameters whose values are not precisely known. Exhibition of imprecise solutions of the concerned model is carried out by using the proposed two methods: generalized Hukuhara difference and generalized Hukuhara derivative (gH-derivative) approaches. Moreover, the stability analysis of the model in two different systems in fuzzy environment is illustrated. Additionally, different illustrative examples for optimization of national income determination model are undertaken with the constructive graph and table for convenience for clarity of the projected approaches.