Abstract
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.
Highlights
During a long-run production, a common phenomenon is the production of defective items even though the production is considered under a smart manufacturing system under the consideration of proper energy consumption
Though the major contribution is the concept of failure rate of a smart production system under energy consideration being introduced with the random time movement from in-control state to out-of-control state
To increase the system reliability, the unit smart production cost is assumed as a sum of development cost, material cost and tool/die cost, where the development cost of products depends on the failure rate and amount of energy consumption
Summary
During a long-run production, a common phenomenon is the production of defective items even though the production is considered under a smart manufacturing system under the consideration of proper energy consumption. No author considered random defective rate for multi-item smart production under energy consideration with budget and space constraints. The proposed model gives a new direction of random defective rate with an indication of system reliability for multi-item smart production and energy consumption with budget and space constraints. Reworking of the imperfect production items to make them as good as perfect quality items was introduced by Chiu et al [7] and they proposed a model in which a portion of imperfect quality items is discarded, while the other portion is reworked by spending some costs They optimized the finite production rate considering scrap production, reworking, and stochastic machine breakdown. Huang et al [22] developed an inventory model and investigated the optimal retailer’s lot sizing policy under partially permissible delay-in-payments and space constraints They considered extra cost payment for rental warehouse, when the capacity of the existing warehouse is full. Problem definition, notation and assumptions are given
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