Abstract
The advertising of any smart product is crucial in generating customer demand, along with reducing sale prices. Naturally, a decrease in price always increases the demand for any smart product. This study introduces a multi-product production process, taking into consideration the advertising- and price-dependent demands of products, where the failure rate of the production system is reduced under the optimum energy consumption. For long-run production systems, unusual energy consumption and machine failures occur frequently, which are reduced in this study. All costs related with the production system are included in the optimum energy costs. The unit production cost is dependent on the production rate of the machine and its failure rate. The aim of this study is to obtain the optimum profit with a reduced failure rate, under the optimum advertising costs and the optimum sale price. The total profit of the model becomes a complex, non-linear function, with respect to the decision variables. For this reason, the model is solved numerically by an iterative method. However, the global optimality is proved numerically, by using the Hessian matrix. The numerical results obtained show that for smart production, the maximum profit always occurs at the optimum values of the decision variables.
Highlights
Any production system may produce both perfect and imperfect products
Many studies based on constant defect rates in single-item production systems have been carried out; very little research based on random defect rates is available
This paper clearly shows the impact of advertisement on the total profit
Summary
Any production system may produce both perfect and imperfect products. During the long-run production process of a smart production system, there may be a chance of machine failure, due to machine breakdown, unskilled laborers, or interrupted energy suppliers, and so on. There has been no research, to our knowledge, on multi-item smart production systems with the optimum consumption of energy and a random defect rate for smart products, with advertisement, price-dependent demand patterns, and reduced failure rates. This proposed model gives a new direction for production systems with budget and space constraints under the effect of energy. Sarkar [13] developed an economic manufacturing quantity (EMQ) model with an investment in the production system for the development of a high system reliability with lower imperfect production This model first considered an advertisement policy, where the demand depends on the price of products.
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