فرایند تولید ناقص برای زمان های مختلف تقاضا با تورم و ارزش زمانی پول - مدل مقدار تولید اقتصادی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|22666||2011||6 صفحه PDF||سفارش دهید||محاسبه نشده|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Expert Systems with Applications, Volume 38, Issue 11, October 2011, Pages 13543–13548
The paper deals with an economic manufacturing quantity (EMQ) model for time-dependent (quadratic) demand pattern. Every manufacturing sector wants to produce perfect quality items. But in long run process, there may arise different types of difficulties like labor problem, machinery capabilities problems, etc., due to that the machinery systems shift from in-control state to out-of-control state as a result the manufacturing systems produce imperfect quality items. The imperfect items are reworked at a cost to become the perfect one. The rework cost may be reduced by improvements in product reliability i.e., the production process depend on time and also the reliability parameter. We want to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process using Euler–Lagrange theory to build up the necessary and sufficient conditions for optimality of the dynamic variables. Finally, a numerical example is discussed to test the model which is illustrated graphically also.
Most of the classical EMQ models were considered with the realistic assumption of constant demand for the whole year, but in real life, the assumption is not true in general. The demand may vary with time. Another assumption is that the items produced by any manufacturing company are all perfect. But in real life situation, it is not true in general i.e., when the production system is going through a long-run process due to high demand of the produced items which may vary time to time, the manufacturing system shifts from in-control to out-of-control state, and then the manufacturing system produces perfect as well as imperfect (defective) quality items due to different types of machinery problems, labor problems, etc. A defective cost is allowed to make the defective items as new as the perfect one. Keeping in mind the above facts, we develop a production-inventory model for an imperfect production system considering the variable reliability parameter with effect of inflation and time value of money. The reliability parameter has an impact on the integrated cost function since no manufacturing company can consider that every machinery systems are reliable for life-time. For more accuracy, we consider the unit production cost and the development cost are the functions of reliability parameter which may vary by changes in technology and resources, etc. The integrated profit function is maximized by Euler–Lagrange’s method. The major contribution of this model is the variable reliability parameter with time dependent quadratic demand along with the effect of inflation and time value of money. The paper is designed as follows: Introduction are given in Section 1. Literature survey is described in Section 2. Problem Definition, Notations and Assumptions are provided in Section 3. The model is formulated in Section 4. A numerical example is given to test the model in Section 5. Finally, conclusions are given in Section 6.
نتیجه گیری انگلیسی
In most of the EMQ models are considered so far depending on the constant demand. But in the real life situation, the assumptions are not true in general. Throughout a year a demand is fixed, it is not true, demand by the customers may vary with time, for that we consider a time dependent quadratic demand model. Another important thing, if the demand is so high then the manufacturing company has to produce large amount of items in a short time. That is why, the machinery systems have to go through a long-run process which results the production of the defective items. The defective items are reworked at a cost to make the product perfect. After that the products are ready for sale. The production of the defective items increases with time and reliability parameter. The reliability parameter η of the machinery system is defined as View the MathML sourceNumberoffailuresTotalunitsofoperatinghours. The smaller value of η results in higher investment in technology, whereas greater value of η causes smaller investment for the cost of technology. Consequently, the unit production cost increases for more investment in technology. Again, we consider the development cost for production system is a function of reliability parameter for more realistic assumption. Keeping in mind the all factors, we discuss a time-dependent quadratic demand pattern production-inventory model in which the development cost and unit production cost are dependent on the reliability parameter incorporating with the inflation and time value of money. The associated profit function is maximized by the Euler–Lagrange method. The major contribution of this model is the variable reliability parameter for quadratic demand pattern with effect of inflation and the time value of money. Hence, the model has a new managerial insight that helps a manufacturing system/industry to gain the profit at optimal level. The numerical example gives us a promising result in practice. Although the closed type formula of optimal solution is not obtained, the Fig. 1 for numerical example shows concavity nature of the profit function. A possible future research issue is to study to consider a multi-item EMQ model with variable demand and also variable reliability with effect of inflation and the time value of money.