Derivation of the Optimal Solution for the Economic Production Quantity Model with Planned Shortages without Derivatives

In this paper, we study a reformulation of the Economic Production Quantity (EPQ) problem. We study a more general version of the problem first and derive the conditions for an optimal solution, as well as the optimal solution itself, all without using derivatives. Then, we apply the approach to the reformulated EPQ problem. This version of the EPQ problem has been tackled by a number of researchers, wherein they have derived the conditions for the optimal solution and proposed algebraic derivations. However, their derivations for the conditions, as well as the optimal solution, have been shown to be questionable. Other than being questionable, the existing approaches are so complicated that they defeat the purpose of simplifying the optimization by using a derivative-free approach. We propose a correct and more succinct, much less complicated approach to derive the conditions and the optimal solution without using derivatives.

Nonlinear pentagonal intuitionistic fuzzy number and its application in EPQ model under learning and forgetting

In this current era, the concept of nonlinearity plays an important and essential role in intuitionistic fuzzy arena. This article portrays an impression of different representation of nonlinear pentagonal intuitionistic fuzzy number (PIFN) and its classification under different scenarios. A new de-intuitification technique of non-linear PIFN is addressed in this article along with its various graphical representations. Additionally, in this paper, we have observed this by applying it in an economic production quantity model where the production is not perfect and defective items are produced which are reworked. The model is considered under learning and forgetting, where learning is considered as linear, nonlinear PIFN and crisps arena. It is observed from the numerical study that high learning effects in rework lead to decrease in production of defective item, which, besides an economic advantage, may have a positive effect on the environment. Even though forgetting has an adverse effect, the average total cost is much less than that of the basic model which ignores worker learning and forgetting. Finally, comparative and sensitivity analysis result shows the utility of this noble work.

Analisis Persediaan Produk Gula Rafinasi Menggunakan Metode Economic Production Quantity

Overload is a condition where the goods stored in the warehouse exceed the existing capacity. With the accumulation, it will increase the storage cost for the products/goods stored. The purpose of this research was to help companies determine the optimal amount of production, optimal production time intervals and maximum product inventory so that there is no excess stock of products in the warehouse, and to obtain a minimum total inventory cost by using the Economic Production Quantity (EPQ) model. To collect the data needed in this study, secondary data was used which consists of production data and product delivery of company X. From the research results, the optimal production rate (Q*) is 13,646 MT/production cycle with an optimal production time interval of 1.16 months. or equal to 35 days, the maximum amount of inventory (Imax) was 429 MT. The total minimum inventory cost in one production cycle/month is Rp.167,925,698.28, -. The difference in total inventory costs generated using the EPQ method and calculations based on company conditions is 9% or equivalent to Rp.16,538,501, -. Based on the results of the sensitivity analysis it was known that all parameters are sensitive to Q*, Imax, and total inventory costs. However, a significant change is the parameter of saving costs, where the increase and decrease in saving costs will decrease and increase Q*, Imax, and the total cost of inventory.

Observations of the Economic Production Quantity Model With Imperfect Quality Items With/Without Inspection

Three observations of the economic production quantity model with imperfect quality items with/without inspection are presented in this report. Salameh and Jaber (2000) and Maddah and Jaber (2008) models do not meet their expected objective functions. The first observation tries to clarify the relationships among their expected objective functions and the actual ones through the derivation, the numerical simulation and statistical comparison. This report concludes s that both models are not very accurate, but capable. Khan et al. (2011) and Khan et al. (2014) ignored the independent condition of properties of the expectation of random variables, which resulted in minor errors in both papers. The second and the third observations are the corrections of the models of two papers, respectively. Numerical comparisons show the differences between the original models and the revisions are minor, but significant. An example of a multi-factor sensitivity analysis is shown in this report.

Observations of the Economic Production Quantity Model With Imperfect Quality Items With/Without Inspection

Three observations of the economic production quantity model with imperfect quality items with/without inspection are presented in this report. Salameh and Jaber (2000) and Maddah and Jaber (2008) models do not meet their expected objective functions. The first observation tries to clarify the relationships among their expected objective functions and the actual ones through the derivation, the numerical simulation and statistical comparison. This report concludes s that both models are not very accurate, but capable. Khan et al. (2011) and Khan et al. (2014) ignored the independent condition of properties of the expectation of random variables, which resulted in minor errors in both papers. The second and the third observations are the corrections of the models of two papers, respectively. Numerical comparisons show the differences between the original models and the revisions are minor, but significant. An example of a multi-factor sensitivity analysis is shown in this report.