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

Modelling ◽  
2022 ◽  
Vol 3 (1) ◽  
pp. 54-69
Author(s):  
Cenk Çalışkan
Keyword(s):  
Optimal Solution ◽  
General Version ◽  
Economic Production Quantity ◽  
Economic Production ◽  
Derivative Free ◽  
Production Quantity

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.

scholarly journals The effect of service constraint on EPQ model with random defective rate

2006 ◽  
Vol 2006 ◽  
pp. 1-5 ◽  
Author(s):  
Yung-Fu Huang
Keyword(s):  
Annual Cost ◽  
Differential Calculus ◽  
Cost Minimization ◽  
Algebraic Approach ◽  
Optimal Solution ◽  
Service Level ◽  
Economic Production Quantity ◽  
Economic Production ◽  
Epq Model ◽  
Production Quantity

Chiu studied the effect of service-level constraint on the economic production quantity (EPQ) model with random defective rate. In this note, we will offer a simple algebraic approach to replace his differential calculus skill to find the optimal solution under the expected annual cost minimization.

scholarly journals EPQ Model for Trended Demand with Rework and Random Preventive Machine Time

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Nita H. Shah ◽  
Dushyantkumar G. Patel ◽  
Digeshkumar B. Shah
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Rate Of Change ◽  
Machine Time ◽  
Economic Production Quantity ◽  
Economic Production ◽  
Model Search ◽  
Demand Rate ◽  
Epq Model ◽  
Production Quantity

Economic production quantity (EPQ) inventory model for trended demand has been analyzed with rework facility and stochastic preventive machine time. Due to the complexity of the model, search method is proposed to determine the best optimal solution. A numerical example and sensitivity analysis are carried out to validate the proposed model. From the sensitivity analysis, it is observed that the rate of change of demand has significant impact on the optimal inventory cost. The model is very sensitive to the production and demand rate.

scholarly journals Economic production quantity model with backorders and items with imperfect/perfect quality options

2019 ◽  
Vol 17 (4) ◽  
Author(s):  
Behrouz Afshar Nadjafi ◽  
Hamed Pourbakhsh ◽  
Mohammad Mirhabibi ◽  
Hasan Khodaei ◽  
Babak Ghodami ◽  
...  
Keyword(s):  
Optimal Solution ◽  
Screening Process ◽  
Economic Production Quantity ◽  
Economic Production ◽  
Decision Variables ◽  
Proposed Model ◽  
Epq Model ◽  
Production Quantity ◽  
The Impact ◽  
Single Batch

In this paper, an economic production quantity (EPQ) model with backorders considering two options for replenishing of items is proposed; with partially imperfect and perfect quality items. First option assumes a produced shipment contains a fraction of imperfect quality items and supplier does not conduct a full inspection. Therefore, these items are detected by a fully perfect screening process by buyer and are sold as a single batch at a discounted price. While the second one assumes that all items that are produced are fully inspected by supplier and all delivered items are perfect; of course with higher unit production price. Ordering size and backordering level are used as decision variables to derive the closed-form optimal solution. The proposed model is ilustrated and discussed by a numerical example. Finally, a sensitivity analysis is done for identifying the impact of crucial parameters on the optimal solution.

A comparative study on economic production quantity (EPQ) model under space constraint with different kinds of data

2019 ◽  
Vol 9 (1) ◽  
pp. 86-100
Author(s):  
Amir Karbassi Yazdi ◽  
Mohamad Amin Kaviani ◽  
Amir Homayoun Sarfaraz ◽  
Leopoldo Eduardo Cárdenas-Barrón ◽  
Hui-Ming Wee ◽  
...  
Keyword(s):  
Cycle Time ◽  
Space Constraint ◽  
Optimal Solution ◽  
Inventory Model ◽  
Fuzzy Data ◽  
Content Type ◽  
Economic Production Quantity ◽  
Economic Production ◽  
Epq Model ◽  
Production Quantity

PurposeThe purpose of this paper is to develop a multi-item economic production quantity (EPQ) strategy under grey environment and space constraint. Since the “demand” cannot be predicted with certainty, it is assumed that data behave under grey environment and compare the proposed inventory model with other studies using crisp or fuzzy environments.Design/methodology/approachThis paper is to optimise the cycle time and total cost of the multi-item EPQ inventory model. For this purpose, the Lagrangian coefficient is used to solve the constrained optimisation problem. The grey relational analysis approach and grey data are applied in developing the EPQ inventory model.FindingsThe results are compared with the analysis using crisp and fuzzy data. Sensitivity analysis is done to illustrate the effect of parameter variations on the optimal solution. The results of the study demonstrate that crisp data outperform the other two data in all scales problems in terms of cycle time and cost; grey data perform better in all scales problems than fuzzy data.Originality/valueThe contribution of this research is the use of grey data in developing the EPQ inventory model with space constraint.

Fuzzy Economic Production Quantity Model for Weibull Deteriorating Items with Ramp Type of Demand

2011 ◽  
Vol 2 (3) ◽  
pp. 55-90 ◽  
Author(s):  
R. Uthayakumar ◽  
M. Valliathal
Keyword(s):  
Deteriorating Items ◽  
Quantity Discounts ◽  
Setup Cost ◽  
Economic Production Quantity ◽  
Deterministic Demand ◽  
Economic Production ◽  
Holding Cost ◽  
Production Quantity ◽  
Delay In Payments ◽  
The Cost

This paper discusses an Economic Production Quantity model for Weibull deteriorating items over an infinite time horizon under fuzzy environment. Fuzziness is introduced by allowing the cost components such as setup cost, production cost, holding cost, shortage cost and opportunity cost due to lost sales to certain extent. Triangular fuzzy numbers are used to represent the mentioned costs. Optimum policies of the described models under fuzzy costs are derived. The proposed model can be extended in several ways. For instance, the deterministic demand function to stochastic fluctuating demand patterns could be considered. The model could also be generalized to allow for quantity discounts, as well as permissible delay in payments.

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