Economic Production Quantity Model Research Articles

An optimal setup cost reduction and lot size for economic production quantity model with imperfect quality and quantity discounts

<p style='text-indent:20px;'>The purpose of this paper concentrates on an economic production quantity model with the factors of imperfect quality and quantity discounts, in which the inspection action occurs during the production stage. There is specific consideration of there being a finite production rate, and the quantity discounts offered by the supplier serves the purpose of stimulating buying greater quantities. This is in contrast to EPQ models that do not take these added factors into consideration. The objective of this paper is to determine the setup cost reduction, which is a function of capital investment, and inventory lot size. An alternative solution procedure was developed that does not employ the Hessian Matrix concavity in the expected total profit. We develop an algorithm to determine the optimal solution for this model. Theoretical results are discussed and a numerical example is proposed. Managerial insights are also examined.

Back-ordered inventory model with inflation in a cloudy-fuzzy environment

In this paper, an Economic Production Quantity model for deteriorating items with time-dependent demand and shortages including partially back-ordered is developed under a cloudy-fuzzy environment. At first, we develop a crisp model by considering linearly time-dependent demand with constant deterioration rate, constant inflation rate and shortages under partially back-ordered, then we fuzzify the model to archive a decision under the cloudy-fuzzy (extension of fuzziness) demand rate, inflation rate, deterioration rate and the partially back-ordered rate which are followed by their practical applications. In this model, we assume ambiances where cloudy normalized triangular fuzzy number is used to handle the uncertainty in information which is coming from the data. The main purpose of our study is to defuzzify the total inventory cost by applying Ranking Index method of fuzzy numbers as well as cloudy-fuzzy numbers and minimize the total inventory cost of crisp, fuzzy, and cloudy-fuzzy model. Finally, a comparative analysis among crisp, fuzzy and cloudy-fuzzy total cost is carried out in this paper. Numerical example, sensitivity analysis, and managerial insights are elaborated to justify the usefulness of the new approach. A comparative inquiry of the numerical result with a new existing paper is also carried out. This paper ends with a conclusion along with advantages and limitations of our solution approach, and an outlook towards possible future studies.

A FEPQ model of sustainable items with time and stock dependent demand under trade credit policy

Nowadays sustainable fuzzy economic production quantity (s-FEPQ) models gets more highlighted over classical fuzzy economic production quantity (EPQ) models. In this paper, we developed a fuzzy inventory model of sustainable items under time dependent quadratic rate of fuzzy demand and exponential holding cost where shortages are allowed and are fully backlogged considering obsolescence cost and carbon emission cost. Also the developed model is compared with stock dependent fuzzy demand. The proposed fuzzy inventory model is solved via generalised Hukuhara derivative approach. Two different cases are considered by using generalised Hukuhara: differentiability and generalised Hukuhara. For the first time, in this sustainable fuzzy EPQ model, an alternative approach of payment is proposed. After that, the proposed model has been solved by using multi-objective genetic algorithm. The proposed model and technique are lastly illustrated by providing numerical examples. The results from the two methods are compared and some sensitivity analyses both in tabular and graphical forms are presented and discussed.

A sustainable production-inventory model for a controllable carbon emissions rate under shortages

Carbon emissions are the key factor of global warming. Nowadays, some countries have focused on reducing carbon emission. Carbon tax and cap policies are the key mechanism utilized in many countries to achieve this. Keeping this issue in mind, a sustainable economic production quantity (SEPQ) carbon tax and cap model has considered for a controllable carbon emissions rate by investing in green technology (GT) efforts under different with and without shortage situations. This study has three models; a) a sustainable economic production quantity carbon tax and cap model with no shortages; b) a sustainable economic production-quantity carbon tax and cap with partial backordering; and c) a sustainable economic production-quantity carbon tax and cap with full backordering with and without green technology investment. A solution methodology has been proposed for determining the optimal strategies of cycle time, green technology investment, and the fraction period length in positive inventory level. Several numerical examples have studied to validate the sustainable economic production quantity models. The results of this paper are a sustainable economic production quantity carbon tax and cap partial backlogging case has a better justifiable profit with the highest cycle time and the lowest value of the fraction length period as well as the lower green technology investment cost compared with other models. Finally, sensitivity analysis has provided with the managerial implication of the optimal feasible solution with respect to some key parameters.

Manufacturer's optimal pricing and lot‐sizing policies under trade‐credit financing

In the year 2006, Teng et al considered an appropriate economic production quantity (EPQ) model in which the manufacturer receives the supplier's trade credit and provides trade credit to the customer simultaneously. The following two payment methods were discussed by Teng et al:The main purpose of this paper is summarized below:Finally, with a view to further motivating the interested researchers for using the methodology and mathematical analytic techniques in several other contexts in the field, we have chosen to include, in Section 12, a number of related recent works in the field.

Arbitrary-order economic production quantity model with and without deterioration: generalized point of view

The key objective of this paper is to study and discuss the application of fractional calculus on an arbitrary-order inventory control problem. Using the concepts of fractional calculus followed by fractional derivative, we construct different possible models like generalized fractional-order economic production quantity (EPQ) model with the uniform demand and production rate and generalized fractional-order EPQ model with the uniform demand and production rate and deterioration. Also, we show that the classical EPQ model is the particular case of the corresponding generalized fractional EPQ model. This greatly facilitates the researcher a novel tactic to analyse the solution of the EPQ model in the presence of fractional index. Furthermore, this attempt also provides the solution obtained through the optimization techniques after using the real distinct poles rational approximation of the generalized Mittag-Leffler function.

Effect of warranty and quantity discounts on a deteriorating production system with a Markovian production process and allowable shortages

This paper explores the retailer's optimal lot sizing and quantity backordering for a deteriorating production system with a two-state Markov production process in which quantity discounts are provided by the supplier. The products are sold with the policy of free reasonable repair warranty employing the fraction of nonconforming items in a lot size. Unlike the traditional economic production quantity (EPQ) model with warranty policy based on the elapsed time of the system in the control state follows an exponential distribution, this paper not only constructs an alternative mathematical model for EPQ model based on the fraction of nonconforming items in a lot size for an imperfect production system but also extends the topics of optimal quantity and shortage to a wider scope of academic research and further finds that some results are different from the traditional EPQ models. We seek to minimize the expected total relevant cost through optimal lot sizing and quantity backordering. We also demonstrate that the optimal lot size is bounded in a finite interval. An efficient algorithm is developed to determine the optimal solution. Moreover, a numerical example is given and sensitivity analysis is conducted to highlight management insights.

The supplier-retailer optimal replenishment decisions under a two-level trade credit model with shortage for deteriorating items

This paper establishes an integrated inventory model of a supplier and a manufacturer under a two-level trade credit contract. The manufacturer's inventory model follows the economic production quantity model and the produced items follow exponentially deterioration rate and price-dependent demand. Shortages are allowed for the manufacturer and are completely backlogged to the next period. Traditional inventory system and one-level trade credit are also concluded as special cases of the developed two-level trade credit model and the supply chain performance under these three policies are compared. The formulated models aim at helping the supply chain decision makers to determine the best delay strategy and find the optimal values for replenishment policy and the manufacturer's selling price in order to maximise the supply chain total net profit. The results have been then validated with a numerical example and the effect of various parameters on the optimal solution is finally studied by performing sensitivity analysis.

A Survey on Multi-Product Sustainable Economic Production Quantity Model Considering Wastewater Emission Costs

Implementing sustainability in production processes is the goal of many companies. A traditional economic production quantity (EPQ) model is used to determine the optimal number of products to produce in one period. Few researchers have considered carbon emission costs. In this study, we made a survey on multi-product sustainable economic production quantity model considering wastewater emission costs. The objective of this study is investigate the possible research to determine the economic production quantity to minimize the total costs per production cycle and waste emissions. The survey consider researches under three scenarios: (1) sustainable EPQ model that considers all CO2 emissions from inventory holding and production; (2) sustainable EPQ with shortage backorder; and (3) multi-product sustainable EPQ model with shortage.

Using a Random Coefficient Regression Model to Jointly Determine the Optimal Critical Level and Lot Sizing

This paper proposes an integrated preventive maintenance and economic production quantity model. A condition-based maintenance policy is described by a random coefficient regression model, based on which the monitored condition is divided into two parts: the actual condition and random error. Products are produced in batches and the system is monitored at the end of each batch. If the observed system condition either reaches or exceeds the critical level, the system should be renewed by preventive maintenance. However, if the actual system condition reaches the failure level during the production process, the system fails and should be renewed immediately. Based on these two renewal situations, we construct a model of expected cost per unit time using the renewal reward theory. The critical level and production lot size are decision variables, which can be obtained by minimizing the cost model. We also develop a simulation process to obtain the optimal results in another way and validate our proposed cost model. Finally, a real case study is given to demonstrate the model and the simulation process.

Optimization of finite Economic Production Quantity Model Under Cloudy Normalized Triangular Fuzzy Number

Optimization of finite Economic Production Quantity Model Under Cloudy Normalized Triangular Fuzzy Number

An economic production quantity model with backlogging and imperfect rework process for uncertain demand

This paper deals with a lot-sizing problem in the economic production quantity model with imperfect production processes and failure in repair where a Brownian motion process governs the inventory level variation. We assume that the unsatisfied demand is fully backlogged. In addition, we assume that all imperfect items produced are stocked separately and then reworked. Reworking and shortage costs are included in the proposed mathematical modelling and analysis. The aim of this research is to determine the optimal production lot size and backorder level such that the long-run total expected cost of the system is minimised. For the proposed model, we prove closed-form expressions for the inventory process and for the backlog costs. Moreover, a computer code using software package for the numerical work is furnished to derive the optimal solution. Some numerical examples and sensitivity analysis are provided to illustrate the validity of the proposed model.

Outsourcing Rework of Imperfect Items in the Economic Production Quantity (EPQ) Inventory Model With Backordered Demand

This paper deals with an economic production quantity (EPQ) model with imperfect items and backordered demand. The manufacturing system is imperfect and generates a fraction of imperfect items, which is a random variable with a distribution function known. All manufactured items are screened and the imperfect items are identified. The rework of imperfect items cannot be done in the same manufacturing system. The company decides to outsource the rework in a repair store. Therefore, after the screen period all imperfect items are withdrawn and sent to the repair store; and at the end of the reparation process all the repaired items come back to the company and are received by the inventory. There are three cases that can occur depending on when the repaired items enter the inventory. Numerical examples and sensitivity analysis are presented to show the applicability of the three cases of the proposed inventory model.

Multi-item fuzzy economic production quantity model with multiple deliveries

Inventory control is one of the most critical issues in corporate management. Many mathematical models have been developed to optimize control strategies for the companies’ inventory. Economic production quantity (EPQ) is one of the classic models for inventory control, which is widely used. To deal with the uncertainty in the real world, we need to develop new and useful models for modeling systems of inventory management. In such cases, fuzzy models play a unique role in the field of inventory management. The main contribution of this study is to apply some well-known metaheuristic to solve an extended EPQ model based on fuzzy numbers considering multiple deliveries. This study aims to develop an EPQ model by considering demand as triangular fuzzy numbers and multiple deliveries (delivering in multiple packages) and by considering limitations in warehouse space as well as the total number of orders. Given these conditions, EPQ costs are calculated, and new modeling is presented. The obtained fuzzy model has been simplified by using the $$ \alpha{\text{-cut}} $$ and changing the variables, and finally, the most well-known metaheuristic algorithms, GA, PSO, GWO, and ICA, are applied in different problem sizes, and obtained results are analyzed in terms of minimizing cost function and CPU time. The result of this paper shows that GWO has superior performance in terms of various parameters.

An EPQ inventory model considering an imperfect production system with probabilistic demand and collaborative approach

PurposeThe purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team.Design/methodology/approachTwo approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain.FindingsA numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain.Originality/valueThe new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

The Simultaneous Effect of Holding Safety Stock and Purchasing Policies on the Economic Production Quantity Model Subject to Random Machine Breakdown

In this paper, we develop an economic production quantity (EPQ) model under machine breakdown and two types of repair (corrective and preventive). also, study the simultaneous effect of holding safety stock and purchasing policy. In order to avoid shortages occurring as a result of the random repair time, in addition to keep safety stock, we suppose that the manufacturer could purchase some quantities from an external supplier. This paper addresses the following question: how the manufacturer determine the optimal values of safety stock, production and purchasing lot sizes, simultaneously, to minimize the expected total cost? The introduced model is then compared with the situations in which the manufacturer only keeps safety stock or just uses an external supplier, respectively. The results through the analysis show that using the simultaneous policy when the system is prone to shortages due to long repair times, have more improvement in the performance of the system rather than using the safety stock or purchasing policies, separately.

The Supplier-retailer Optimal Replenishment Decisions Under a Two-level Trade Credit Model with Shortage for Deteriorating Items

This paper establishes an integrated inventory model of a supplier and a manufacturer under a two-level trade credit contract. The manufacturer's inventory model follows the economic production quantity model and the produced items follow exponentially deterioration rate and price-dependent demand. Shortages are allowed for the manufacturer and are completely backlogged to the next period. Traditional inventory system and one-level trade credit are also concluded as special cases of the developed two-level trade credit model and the supply chain performance under these three policies are compared. The formulated models aim at helping the supply chain decision makers to determine the best delay strategy and find the optimal values for replenishment policy and the manufacturer's selling price in order to maximise the supply chain total net profit. The results have been then validated with a numerical example and the effect of various parameters on the optimal solution is finally studied by performing sensitivity analysis.

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

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.

An analysis of multi-item inventory model using particle swarm optimization under discrete delivery orders and limited storage space

This study explores an economic production quantity (EPQ) model designed with the assumptions of discrete delivery orders and storage capacity constraints for a multi-item production inventory system. The main purpose of this study is to determine the optimal order quantity, the optimal number of deliveries and the optimal delivery quantity. First, the developed model as part of this study was analyzed using Genetic Algorithm (GA). Numerical analysis results were compared with those of previous studies and it was found that it is possible to have better results with an increasing number of iteration. The same model was then analyzed using Particle Swarm Optimization (PSO) algorithm. A comparison of the optimization methods showed that PSO gives better results over the GA under the same number of iterations and using the same population. The effects of important model parameters such as number of iterations, population, crossover, mutation rate on the optimal solution were analyzed. The results showed that PSO performs better than the GA with respect to the total cost and the total runtime as the solution of the problem in question.

Optimization of imperfect economic manufacturing models with a power demand rate dependent production rate

The constant demand rate is the most common assumption of the basic economic production quantity model, which is not very frequent in practice. In real world situations, demand usually varies with time. With regard to the widespread necessity of power demand pattern, demand is supposed to follow a power law. Another unrealistic assumption is perfect quality of all items. This paper presents a production system with defective items to determine the optimal replenishment quantity, cycle length and backordered size with a power demand rate dependent production rate. We assume that a manufacturer may be faced with three different cases regarding to the date that defective items are drawn from inventory. The set-up, backordering, inspection, and production costs, as well as holding cost of both perfect and imperfect items are accounted in the inventory system. An algorithm is offered to optimize total inventory cost and then numerical analyses are presented to demonstrate the applicability of the proposed models. Finally, some sensitivity analyses and managerial insights are provided.