Economic Production Quantity Model Research Articles

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.

An integrated stochastic EPQ model under quality and green policies: generalised cross decomposition under the separability approach

ABSTRACT In this paper, a bi-objective multi-product constrained and integrated economic production quantity model is designed by considering the quality control and green production policies. The aforementioned model comes with stochastic constraints. Moreover, to create a kind of green approach policy, tax cost of greenhouse gas emissions and limitations are considered. The aim of this study is to optimise the total inventory cost and the total profit, while the stochastic constraints are satisfied. Due to the inconsistency of objectives, an Lp-metric function is utilised to integrate and achieve a single objective function. Therefore, the mathematical formulation of the problem is bi-objective stochastic mixed integer nonlinear programming large scale and hard to solve. Accordingly, generalised cross decomposition under the separability approach is utilised as an effective algorithm for global optimisation. Moreover, sensitivity analysis revealed that increasing the cost function weight versus decreasing the profit function weight leads to the change rate of the integrated-objective function becomes positive with a steep slope.

Optimal pricing and ordering policies for perishable products under advance-cash-credit payment scheme

Recently, market globalization and competition have forced companies to find alternative means to boost sales and revenue. The use of the cash flow is increasingly becoming a viable alternative for managers to improve their company’s profitability in a supply chain. In today’s business transactions, a supplier usually asks a manufacturer to pay via the advance-cash-credit (ACC) payment scheme if the number of goods procured is high. Additionally, product perishability has been considered in an economic production quantity (EPQ) model since it is a real phenomenon. The present work develops an EPQ model for perishable products under the ACC payment scheme. The objective of the proposed model is to determine the optimal selling price and cycle time while maximizing profit under the ACC payment scheme using a discounted cash flow analysis. A nonlinear optimization algorithm is also proposed to solve the problem. In addition, some numerical examples are employed to illustrate the solution approach and show the concavity of the present value of the total annual profit in terms of both selling price and cycle time. The numerical results show that our proposal algorithm could be applied well to solve the problems. In addition, a sensitivity analysis is conducted to obtain some managerial insights. For example, if the impact of advance payment on procurement cost is relatively smaller than that of cash payment, then it is more profitable for the manufacturer to ask for a cash payment than to receive an advance payment and vice versa.

Model Economic Production Quantity dengan Rework Process dan Batasan Gudang

Rework products and warehouse capacity are common problems experienced by companies in the production process. Several Economic Production Quantity (EPQ) models were developed to minimize the costs of purchasing raw materials. This study aims to develop an Economic Production Quantity (EPQ) model with rework processes and warehouse constraints, assuming that the product is not perfect and can rework. The proposed model considers several cost components, including setup, holding, production, rework, and warehouse. The two proposed models are EPQ models with reworks and warehouse costs, and EPQ models with reworks and warehouse constraints. Based on several tests conducted, it obtains that the increase in the value of the maximum inventory amount did not have an impact on the production costs and the cost of the rework process. Based on several numerical experiments, the total cost of the rework process and production costs do not change to the maximum inventory value.

Optimizing profit for pricing and advertisement sensitive demand under unreliable production system

ABSTRACT This article deals with an imperfect economic production quantity (EPQ) model with an unreliable production system where the customers' demand depends on both selling price and advertisement. During the long run production process the machinery system goes into ‘out-of-control’ state after a random time τ and after that the system produces both perfect and imperfect quality items together. The imperfect or defective quality items are reworked to get it back as the perfect ones at a cost just after the regular production run time. The production process of imperfect quality items depends on the reliability of the machinery system where the failure rate may be variable. Here, we consider that the random time variable τ follows the two parameters ‘Weibull distribution’. The objective of this article is to maximize the expected average profit function of the unreliable system with respect to ordering lot size, selling price and frequency of advertisement. We use the incomplete gamma function to formulate the expected average profit function. The model is validated by numerical examples and sensitivity analysis is provided to illustrate the model.

A deteriorating inventory model for determining optimal replenishment run time with failure rework and shortage

Many researchers focused on economic production quantity model for defective/deteriorating items under the assumptions (a) all the defective items can be reproduced as serviceable items (b) all the deteriorating items can be detached from inventory through screening process (c) shortages are not permitted. In an actual manufacturing environment, due to controllable or uncontrollable factors, some of the defective items may not be reproduced as serviceable items and due to human error or other factors, the internally deteriorated items may pass on to customers which will make negative impact on corporate image. This paper investigates an imperfect production inventory model with imperfect inspection of deteriorating items and failure rework under finite planning horizon. This system consists of m replenishment runs with failure rework and shortage. The main objective is to determine the optimal replenishment run time, optimal economic production quantity and optimal replenishment cycle time with the aim of minimising the total cost of the model. A solution procedure with an algorithm is proposed and a numerical example is provided to the theoretical results and to highlight the managerial insights.

Low Carbon Economic Production Quantity Model for Imperfect Quality Deteriorating Items

This paper presents an economic production quantity (EPQ) model for deteriorating items with a certain percentage of defective products due to an imperfect process. The defective products are sold to a secondary market at a discount price. Due to environmental concern and carbon tax regulation, the manufacturer incorporates the control of carbon emission cost into its decision model. Carbon emission cost is a function of electricity consumption during production and inventory storage; it is also dependent on the carbon tax rate. Since the production process results in work-in-process inventory and carbon emission, the study tries to optimize the throughput time. We also examine the effect of carbon tax regulation on the potential emission reduction from the developed deteriorating item model. A numerical example and sensitivity analysis have been provided, and the result confirms the influence of carbon tax regulation in reducing carbon emission.

Multi-objective economic production quantity model for fully backlogged problem where demand depend on some conditions and permissible delay in payment

For any business, inventory system takes a monumental part. Keep this aspect in mind, we formulate multi-objective displayed EPQ model consider with non-instantaneous deteriorating things where production depends on demand and variable demand pattern depends on display self-space, selling price and frequency of advertisement of the item. The customers are more attracted to buy an item by observing self-space, selling price and advertisement. Imperfect materials are now and again come back to providers for a discount or credit. Here price discount is available for deteriorated and defective items. Holding cost varies with time where shortages are allowed and fully backlogged. Fuzzy environment touches the reality instead of the crisp environment. So, we assumed the cost components as Triangular Fuzzy Numbers and Nearest Interval Approximation Method is used to defuzzify the model. Finally, numerical examples as well as sketches are given to illustrate the model.

Manufacturer's pricing and lot-sizing decisions for perishable goods under various payment terms by a discounted cash flow analysis

In practice, a cash payment is a classical payment term, a credit payment is commonly applied to stimulate sales, and an advance payment is used to avoid order cancellations. A combination of these three payment types is considered an advance-cash-credit (ACC) payment scheme, which is commonly used in business transactions. For instance, a home buyer must pay a homeowner 1% of the listing price as a good-faith deposit (i.e., an advance payment) to start negotiating the price, then pay 10% of the agreed-upon price (i.e., a cash payment) when signing the contract, and then has a delay before the final payment (i.e., a credit payment, a mortgage) is approved. In this paper, we develop an economic production quantity (EPQ) model for perishable goods in a three-echelon supplier-manufacturer-customer chain: (1) demand rate depends on selling price and freshness of a perishable item (i.e., time to sell-by date), and (2) the supplier offers an upstream ACC payment to the manufacturer, while the manufacturer grants a downstream cash-credit payment to customers. Consequently, the manufacturer must determine optimal selling price, production run time, and replenishment cycle time to maximize the present value of total annual profit by using a discounted cash flow (DCF) analysis. The proposed model fits in a general framework that includes numerous previous models as special cases. The numerical results reveal that the present value of total profit is joint concave in both selling price and cycle time. Finally, a sensitivity analysis is performed and managerial insights are also provided.

Extended Economic Production Quantity Models with Preventive Maintenance

This paper generalizes the standard economic production quantity (EPQ) model in process manufacturing industry by incorporating regular preventive maintenance (PM) activities into classic EPQ model. The PM program improves the condition of the production to an acceptable level, and avoids potential stoppages and disruptions, hence, it is a vital task in every production process. However, the standard EPQ model does not consider PM activities and then is not applicable to real-world situations. We consider manufacturer which produces a product under EPQ setting with a defective production process, in which every production cycle involves a number of sub-production cycles. Two models are proposed, based on the disposal time of defective items, to determine optimal number of sub-production cycles. In model I, the disposal of defective items is performed once per cycle at the end of each production cycle, while in model II, the disposal of defective items is performed multiple times per cycle, at the end of each sub-production cycle. The total cost functions are derived for each model separately, and then simple solution algorithms are designed. A numerical example is presented and discussed to evaluate proposed models. The results illustrate that model II is more cost effective than model I.

Multi-constraints in an integrated inventory model with learning and screening errors under greenhouse gas emissions

An inventory model is developed for an economic production quantity model with learning in production and screening errors under greenhouse gas emissions. The main contribution of this paper is determining an optimal vendor–buyer inventory policy by accounting quality inspection errors at the buyer's end and learning in production at the vendor's end and also considering the Government's penalty and incentive policies to reduce the emission. The buyer warehouse has limited capacity and there is an upper bound on the purchase of products. Moreover, we consider the ordering cost is reduced by an extra investment. Also to find an optimal policy of the proposed mathematical model, a genetic algorithm is established. Numerical examples and sensitivity analysis are shown to illustrate the models.

Imperfect economic production quantity models under predictive maintenance and reworking

Due to the popularity of Industry 4.0, many companies have begun to develop intelligent production systems and perform predictive maintenance. These innovations monitor production systems by using sensors and data analysis, and they maintain production systems before they become ‘out of control'. This paper develops imperfect economic production quantity (EPQ) models that consider predictive maintenance and reworking of defective products. The objective is to determine the optimal predictive maintenance effort and production runtime and minimise the total expected cost. Two situations are considered: (1) the production system continuously producing products when it shifts to the out-of-control state and (2) the production system stops producing when it shifts to the out-of-control state. We formulate the cost functions and provide algorithms to solve the problems. A numerical study is conducted to illustrate our models and the solution procedure. We also discuss the influence of system parameters (such as predictive and corrective maintenance costs) on the predictive maintenance effort and production runtime decisions and total cost. The results could be used by managers as a reference when consider imperfect economic production quantity models under predictive maintenance and reworking.

Development of EPQ Model with Time Induced Demand Under Reduction Delivery

In this paper production inventory model with integrates cost reduction delivery policy is considered. Production and demand both are simultaneous process in factual globe Production and demand rate are considered to be time-linked. Two model (i) production inventory and (ii) production inventory model with integrating cost reduction cost delivery policy. The mathematical formulations are provided to find optimal solution for both models. Purpose of this learning is to obtain optimal order quantity and to investigate the effect of reduction of cost delivery policy in the EPQ (Economic Production Quantity) model, optimal production extent model is developed which minimizes the total cost. The sensitivity analysis is discussed for the variation of different parameters

Delayed payment policy in multi-product single-machine economic production quantity model with repair failure and partial backordering

This study develops a single-machine manufacturing system for multi-product with defective items and delayed payment policy. Contradictory to the literature limited production capacity and partial backlogging are considered for more realistic result. The objective of this research is to obtain the optimal cycle length, optimal production quantity, and optimal backorder quantity of each product such that the expected total cost is minimum. The model is solved analytically. Three efficient lemmas are developed to obtain the global optimum solution of the model. An improved algorithm is designed to obtain the numerical solution of the model. An illustrative numerical example and sensitivity analysis are provided to show the practical usage of proposed method.

Production models of multiple products using a single machine under quality screening and reworking policies

PurposeThe purpose of this study is to formulate two multi-product single-machine economic production quantity (EPQ) models by considering imperfect products. Two policies are assumed to deal with imperfect products: selling them at discount and applying a reworking process.Design/methodology/approachA screening process is used to identify imperfect items during and after production. Selling the imperfect items at a discount is examined in the first model and the reworking policy in the second model. In both models, demand during the production process is satisfied only by perfect items. Data collected from a case company are used to illustrate the performance of the two models. Moreover, a sensitivity analysis is carried out by varying the most important parameters of the models.FindingsThe case study in this research is used to demonstrate the applicability of the proposed models, i.e. the EPQ model with salvaging and reworking imperfect items. The models are applied to a high-tech un-plasticized polyvinyl chloride (UPVC) doors and windows manufacturer that produces different types of doors and windows. ROGAWIN Co. is a privately owned company that started in 2001 with fully automatic production lines. Finally, the results of applying the different ways of handling the imperfect items are discussed, along with managerial insights.Originality/valueIn real-world production systems, manufacturing imperfect products is unavoidable. That is why, it is important to make a proper decision about imperfect products to reduce overall production costs. Recently, applying a reworking strategy has gained the most interest when it comes to handling this problem. The principal idea of this research is to maximize the total profit of manufacturing systems by optimizing the period length under some capacity constraints. The proposed models were applied to a company of manufacturing UPVC doors and windows.