Traditional Economic Production Quantity Research Articles

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.

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.

Optimal Economic Production Quantity Policies Considering the Holding Cost of Deteriorating Raw Materials under Two-Level Trade Credit and Limited Storage Capacity

The traditional economic production quantity (EPQ) model assumes that raw materials are supplied timely. But during the production and transport process of raw materials could change the holding cost of raw materials, therefore, they should be considered in the total relevant cost. [1] combined [2]’s concept of holding cost of raw materials and [3]’s two-level trade credit and limited storage capacity model to develop innovative and detailed EPQ model that consider the holding cost of non-deteriorating raw materials. It’s closer to the real world. However, in reality, most of the raw materials are deteriorating; it also needs to be considered. Therefore, this research extends [1]’s model to consider the holding cost of deteriorating raw materials. We use cost minimization to develop the total relevant cost and determine the optimal cycle time by four theorems. Finally, we use sensitivity analyses to investigate the effects of the parameters on ordering policies.

EPQ Policies Considering the Holding Cost of Raw Materials with Two-Level Trade Credit under Alternate Due Date of Payment and Limited Storage Capacity

The traditional Economic Production Quantity (EPQ) model focused on production process, used the ordering cost that includes relevant costs during the pre-production process. But, the ordering cost comprises the holding of raw materials that would affected by other factors would increase the total relevant cost, it cannot simply use the ordering cost to cover all. Therefore, this paper presents a new inventory model by considering the holding of raw materials under conditions of two-level trade credit under alternate due date of payment and limited storage capacity. According to cost-minimization strategy it develops four theorems to characterize the optimal solutions. Finally, it executes the sensitivity analysis and investigates the effects of the parameters in the annual total relevant costs.

이중생산속도를 가지는 생산시스템에서 확률적인 수요와 주문취소를 고려한 경제적 재고량 결정

We consider the problem to find economic inventory quantity of a single commodity under stochastic demands and order cancellation. In contrast to the traditional economic production quantity (EPQ) model, we assume that once the amount of inventory reaches to a predetermined level of quantity then the production is not halted but its production speed decreases until the inventory level drops to zero. We establish two probabilistic models representing the behaviors of both the high-production period and low-production period, respectively, and derive the relationship between the level of inventory and costs of production, cancellation, and holding, from which the quantity of economic inventory is obtained.

The EPQ model under conditions of two levels of trade credit and limited storage capacity in supply chain management

An inventory problem involves a lot of factors influencing inventory decisions. To understand it, the traditional economic production quantity (EPQ) model plays rather important role for inventory analysis. Although the traditional EPQ models are still widely used in industry, practitioners frequently question validities of assumptions of these models such that their use encounters challenges and difficulties. So, this article tries to present a new inventory model by considering two levels of trade credit, finite replenishment rate and limited storage capacity together to relax the basic assumptions of the traditional EPQ model to improve the environment of the use of it. Keeping in mind cost-minimisation strategy, four easy-to-use theorems are developed to characterise the optimal solution. Finally, the sensitivity analyses are executed to investigate the effects of the various parameters on ordering policies and the annual total relevant costs of the inventory system.

Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging

The traditional economic production quantity (EPQ) model assumes that the production products are all perfect. It is not always true in the real production system, due to imperfect production process or other factors, imperfect quality items may be produced. Furthermore, it is well-known that the total production-inventory costs can be reduced by reworking the imperfect quality items produced with a relatively smaller additional reworking and holding costs. In addition, the permissible delay in payments offered by the supplier is widely adopted in the practical business market. In this study, we explore the effects of the reworking imperfect quality items and trade credit on the EPQ model with imperfect production processes and complete backlogging. A mathematical model which includes the reworking and shortage costs, interest earned and interest charged is presented. Besides, an arithmetic-geometric mean inequality approach is employed and an algorithm is developed to find the optimal production policy. Furthermore, some numerical examples and sensitivity analysis are provided to demonstrate the proposed model.

An EPQ Model with Unit Production Cost and Set-Up Cost as Functions of Production Rate

Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where unit production and set-up costs must be considered as functions of production rate. In this paper, we address the problem of determining the optimal production quantity and rate of production in which unit production and set-up costs are assumed to be continuous functions of production rate. Based on the traditional economic production quantity (EPQ) formula, the cost function associated with this model is proved to be nonconvex and a procedure is proposed to solve this problem. Finally, utility of the model is presented using some numerical examples and the results are analyzed.

The Optimal Inventory Policy of Production Management

The traditional Economic Production Quantity (EPQ) assumes that the replenishments are instantaneous and the relevant cost only consists of setup cost, stock-holding cost of the finished goods and the purchasing cost of raw materials. As a manager of a manufactory, there is a problem that must be taken into consideration. If the establishment buys all of the raw materials at the beginning, the stock-holding cost for the raw materials should be accounted into the relevant cost. The main purpose of this paper will add the stock-holding cost of raw materials to the EPQ model. Base on this new modified EPQ model, two more useful models are established. One of the new models contains the reusable raw materials instead of the raw materials. The other one considers the stock-holding cost of the raw materials and the imperfect-quality items are considered. We present the optimal cycle length from each of these three models.

Production system with process quality control: modelling and application

Over the past decade, there has been a great deal of research dedicated to the study of quality and the economics of production. In this article, we develop a dynamic model which is based on the hypothesis of a traditional economic production quantity model. Taguchi's cost of poor quality is used to evaluate the cost of poor quality in the dynamic production system. A practical case from the automotive industry, which uses the Six-sigma DMAIC methodology, is discussed to verify the proposed model. This study shows that there is an optimal value of quality investment to make the production system reach a reasonable quality level and minimise the production cost. Based on our model, the management can adjust its investment in quality improvement to generate considerable financial return.

Optimal pricing and production lot-sizing for seasonal products over a finite horizon

In day-to-day time-based competition, the unit selling price of a hightech product declines significantly over its short life cycle. In this paper, we introduce dynamic pricing to traditional Economic production quantity (EPQ) models for time and price sensitive products. From manufacturer/producer point of view, the model is developed to maximise total profit. We prove that the total profit is a concave function of selling price within fixed planning horizon. A solution procedure is presented to determine optimal prices, optimal number of production cycles, optimal lot size and optimal profit simultaneously. We illustrate the model with numerical examples and sensitivity analysis is also performed.

AN ECONOMIC PRODUCTION LOT SIZE FOR CONTINUOUS DECREASE IN UNIT PRODUCTION COST

It is common that prices of raw materials, parts or products decrease significantly after they come onto the market. High technology products are good examples, such as PCs, CPUs, DRAM, and mobile phones. Consequently, the traditional economic production quantity (EPQ) model assuming a constant unit production cost is no longer suitable for today's time-based competition. This study incorporates linearly and exponentially decreasing unit production costs during the mature stage of a product life cycle and presents a mathematical inventory model for production policy. A recursive algorithm is developed to obtain the optimal production schedule and a one-dimension search method is applied to find the optimal number of production cycles. In addition, numerical examples to illustrate the proposed model and its significance with or without considering a continuous reduction in unit production costs for the production policy are discussed as well.

Deterministic economic production quantity models with time-varying demand and cost

In today’s time-based competition, the unit cost of a high-tech product declines significantly over its short product life cycle. Consequently, in this paper, we relax the traditional economic production quantity model to allow for time-varying cost. We then prove that the optimal production schedule uniquely exists. In addition, we also show that the total cost is a convex function of the number of replenishments, which reduces the search for the optimal solution to finding a local minimum. Furthermore, we characterize the influences of both demand and cost over the length of production run time and the economic production quantity.