The basic EPQ models with non-instantaneous deteriorating items: modelling and optimal policy

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.

To analyze the effects of activity-based costing (ABC) on the economic production quantity (EPQ) model in production-inventory system, a new EPQ model based on ABC is developed in this paper. In the new model, based on ABC perspectives, we analyze the cost drivers other than conventional ones specified in the production-inventory system, and then revise the cost functions according to these cost drivers. In this paper, numerical examples are also given to illustrate the new model by comparing with the classical EPQ model. The results show the new model is more effective than the classical EPQ model in cost control.

Joint determination of rotation cycle time and number of shipments for a multi-item EPQ model with random defective rate

This paper derives an inspection policy for an economic production quantity (EPQ) model under the assumption that a process may produce non-conforming (NC) items. In various stages of a production process, a department receiving an order uses a single sampling inspection policy to detect NC items. Under such a policy, a lot is accepted if the number of NC items in the inspected sample is equal to or less than the acceptance number. The proposed model considers both EPQ- and quality-related costs. Moreover, economic production order quantity, sample size and acceptance number are considered decision variables. A numerical example is presented, and a set of sensitivity analysis are provided to highlight the effectiveness of the proposed model. The results reveal that when the inspection cost is high, the classical EPQ model achieves a lower expected total cost for the production system compared with the EPQ model with the inspection. In contrast, when the NC cost is high, the EPQ model with the inspection policy outperforms the classical EPQ model, which can significantly decrease the expected total cost.

ABSTRACTThis paper extends an economic production quantity (EPQ) model for deteriorating items when the delivery policy is based on multiple shipments. A continuous inventory policy for satisfying demand has been considered in the classic EPQ model. While in an integrated production–inventory–delivery system, the multi-shipment approach is actually used instead of the continuous issuing policy. On the other hand, the EPQ model has not been developed for deteriorating items with multiple shipments. This paper considers the time-varying deterioration rate and finds optimal replenishment lot size which minimises the long-run average cost function after proving its convexity. Finally, mathematical modelling and analysis are employed for a laboratory kit production system. Then, impact factors which can modify total cost are recognised and optimal replenishment lot size, as well as optimal quantity of each shipment, is found in different situations.

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.

Economic production quantity (EPQ) models are traditionally used in operations management. Despite the large number of papers that describe the models, the classic EPQ model does not consider either imperfect quality batches or shortages. However, some industries may be able to sell imperfect items for a lower price, reducing the total production cost. This paper proposes an EPQ model with partial backordering and discount for imperfect quality batches and an algorithm that returns optimal values for the problem. From a numerical example, it is possible to analyse how the changes in the variables affect each part of the total cost function, which provides a useful tool for strategic decision-making. We conclude that it is better to sell imperfect items as soon as possible because the savings in holding costs results in a total cost reduction. It is more profitable for the producer to have planned shortages considering that some costumers are willing to wait. Furthermore, the reduction of the goodwill cost does not necessarily reduce the total cost.

The objective of this work is to study the optimal policy of the classical economic production quantity (EPQ) model under interval uncertainty using interval inequality. To serve this purpose existing arithmetic mean-geometric mean (AM-GM) inequality is extended for interval numbers using c-L interval order relation. Then, using the said AM-GM interval inequality, the optimal policy of the classical EPQ model in the interval environment is developed. Thereafter, the optimality policy of the classical EPQ model in a crisp environment is obtained as a special case of that of the interval environment. Finally, all the optimality results are illustrated with the help of some numerical examples.

This paper is concerned with determining the optimal common production cycle policy for a multi-item economicproduction quantity (EPQ) model with scrap, rework and multiple deliveries. The classic EPQ model considers theoptimal replenishment quantity of single product under a perfect production assumption and a continuous inventoryissuing policy. However, in real life production planning, manufacturing firms often plan to have multiple productsmade in turn on a single machine in order to maximize the machine utilization. Also, dealing with random defectiveitems during the production run seems to be an inevitable task, and the multi-delivery policy is commonly adopted fordistributing finished items to customers. In this study, we assume a portion of nonconforming items is scrap and theother portion of them can be reworked and repaired in the same production cycle with additional cost. The objective isto determine an optimal common production cycle time that minimizes the long-run average cost per unit time for sucha specific multi-item EPQ model with scrap, rework and multi-delivery policy. Mathematical modeling and analysis isused and a closed-form optimal common cycle time for multi-item production planning is obtained. A numericalexample is provided to demonstrate the practical usage of research result.

The classic economic production quantity (EPQ) model has been widely used to determine the optimal production quantity. However, the analysis for finding an EPQ model has many weaknesses which lead many researchers and practitioners to make extensions in several aspects on the original EPQ model. The basic assumption of EPQ model is that 100% of manufactured products are non-defective that is not valid for many production processes generally. The purpose of this paper is to develop an EPQ model with grey demand rate and cost values with maximum backorder level allowed with the good quality items in units under an imperfect production process. The imperfect items are considered to be low quality items which are sold to a particular purchaser at a lower price and, the others are reworked and scrapped. A mathematical model is developed and then an industrial example is presented on the wooden chipboard production process for illustration of the proposed model.

Determining the optimal replenishment lot size and shipment policy for a production setup has been of greater interest during the last few years. This paper derives the optimal replenishment lot size and shipment policy for an Economic Production Quantity (EPQ) model with rework of defective items. However, in a real life situation, multi-shipment policy is used in lieu of continuous issuing policy and generation of defective items is inevitable. The proposed research assume that all imperfect quality items are reworked to perfect quality items and then all perfect quality items are delivered to the customers. Mathematical modeling is used in this study and the long-run average production–inventory-delivery cost function is derived. Convexity of the cost function is proved by using the Hessian matrix equations. The closed-form optimal replenishment lot size and optimal number of shipments that minimize the long-run average costs for such an EPQ model are derived.

This dissertation is on inventory management and supply chain coordination mechanisms within an economic order quantity framework. Specifically, this research focuses on modeling optimal order policies and coordination mechanisms for a supply chain involving items which experience probabilistic failure during storage. These items are common types of manufactured items which, nonetheless, require specialized order policy considerations due to their unique characteristics. We first develop the solution for the buyer's problem through the use of an economic order quantity (EOQ) model incorporating item failure. We then proceed to model the manufacturer's problem through the use of an economic production quantity (EPQ) model. Finally, we consider mechanisms to promote mutually-beneficial cooperation between the supplier and n buyers in service of coordinating the entire supply chain. While prior research has focused on items which can be repaired or sold at a discount upon failure, such models are inappropriate for systems where repair costs exceed or are equivalent to item costs and imperfect items are unacceptable. Examples of industries featuring these inventory conditions include the medical, defense, and electronics industries where defective items are largely useless. First, our EOQ model considers a buyer-supplier relationship featuring delivery and stocking of items which experience probabilistic failure in storage. Thereafter, our EPQ model considers in-house production of such items. Collectively, our EOQ and EPQ models provide methods for developing optimal order policies necessary to achieve practicable supply chain coordination. In order to validate the necessity of the developed models, we include an empirical analysis of item reliability for some common mechanical components used in the defense industry, thereby identifying items which fail in the manner modeled in this dissertation. Having considered optimal order policies for both buyers and suppliers, we next develop an optimal solution for a coordinated supply chain. The proposed solution allows the manufacturer to coordinate a supply chain consisting of n buyers in order to achieve a common replenishment time. Through this optimization framework, we minimize total system-wide costs and derive the cost savings associated with our coordinated solution. Numerical examples are then used to demonstrate the magnitude of cost savings achievable through our coordination framework. We conclude by proposing several mechanisms for leveraging the resulting cost savings to induce mutually-beneficial cooperation between the supplier and multiple buyers. Given the lack of buyer-supplier cooperation noted in empirical research related to supply chain coordination, our identification of specific mechanisms useful for inducing mutually-beneficial cooperation between buyers and suppliers represents an important practical contribution to the supply chain coordination literature. These models are accompanied by a thorough overview and discussion of economic order quantity theory, optimal order policies, and supply chain coordination mechanisms.

Determining replenishment lot size and shipment policy for an extended EPQ model with delivery and quality assurance issues

A great deal of research has been done on economic production quantity (EPQ) model, which concern deterministic or stochastic or fuzzy demand and cost situations. In this paper, the EPQ model with imprecise demand and production preparation time is considered which are characterized as independent fuzzy variables rather than fuzzy numbers as in previous studies. Based on an expected value criterion or a credibility criterion, a fuzzy expected value model (EVM) is constructed. The purpose of the fuzzy EVM is to determine the optimal policy such that the fuzzy expected value of the total cost is minimal. In order to obtain the exact expected value directly, instead of relying on simulation procedure, the results for uncertain variables with uncertainty distribution are exploited by treating them as fuzzy variables with credibility distribution. The mathematical analysis is carried out to compute exact expected values. Numerical study is also provided to demonstrate the contribution of our model.

The traditional economic production quantity (EPQ) model assumes that during the production process no imperfect item is produced. But 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 smaller additional reworking and holding costs. In addition, the permissible delay in payments offered by the supplier is widely adopted in the businesses. In this study, we explore the effects of both reworking imperfect quality items and trade credit policy on the EPQ model with imperfect production processes and backlogging. A mathematical model considering reworking and shortage costs, interest earned and interest charged in addition to traditional inventory costs is developed. Besides an arithmetic-geometric mean inequality method 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 applicability of proposed model.