Deterministic ordering policy with price- and stock-dependent demand under fluctuating cost and limited capacity

In this paper, we extend the classical economic order quantity model to allow for the demand rate influenced by both selling price and displayed stock level. A finite period system is considered under inflation for deteriorating items. In addition, we impose a ceiling on the number of on-display stocks. We also allow for shortages and general partial backlogging. The objective is to maximize the discounted total profit by finding the optimal replenishment number, replenishment schedule and selling price changed periodically. An effective search procedure is provided to find the optimal solution by employing the properties derived in this paper and particle swarm optimization algorithm. Several numerical examples are used to illustrate the features of the proposed model.     

Optimal manufacturer's pricing and lot-sizing policies under trade credit financing

In this paper, we extend Goyal's economic order quantity (EOQ) model to allow for the following four important facts: (1) the manufacturer's selling price per unit is necessarily higher than its unit cost, (2) the interest rate charged by a bank is not necessarily higher than the manufacturer's investment return rate, (3) the demand rate is a downward‐sloping function of the price, and (4) an economic production quantity (EPQ) model is a generalized EOQ model. We then establish an appropriate EPQ model accordingly, in which the manufacturer receives the supplier trade credit and provides the customer trade credit simultaneously. As a result, the proposed model is in a general framework that includes numerous previous models as special cases. Furthermore, we provide an easy‐to‐use closed‐form optimal solution to the problem for any given price. Finally, we develop an algorithm for the manufacturer to determine its optimal price and lot size simultaneously.     

Economic production quantity (EPQ) models under an imperfect production process with shortages backordered

In this paper, we develop economic production quantity (EPQ) models to determine the optimal production lot size and backorder quantity for a manufacturer under an imperfect production process. The imperfect production process is characterised by the fraction of defective items at the time of production γ. The paper considers different cases of the EPQ model depending on (1) whether γ is known with certainty or is a random variable, and (2) whether imperfect items are drawn from inventory (a) as they are detected, (b) at the end of each production period or (c) at the end of each production cycle. Straightforward convexity results are shown and closed-form solutions are provided for the optimal order and backorder quantities for each of the cases we considered. We provide two numerical examples: one in which the defective probability follows a uniform distribution and the second which we assume follows a beta distribution, to illustrate the effects of yield variability and timing of the withdrawal of defectives on the optimal solutions. We obtain similar results for both numerical examples, which show that both the yield variability and the withdrawal timing are not critical factors.     

An economic production quantity model for deteriorating items with preventive maintenance policy and random machine breakdown

In recent years, many researches on economic production quantity (EPQ) models with machine breakdown and preventive maintenance have been developed, but few of them have developed integrated models for deteriorating items. In this study, we develop EPQ models for deteriorating items with preventive maintenance, random machine breakdown and immediate corrective action. Corrective and preventive maintenance times are assumed to be stochastic and the unfulfilled demands are lost sales. Two EPQ models of uniform distribution and exponential distribution of corrective and maintenance times are developed. An example and sensitivity analysis is given to illustrate the models. For the exponential distribution model, it is shown that the corrective time parameter is one of the most sensitive parameters to the optimal total cost.     

An integrated production-inventory-marketing model for deteriorating items

Generally, inventory control policies for deteriorating items are very sensitive to different marketing policies especially in chemical, food and pharmaceutical industries. Realizing the importance of such inventory policies in practice, an integrated production-inventory-marketing model is developed for determining the economic production quantity (EPQ) and economic order quantity (EOQ) for raw materials in a multi-stage production system. This model considers the effect of different marketing policies such as the price per unit product and the advertisement frequency on the demand of a perishable item. A search method is employed to determine the values of EPQ and EOQ which would result in the maximum total net profit.     

Economic production quantity models for deteriorating/imperfect products and service with rework

In this paper, two economic production quantity (EPQ) models are proposed for deteriorating/imperfect items with rework process. The production process is imperfect, and imperfect quality items are reworked to become serviceable. At the same time, the remaining good quality items may deteriorate. The inspection of deteriorated items is also imperfect, so that deteriorated items may be sold to customers, which will create negative impact on corporate image. In the first model, a single production-rework plant system is considered. The optimal production times and the economic production quantities are obtained analytically. In the second model, a system that consists of n production plants and one rework plant is considered. A solution procedure is developed in order to obtain the optimal operating cost. Numerical examples are provided to compare the performance of the two systems.     

Economic production quantity model for items with continuous quality characteristic,rework and reject

The economic production quantity (EPQ) model is a well-known and commonly used inventory control technique. However, the model is built on an unrealistic assumption that all the produced items need to be of perfect quality. Having relaxed this assumption, some researchers have studied the effects of the imperfect products on the inventory control techniques. This article, thus, attempts to develop an EPQ model with continuous quality characteristic and rework. To this end, this study assumes that a produced item follows a general distribution pattern, with its quality being perfect, imperfect or defective. The analysis of the model developed indicates that there is an optimal lot size, which generates minimum total cost. Moreover, the results show that the optimal lot size of the model equals that of the classical EPQ model in case imperfect quality percentage is zero or even close to zero.     

Economic production quantity model with a shifting production rate

Typical models for determining the economic production quantity (EPQ) assume perfect product quality and perfect production processes. Deteriorating processes may affect production systems in several ways. They may decrease the quality of the items produced, cause production stoppage and breakdowns and/or reduce the production rate due to production process inefficiency. The purpose of this paper is to present an EPQ model that incorporates the effect of shifts in production rate on lot sizing decisions due to speed losses. The cycle starts with a certain production rate and after a random time, the production rate shifts to a lower value. A mathematical model to determine the optimal production policy under these conditions is developed and analyzed. Numerical examples are presented for illustrative purposes.     

Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period

A profitable decision policy between a supplier and the retailers can be characterized by an agreement on the trade credit scenario such as permissible delay in payments. In real life business, we observe that the demand is a function of both the selling price and credit period rather than the constant demand. Incorporating this demand function to the retailer of a supply chain, we develop an EPQ – based model for perishable items under two-echelon trade financing. The purpose of this paper is to maximize the profit by determining the optimal selling price, credit period and replenishment time. It is shown that the model developed by Jaggi et al. [Jaggi, J. K., Goyal, S. K., & Goel, S. K., 2008. Retailer’s optimal replenishment decisions with creditlinked demand under permissible delay in payments. European Journal of Operational Research, 190, 130–135] can be treated as a special case of this paper. Finally, through numerical examples, sensitivity analysis shows the influence of key model parameters.     

Combining an alternative multi-delivery policy into economic production lot size problem with partial rework

This paper combines an alternative multi-delivery policy into an imperfect economic production quantity (EPQ) model with partial rework, with the purpose of reducing supplier’s stock holding cost. We extend the problem examined by Chiu et al. [Chiu, Y.-S. P, Chiu, S. W., Li, C.-Y., & Ting, C.-K. (2009). Incorporating multi-delivery policy and quality assurance into economic production lot size problem. Journal of Scientific and Industrial Research, 68(6), 505-512] by considering an n + 1 delivery policy in lieu of n multi-delivery plan for the specific EPQ model with partial rework. Under such a policy, an initial delivery of perfect (finished) items is distributed to customer for satisfying product demand during manufacturer’s regular production time and rework time. At the end of rework, fixed quantity n installments of the finished products are delivered to customer at a fixed interval of time. As a result, a closed-form optimal replenishment batch size solution to the problem is obtained. A numerical example with analysis and comparison is provided to show practical usage of the proposed model and demonstrate its significant savings in stock holding cost.     

Stock Trading Using RSPOP: A Novel Rough Set-Based Neuro-Fuzzy Approach

This paper investigates the method of forecasting stock price difference on artificially generated price series data using neuro-fuzzy systems and neural networks. As trading profits is more important to an investor than statistical performance, this paper proposes a novel rough set-based neuro-fuzzy stock trading decision model called stock trading using rough set-based pseudo outer-product (RSPOP) which synergizes the price difference forecast method with a forecast bottleneck free trading decision model. The proposed stock trading with forecast model uses the pseudo outer-product based fuzzy neural network using the compositional rule of inference [POPFNN-CRI(S)] with fuzzy rules identified using the RSPOP algorithm as the underlying predictor model and simple moving average trading rules in the stock trading decision model. Experimental results using the proposed stock trading with RSPOP forecast model on real world stock market data are presented. Trading profits in terms of portfolio end values obtained are benchmarked against stock trading with dynamic evolving neural-fuzzy inference system (DENFIS) forecast model, the stock trading without forecast model and the stock trading with ideal forecast model. Experimental results showed that the proposed model identified rules with greater interpretability and yielded significantly higher profits than the stock trading with DENFIS forecast model and the stock trading without forecast model.     

Joint management of finished goods inventory and demand process for a make-to-stock product: a computational approach

In this paper, we consider the joint management of finished goods inventory and demand for a product in a make-to-stock production system. The production process is random with controllable mean rate, and the demand process is stochastic with changeable mean rate dependent on the sale price being high or low. The management issue is how to dynamically adjust the production rate and the sale price to maximize the long run total discounted profit. We show that: 1) the optimal management of the finished goods inventory follows a base stock policy: when the inventory is above certain base stock level, the production is halted; otherwise the maximum production rate is deployed to raise the inventory to the base stock level; and 2) the optimal management of the demand process follows a price switch threshold policy: when the inventory is above the threshold, the low sale price is chosen to sell the product; and below it the high price is chosen to reduce the demand. We provide an algorithm to compute the base stock level and price switch threshold. Extension to multiple price choices is given with proofs highlighted.     

Optimal inventory replenishment policy for the EPQ model under trade credit derived without derivatives

Within the economic production quantity (EPQ) framework, the main purpose of this article is to deal with Chung and Huang's model (K.J. Chung, and Y.F. Huang,“The optimal cycle time for EPQ inventory model under permissible delay in payments,” Int. J. Prod. Econ., 84, pp. 307–318, 2003) and extend Chung and Huang's model (2003) by considering the unit selling price higher than the unit purchasing cost using the algebraic method to determine the optimal inventory replenishment policy for the retailer under trade credit. This article provides this algebraic approach which could be used easily to introduce the basic inventory theories to younger students who lack the knowledge of calculus. In addition, we develop an easy-to-use procedure to find the optimal inventory replenishment policy for the retailer in the extended model developed in this article. Finally, numerical examples are given to illustrate the result obtained in our extended model.     

Trend following deep Q-Learning strategy for stock trading

Computers and algorithms are widely used to help in stock market decision making. A few questions with regards to the profitability of algorithms for stock trading are can computers be trained to beat the markets? Can an algorithm take decisions for optimal profits? And so forth. In this research work, our objective is to answer some of these questions. We propose an algorithm using deep Q-Reinforcement Learning techniques to make trading decisions. Trading in stock markets involves potential risk because the price is affected by various uncertain events ranging from political influences to economic constraints. Models that trade using predictions may not always be profitable mainly due to the influence of various unknown factors in predicting the future stock price. Trend Following is a trading idea in which, trading decisions, like buying and selling, are taken purely according to the observed market trend. A stock trend can be up, down, or sideways. Trend Following does not predict the stock price but follows the reversals in the trend direction. A trend reversal can be used to trigger a buy or a sell of a certain stock. In this research paper, we describe a deep Q-Reinforcement Learning agent able to learn the Trend Following trading by getting rewarded for its trading decisions. Our results are based on experiments performed on the actual stock market data of the American and the Indian stock markets. The results indicate that the proposed model outperforms forecasting-based methods in terms of profitability. We also limit risk by confirming trading actions with the trend before actual trading.     

Implementing an optimal policy for set-up time reduction in an economic production quantity model

An economic production quantity (EPQ) system consisting of single and multiple items with an optimal policy of set-up time reduction and a fixed increment cost are discussed in the present study. The set-up time reduction ratio as a decision variable under various cases of demand in the EPQ model is considered. It is assumed that the set-up cost is linearly related to the set-up time. The set-up time reduction ratio and the lot size are solved simultaneously to obtain an optimal value of the total annual cost. Numerical examples are presented to demonstrate the accuracy of the proposed method.     

含模糊修复速率的生产库存模型

研究了缺陷产品可修复且修复速率为模糊变量情况下的生产库存模型;给出了基于模糊结构元理论的求解模糊库存总成本最小化的方法步骤;得到了含有模糊结构元的最佳生产批量的表达式;应用Hessian矩阵的正定性验证了最小成本的存在性;分析了其与经典EPQ公式之间的联系;最后通过具体算例,证明了模型求解方法的可行性。     

Optimal replenishment decision in an EPQ model with defective items under supply chain trade credit policy

The traditional inventory of the economic order quantity model assumes perfect items in an ordered lot and an infinite replenishment rate. However, such conditions are rare in actual production environments. Additionally, most studies of this problem have only considered suppliers offering the wholesaler a grace period. In practice, wholesalers often extend a fixed credit period to downstream customers as well. This study therefore proposes a production model for a lot-size inventory system with finite production rate and defective quality under the condition of two-level trade credit policy and the condition that defective items involve both imperfect quality and scrap items. Thus, optimal wholesaler replenishment decisions can be determined for defective items under two-level trade credit policy in the EPQ framework. Four theorems for determining the optimal cycle time and the results in this study can be deduced as a special case of earlier models. Finally, illustrative examples are provided to verify the theoretical results.     

A multi-machine multi-product EPQ problem for an imperfect manufacturing system considering utilization and allocation decisions

This paper considers a multi-product problem with non-identical machines. This manufacturing system consists of various machine types with different production capacities, production costs, setup times, production rates and failure rates. One of the major issues in the planning phase of a manufacturing system is to take the best decision about which machines must be utilized to manufacture which items. As a result, the decision makers face three critical questions: what machines must be purchased, which items should be allocated to each machine, and what is the optimal cycle length. These decisions must be made to minimize system costs including utilization, setup, production, holding and scrap costs. The multi-machine multi-product economic production quantity (EPQ) problem for an imperfect manufacturing system is formulated as a mixed integer non-linear programming (MINLP), where the convexity property of multi-product single machine EPQ model is used to convert the problem into a bi-level decision-making problem. In the first level, decisions about machine utilization and items allocation are made. After, in the second level the optimal cycle length for each machine is determined. To solve the problem at hand, a hybrid genetic algorithm (HGA) is proposed integrating genetic algorithm and derivatives method. In the proposed HGA, the solutions of the first level are obtained randomly and then, for the second level, the derivatives method is applied to obtain optimal cycle length based on solutions of the first level. Finally, the results of HGA method are compared to the results of general algebraic modeling system (GAMS) and it is found that HGA method has better and more efficient results. Also, a numerical experimentation and a sensitivity analysis of the model are done.     

Recency-based storage assignment and warehouse configuration for recurrent demands

Storage assignment is an important decision problem in warehouse operation management. In conventional problem settings of distribution warehouses, stock items are stored in bulk but retrieved in small quantities. Storage assignment methods typically make use of demand attribute information of order quantity, order frequency and correlation between demands. In this paper, we address a different problem in which the request for the same stock items is stochastically recurrent. The problem arises when the items are needed in production and, after production, are returned to warehouses for later reuse. Examples of such items include tooling in factory, books in library and digital objects in data warehouses. Utilizing the recurrent characteristics, a salient recency-based storage assignment policy and an associated cascaded warehouse configuration are proposed and analyzed in this paper. This paper has four parts. In the first part, a model of recurrent demand is described. In the second part, the efficiency of the recency-based policy and a traditional ID-based policy is analyzed. In the third part, a mathematical programming model for optimal configuration of cascaded warehouses is presented. Finally, a case study of hospital visits is presented. This paper concludes with recommendations on cascading and zoning the warehouse for applying the recency-based policy.     

Price discounts for increased profitability under partial backordering

If some, but not all, customers are willing to wait for an out‐of‐stock product to become available, sellers may be able to increase their profits by offering a price discount to increase the number of backordered demands rather than losing those sales. We modify an existing model for the deterministic economic order quantity with partial backordering by making the backordering percentage a function of the size of the discount. We combine results about the optimal solution for a partial backordering model with a fixed backorder percentage and a search procedure to determine whether offering a discount is optimal and, if so, how large the discount should be to maximize profit.