An economic and recycling production quantity model for remanufactured products under two-level trade-credit and trade-in programmes

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.

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.

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.

An EOQ model with noninstantaneous receipt and exponentially deteriorating items under two-level trade credit

The traditional economic order quantity models usually assume that the purchasing cost must be paid for the items as soon as the items are received. However, in practice trade credit is one of the main measures to promote the sale of goods. On the other hand, the retailer would offer the trade credit period to his/her customers. That is a two-level trade credit. In this paper, we develop an EPQ model for deteriorating items under two-level trade credit, where the demand rate of the items is dependent on the current stock level, and the inventory system with inventory-level-dependent demand rate is further extended. Then we provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could make the average cost per unit time to a minimum. Easy solution methods are shown to find the optimal replenishment policy of the considered problem and some theoretical evidences are provided for retailers to make the practical inventory decision. At last, numerical examples are presented to illustrate the developed model.

This paper develops an economic lot-sizing production model for deteriorating items with time dependent quadratic demand and delay in payments under two levels of trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M < N and are investigated. In addition, the demand rate is assumed to be time and deterioration rate dependent quadratic demand. This paper deals with the problem of determining the optimal replenishment cycle length, optimal total cost and economic order quantity for an integrated inventory system under both two-level trade credit and time dependent quadratic demand rate. Numerical examples are presented to illustrate the developed model.

The development of technologies such as the Internet of Things has transformed traditional physical products into smart connected products (SCPs) that combine hardware, sensors, data storage, microprocessors, software, and connectivity in myriad ways. SCPs raise a new set of strategic choices for creating value and pricing products, how relationships with business partners such as channels are redefined, and what role companies should play as industry boundaries are expanded. This study develops an inventory model that considers optimal pricing, production, and intelligent policies for SCPs. In this model, customer demand is assumed to increase as the selling price decreases and the effort to improve product intelligence (i.e., intelligent effort) increases. In addition, a two-level trade credit is included in the SCPs supply chain channel. The manufacturer often receives a permissible delay-in-payment (trade credit) from the supplier while also offering a delayed payment to end customers to attract more sales. Trade credit is particularly important for SCPs as it can act as a payment plan to reduce the product’s price barrier. This study aims to determine the optimal selling price, lot size, and level of intelligent effort while maximizing the manufacturer’s profit under a two-level trade credit. The optimal solution is clarified, numerical examples are provided, and a sensitivity analysis is performed to illustrate the theoretical results and solution approach. The results reveal that considering the level of intelligent effort as a decision can benefit the manufacturer. Notably, as the intelligent effort coefficient increases by 55%, the total profit increases by 65.8%.

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.

Trade credit is an increasingly important payment behavior in real business transactions. In practice, the supplier allows a certain fixed credit period to settle the account for stimulating retailer's demand. From the retailer's viewpoint, during the credit period before payment must be made, he/she can sell the items and continue to accumulate revenue and earn interest. The main purpose of the present paper is to explore the impact of credit period on the retailer's demand, which may be instant or delayed. An EPQ (Economic Production Quantity) model under the condition of two echelon trade credit with credit sensitive demand has been analyzed. The optimal credit period offered by the retailer and the optimal replenishment time has been jointly evaluated in order to maximize retailer's profit.

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.

Retailer’s optimal replenishment and payment policies in the EPQ model under cash discount and two-level trade credit policy

Economic production quantity (EPQ) research has typically focused on the cost of production processes, but has not employed accurate calculation to assess factors influencing ordering costs, because one of their assumptions is the raw materials that are product timely. However, the production and transport process of raw materials are influencing factors and increase the holding cost of raw materials, either by increasing or reducing 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 considers the holding cost of non-deteriorating raw materials to closer to the real world. However, some raw materials have deteriorated should be considered. Therefore, this research extends [1]’s model to consider the holding cost of deteriorating raw materials. Four theorems for determining the optimal cycle time and the total relevant cost were developed using cost minimization. Finally, sensitivity analyses are used to find out the effects of the parameters to determine the ordering policies.

In order to reduce default-risk, a retailer in practice frequently requests its credit risk customers to pay a part of the purchase amount as collateral deposit at the time of ordering, and then offers a trade credit for the outstanding balance (partial down-stream trade credit). In contrast, the retailer usually receives a full trade credit on the purchase amount from the manufacturer (up-stream full trade credit). The present study develops a single manufacturer single retailer integrated supply chain model under two-level trade credit in which the retailer receives a full trade credit from the manufacturer but offers a partial trade credit to its customers. The manufacturer delivers the retailer’s order quantity in a number of equal shipments. An arriving lot from the manufacturer contains a certain proportion of defective items. The market demand rate is sensitive to the length of the customer’s trade credit period which is offered by the retailer. The present study aims to determine the optimal replenishment cycle time, the order quantity and the number of lots from the manufacturer to the retailer such that the total profit of the integrated supply chain system is maximized. Solution algorithms are designed to find the optimal solution of the model. The theoretical results developed in the paper are illustrated through a numerical example. Sensitivity analysis of some important parameters is presented to study their influence on the optimal solution.

In the traditional inventory system, it was implicitly assumed that the buyer pays to the seller as soon as he receives the items. In today’s competitive industry, however, the seller usually offers the buyer a delay period to settle the account of the goods. Not only the seller but also the buyer may apply trade credit as a strategic tool to stimulate his customers’ demands. This paper investigates the effects of the latter policy, two-level trade credit, on a retailer’s optimal ordering decisions within the economic order quantity framework and allowable shortages. Unlike most of the previous studies, the demand function of the customers is considered to increase with time. The objective of the retailer’s inventory model is to maximize the profit. The replenishment decisions optimally are obtained using genetic algorithm. Two special cases of the proposed model are discussed and the impacts of parameters on the decision variables are finally investigated. Numerical examples demonstrate the profitability of the developed two-level supply chain with backorder.

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.