Three level partial trade credit with promotional cost sharing

In this paper, an economic ordered quantity (EOQ) model, specifically for a newly launched product has been developed with selling price, customers’ credit period and customers’ credit amount induced demand under three levels of partial trade credit policy, where a supplier, a wholesaler and a retailer offer some credit periods on some fraction of the total purchased amount to the wholesaler, the retailer and the customer respectively. Also, here it is assumed that the retailer obtained a quantity discount from the wholesaler on purchased units above a certain level. In addition, the wholesaler and the retailer both enjoy freight charge discount according to the ordered quantity. Retailer introduces a promotional cost to increase the base demand of the item. Objective of this investigation is to maximize the profit of the retailer as well as the wholesaler. It is established that if the wholesaler contributes some portion of the promotional cost then individual profits as well as the joint profit increases. Due to the uncertainty and vagueness of different inventory costs, the proposed model is also discussed in fuzzy and rough environments. Combining the features of particle swarm optimization (PSO) and simulated annealing (SA) a hybrid algorithm named Particle Swarm-Simulated Annealing (PSSA) is developed to find the most appropriate strategies for the proposed model. Efficiency of this algorithm is tested and compared with PSO and genetic algorithm (GA) for a set of benchmark test problems. The model is illustrated with numerical examples and some managerial insights are outlined.     

The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit

In this paper, we proposed a generalized, integrated, supplier–retailer inventory model using a 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 M ? N are explored thoroughly. In addition, the demand rate is assumed to be a function of both retail price and the customers’ credit period. Consequently, this paper deals with the problem of determining the optimal retail price, economic order quantity, and the number of shipments from the supplier to the retailer in one production run for an integrated inventory system under both two-level trade credit and price-and-credit-linked demand rate. Algorithms are developed in order to determine the joint optimal policies. Numerical examples are presented to illustrate the proposed models, as well as sensitivity analysis of key parameters.     

A fuzzy framework for coordinating pricing and inventory policies for deteriorating items under retailer partial trade credit financing

In this paper, we proposed a generalized economic order quantity (EOQ) – based inventory model using a trade credit policy in a fuzzy sense. 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, partially provides customers a permissible delay period N. This study considers fuzzy EOQ model to allow for: (1) selling price dependent demand rate which is imprecise in nature, (2) a profit maximization objective and (3) an imprecise holding cost, ordering cost, purchasing cost, interest earned and interest charged rate. Besides, the cases N ? M and N ? M are explored thoroughly. The objective function for the retailer in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method. For the defuzzified objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally, numerical examples are presented to illustrate the proposed model and the effect of key parameters on optimal solution is examined.     

Retailer's optimal policy under inflation in fuzzy environment with trade credit

Trade credit plays an important role in financing many industries. In the classical inventory model it is assumed that the buyer must pay for the items as soon as the items are received. In this problem, it is considered that the retailer can pay the supplier either at the end of the credit period or later pay interest on the unpaid amount for the overdue period. Here, the retailer's inventory model for the optimal cycle time and payment time for a retailer is developed. The effects of the inflation rate, deterioration rate and delay in payment have been discussed. The whole study is performed in a fuzzy environment by taking the opportunity cost, interest earned and interest paid rate as a triangular fuzzy number. Fuzzy profit functions, which involve fuzzy arithmetic operation, are defined using the function principle. We use the signed distance method to defuzzify the fuzzy profit function. Moreover, numerical and sensitivity analysis is performed to validate the proposed model.     

How to make the replenishment and payment strategy under flexible two-part trade credit

In the existing inventory models concerning the two-part trade credit, a common assumption is that the retailer either pays for all the ordered items within a short permissible delay period and receives a cash discount or pays for all the ordered items within a long permissible delay period at the regular price. In this paper, this unrealistic assumption is relaxed. We assume that the retailer may pay any fraction of the purchase cost within the short permissible delay period and receives a cash discount and then the rest is paid within the long permissible delay period. A decision model is proposed for a retailer to determine the optimal ordering policy and payment plan. The closed-form optimal solution to the model is developed and analyzed. Numerical studies show that a retailer can obtain more benefits from the proposed payment plan than from the extreme payment plan in the existing literature.     

Dynamic pricing,promotion and replenishment policies for a deteriorating item under permissible delay in payments

We study the problem of dynamic pricing, promotion and replenishment for a deteriorating item subject to the supplier's trade credit and retailer's promotional effort. In this paper we adopt a price- and time-dependent demand function to model the finite time horizon inventory for deteriorating items. The objective of this paper is to determine the optimal retail price, the promotional effort and the replenishment quantity so that the net profit is maximized. We discuss the properties and develop an algorithm for solving the problem described. The numerical analyses show that an appropriate promotion policy can benefit the retailer and that the promotion policy is important, especially for deteriorating items. Furthermore dynamic decision-making is shown to be superior to fixed decision-making in terms of profit maximization. Some special cases, such as with no credit period and for non-deteriorating items, are discussed as is the influence of the time-varying demand, the rate of deterioration and the credit period on the retailer behavior.     

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.     

Supply chain model with price- and trade credit-sensitive demand under two-level permissible delay in payments

This article develops a single-manufacturer and single-retailer supply chain model under two-level permissible delay in payments when the manufacturer follows a lot-for-lot policy in response to the retailer's demand. The manufacturer offers a trade credit period to the retailer with the contract that the retailer must share a fraction of the profit earned during the trade credit period. On the other hand, the retailer provides his customer a partial trade credit which is less than that of the manufacturer. The demand at the retailer is assumed to be dependent on the selling price and the trade credit period offered to the customers. The average net profit of the supply chain is derived and an algorithm for finding the optimal solution is developed. Numerical examples are given to demonstrate the coordination policy of the supply chain and examine the sensitivity of key model-parameters.     

Two-echelon competitive integrated supply chain model with price and credit period dependent demand

This study considers a two-echelon competitive supply chain consisting of two rivaling retailers and one common supplier with trade credit policy. The retailers hope that they can enhance their market demand by offering a credit period to the customers and the supplier also offers a credit period to the retailers. We assume that the market demand of the products of one retailer depends not only on their own market price and offering a credit period to the customers, but also on the market price and offering a credit period of the other retailer. The supplier supplies the product with a common wholesale price and offers the same credit period to the retailers. We study the model under a centralised (integrated) case and a decentralised (Vertical Nash) case and compare them numerically. Finally, we investigate the model by the collected numerical data.     

Supplier–retailer inventory coordination with credit term for inventory‐dependent and linear‐trend demand

In this paper, a nonintegrated and collaborative replenishment policy is considered, respectively, which incorporates varying demand depending on both inventory level and time during the finite planning horizon. For additional cost savings realized from coordination, the paper adopts trade credit as a cost‐saving shift means and introduces a brand new parameter, that is, credit period rate. Then, the equitable credit period rate is determined, and different values of the credit period rate reflect the allocation of additional cost savings between the supplier and retailer. Furthermore, the conditions for the existence and uniqueness of an optimal solution are proved for the nonintegrated and collaborative replenishment policy, and an efficient solution procedure is developed to determine the optimal results and coordination of the inventory model. Finally, several numerical examples are provided to illustrate the proposed strategy and algorithm, and the sensitivity analysis of the optimal solution with respect to each parameter is presented. The sensitivity analysis suggests that the size of the credit period rate has a strong relationship with the supplier's and retailer's inventory cost (including capital cost) and setup cost. In real‐life situations, this proposed strategy may be applied to some consumer products in the growth phase or best‐selling consumer goods, etc.     

An integrated inventory model with capacity constraint and order-size dependent trade credit

Trade credit has many forms in today’s business practice. The most common form of trade credit policy that is used to encourage retailers to buy larger quantities is order-size dependent. When the number of ordered units exceeds the capacity of the own warehouse, an additional rented warehouse is required to store the excess units. Therefore, to incorporate the concept of order-size dependent trade credit and limited storage capacity, we proposed an integrated inventory model with capacity constraint and a permissible delay payment period that is order-size dependent. In addition, the unit production cost, which is a function of the production rate, is considered. Three theorems and an algorithm are developed to determine the optimal production and replenishment policies for both the supplier and the retailer. Finally, numerical examples are presented to illustrate the solution procedure and the sensitivity analyses of some key parameters are provided to demonstrate the proposed model.     

An optimization approach for joint pricing and ordering problem in an integrated inventory system with order-size dependent trade credit

Under a business trading environment, it is common for the trade credit to depend on the order size. Therefore, it is important to discuss the single-supplier and single-buyer supply chain problem which includes order-size dependent trade credit. In this study, an integrated inventory model with a price sensitive demand rate, determining jointly economic lot size of the buyer’s ordering and the supplier’s production batch, are developed to maximize the total profit per unit time. An efficient algorithm is provided to obtain the optimal solution, and then numerical examples are presented to illustrate the theoretical results. Finally, the comparison between whether an optimal solution is jointly or independently determined is also provided.     

A single-period inventory and payment model with partial trade credit

In this paper, we consider the ordering and payment issues for a retailer facing stochastic demand. We assume that the retailer can enjoy the partial trade credit from his supplier and borrow money from bank as well if needed, and he can also earn return by investing his superfluous on-hand cash (if any). The retailer’s objective is to maximize the expected cash level at the end of the selling period. We formulate the model of this problem by taking initial inventory and capital levels as the two-dimensional state. First, given the exogenous fraction of immediate payment, we show that unlike the critical fractile solution the retailer’s optimal ordering strategy is a two-threshold policy, which is independent of the retailer’s initial inventory level and capital level. Second, we consider an extensive model where the fraction of immediate payment is decided by the retailer. We employ the sequential optimization procedure to solve the extensive problem, and present the structure of the retailer’s optimal policies under different partial-trade-credit penalty rates. Numerical experiments show that if the fraction of immediate payment is exogenous, both partial trade credit and loan opportunity are detrimental to the capital-constrained retailer in many cases, although they can stimulate the retailer to order more.     

考虑消费者缺货容忍的变质品订购与信用期策略研究

考虑消费者存在缺货容忍行为,研究变质品的联合订购和信用期决策问题.假设延迟订购消费者面对缺货等待时存在一个容忍期限(即在该容忍期限内零售商无需支付缺货成本),同时考虑市场需求受商业信用期的影响,库存系统允许缺货且短缺量部分延迟订购.以零售商的平均利润最大化为目标,分两种情形构建变质品的订购和信用期决策模型.从理论上证明...     

Integrated supply chain model for a deteriorating item with procurement cost dependent credit period

This study develops an integrated production inventory model of supplier and retailer where a delay in payment is offered by supplier to retailer for a constant deteriorating item. Here shortages are not allowed. In this model retailer’s procurement cost linearly depends on the credit period and supplier’s process cost also is a linear function of the amount of quantity purchased by retailer. In this model, the objective is to decide the position of the credit period and number of replenishment of retailer in finite time horizon in such a way that the integrated system gets the optimum cost. The model is explained with the help of numerical examples and the sensitivity analysis of some parameters are also carried out.     

The evaluation of drop shipping option for e-commerce retailers

Many e-commerce retailers use drop shipping to satisfy demand. A retailer simply forwards customers' orders to the manufacturer who fills the orders directly to the customers and is paid a predetermined price by the retailer. Advantages of drop shipping include lower costs of holding inventory, materials handling, and obsolescence. Disadvantages of drop shipping include fragmented order delivery when a single customer order involves products from different manufacturers and longer delivery times. A mix of holding inventory and drop shipping is frequently optimal for e-retailers. In this paper, we design an optimal mix strategy which captures the advantages of drop shipping and avoids many of its shortcomings. We use two different optimization criterion, maximizing the expected profit and maximizing the probability of achieving a target profit. We provide results for uniform, exponential, and normal demand distributions. We illustrate the results with numerical examples.     

Pricing and inventory policies for Hi-tech products under replacement warranty

Companies, especially in the Hi-tech (high-technology) industry (such as computer, communication and consumer electronic products), often provide a replacement warranty period for purchased items. In reality, simultaneously determining the price and inventory decisions under warranty policy is an important issue. The objective of this paper is to develop a joint pricing and inventory model for Hi-tech products under replacement warranty policy. In the first model, we consider a Hi-tech product feature in which the selling price is declining in a trend. We determine the optimal inventory level for each period and retail price for the first period while maximising the total profit. In the second model, we further determine the optimal retail price and inventory level for each period in the dynamic demand market. This study develops solution approaches to solve the problems described above. Numerical analysis discusses the influence of system parameters on the company's decisions and behaviours. The results of this study could serve as a reference for business managers or administrators.     

A particle swarm optimization for solving joint pricing and lot-sizing problem with fluctuating demand and trade credit financing

Pricing is a major strategy for a retailer to obtain its maximum profit. Furthermore, under most market behaviors, one can easily find that a vendor provides a credit period (for example 30 days) for buyers to stimulate the demand, boost market share or decrease inventories of certain items. Therefore, in this paper, we establish a deterministic economic order quantity model for a retailer to determine its optimal selling price, replenishment number and replenishment schedule with fluctuating demand under two levels of trade credit policy. A particle swarm optimization is coded and used to solve the mixed-integer nonlinear programming problem by employing the properties derived in this paper. Some numerical examples are used to illustrate the features of the proposed model.     

Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments

In this paper, we have investigated multi-item integrated production-inventory models of supplier and retailer with a constant rate of deterioration under stock dependent demand. Here we have considered supplier’s production cost as nonlinear function depending on production rate, retailers procurement cost exponentially depends on the credit period and suppliers transportation cost as a non-linear function of the amount of quantity purchased by the retailer. The models are optimized to get the value of the credit periods and total time of the supply chain cycle under the space and budget constraints. The models are also formulated under fuzzy random and bifuzzy environments. The ordering cost, procurement cost, selling price of retailer’s and holding costs, production cost, transportation cost, setup cost of the supplier’s and the total storage area and budget are taken in imprecise environments. To show the validity of the proposed models, few sensitivity analyses are also presented under the different rate of deterioration. The models are also discussed in non deteriorating items as a special case of the deteriorating items. The deterministic optimization models are formulated for minimizing the entire monetary value of the supply chain and solved using genetic algorithm (GA). A case study has been performed to illustrate those models numerically.     

The effect of advance payment with discount facility on supply decisions of deteriorating products whose demand is both price and stock dependent

Generally, in the business world, it is observed that suppliers give different kinds of benefits to retailers due to advance payment. One of the popular benefits is instant cash discount due to advance payment. If a retailer pays off his total purchase cost before receiving the products, then he receives a certain percentage of cash discount instantly. However, if the retailer pays off a certain fraction of the total purchasing cost, then price discount is given only at the time of receiving the products while paying the remaining amount of the total purchasing cost. Using this concept, this paper formulates, under both cases of advance payment (full or partial), an inventory model for deteriorating products where shortages are allowed and demand function is considered as price and stock dependent. The closed‐form solutions for each case are presented and two numerical examples are solved. In addition, a sensitivity analysis is also performed to show the effects of advance payment with discount facility.