Optimal pricing and ordering policy under permissible delay in payments

The inventory models under conditional trade credit in a supply chain system

A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments

Most researchers established their inventory lot-size models under trade credit financing by assuming that the supplier offers the retailer fully permissible delay in payments and the products received are all non-defective. However, in the real business environment, it often can be observed that the supplier offers the retailer a fully permissible delay in payments only when the order quantity is greater than or equal to the predetermined quantity Q d . In addition, an arriving order lot usually contains some defective items due to imperfect production processes or other factors. To capture this reality, the paper extends Huang (2007) economic order quantity (EOQ) model with partially permissible delay in payments to consider defective items. We formulate the proposed problem as a profit maximization EOQ model in which the replenishment cycle time is the decision variable. Then we use the arithmetic-geometric mean inequality approach to determine the optimal solution under various situations. An algorithm to obtain the optimal solution is also provided. Finally, the numerical examples and sensitivity analysis are given to illustrate the results.

In this paper, an inventory policy for the production units is presented with stochastic inflation, variable demand rate, deteriorating and ameliorating items in warehouse and permissible delay in payment. Shortages, backlogging and lost sale, are allowable. Also, inflation is constantly changing due to economic, political, social and cultural issues in the real world and we assume it uniform distribution. The demand rate is depended on selling price and permissible delay in payment and increases as delay in payment increases, however, decreases as selling price increases. The objective function considers optimal pricing policy, the number of production cycles and time fraction without shortage. So, the purpose is to derive the optimal replenishment policy that minimises the net present value of total cost per unit time. The study shows that the optimal solution not only exists but also is unique. Finally, some numerical examples and sensitivity analysis on parameters are made to validate the results of the proposed inventory system.

Multivariate demand is a practical approach in today's business scenario. The entropy of a system is a measurement of the amount of disorder. Inflation is one of the major factors in inventory modeling. It makes the inventory model to realistic. Permissible delay in payment also plays an important role in a highly competitive market. It is a promotional tool to push the product, which indirectly reduces the selling price of the product. This paper developed an Entropic inventory model of imperfect product quality with multivariate demand and permissible delay in payment under the inflationary environment. The finding of this paper is that cost of entropy behaves the same as the selling price and EOQ. The numerical example is carried out using the software MATHEMATICA12.0. Sensitivity Analysis is carried out to see the behavior of different parameters.

ABSTRACTFor a supply chain coordination to be effective and profitable, it requires a working mechanism among the members of a supply chain to financially entice some players to cooperate. Permissible delay in payments is one of the most commonly practised incentives by businesses to achieve this cooperation. This paper investigates a two-level (manufacturer–retailer) supply chain, with a permissible delay in payments as a decision variable. First, the paper modifies three known models of different production and shipping policies to account for delays in payments; it then compares them and highlights the production policy that performed the best with total system cost as a performance measure. A sensitivity analysis is also utilised to test and identify the limitations of the three models.

This study develops an improved inventory model to help the enterprises to advance their profit increasing and cost reduction in a single vendor single‐buyer environment with general demand curve, adjustable production rate, and imperfect reworking process under permissible delay in payments. For advancing practical use in a real world, we are concerned with the following strategy determining, which includes the buyer_s optimal selling price, order quantity, and the number of shipments per production run from the vendor to the buyer. An algorithm and numerical analysis are used to illustrate the solution procedure.

The purpose of this inventory model is to investigate the retailer’s optimal replenishment policy under permissible delay in payments. In this paper, we assume that the supplier would offer the retailer partially permissible delay in payments when the order quantity is smaller than a predetermined quantity (W). The most inventory systems are usually formed without considering the effect of deterioration of items which deteriorate continuously like fresh fruits, vegetables etc. Here we consider the loss due to deterioration. In real world situation, the demand of some items varies with change of seasons and occasions. So it is more significant if the loss of deterioration is time dependent. Considering all these facts, this inventory model has been developed to make more realistic and flexible marketing policy to the retailer, also establish the result by ANOVA analysis by treating different model parameters as factors.

The main purpose of this paper wants to investigate the effect of trade credit policy with limited storage capacity within the economic order quantity (EOQ) framework. Goyal is frequently cited when the inventory systems under conditions of permissible delay in payments are discussed. But Goyal assumed that the retailer’s storage capacity is unlimited. This assumption is debatable. So, we want to extend Goyal’s model to the case that the retailer’s storage capacity is limited. Then, two theorems present solution procedures to locate the optimal cycle times of the annual total relevant cost function. In essence, the inventory model discussed in this paper generalizes that of Goyal. Finally, numerical examples are given to illustrate all theorems obtained in this paper.

In the economic order quantity models, it is often assumed that the payment of an order is made on the receipt of items by the inventory system. Such assumption is usually not fulfilled in practice. The phenomenon that a supplier may offer a credit period to the retailers in order to stimulate demand is very common in the market. In this paper, the stock-dependent demand rate and conditions of permissible delay in payments used in conjunction with the economic order quantity model are the focus of discussion. We shall be concern with finding the optimal replenishment cycle under conditions of permissible delay in payments. Numerical examples are presented to illustrate the proposed models.

This article wants to investigate the retailer’s optimal cycle time and optimal payment time under supplier credits including conditionally permissible delay in payments and cash discount depending on retailer payment time. That is, the retailer can obtain fully permissible delay in payments and cash discount if the payment is paid before the period of full delay payments permitted by the supplier. Otherwise, the retailer will just obtain partially permissible delay in payments within the period of partial delay payments permitted by the supplier. The supplier uses this policy to attract retailer to pay the payment as soon as possible to shorten its collection period. Mathematical models have been derived for obtaining the optimal cycle time and optimal payment time for item so that the annual total relevant cost is minimized. One theorem is developed to efficiently determine the optimal replenishment and payment policy for the retailer.

In today’s competitive business environment, it is very common that suppliers are always willing to provide the purchaser with certain incentives. As a result, suppliers frequently offer two distinct alternatives to increase possible volume of procurement. One is that if the order quantity is greater than or equal to a predetermined quantity, the purchaser obtains a longer permissible delay in payments. The other is that if the order quantity is greater than or equal to a predetermined quantity, the purchaser gets a cash discount with a shorter permissible delay in payments. Viewed from above perspective, this study develops an inventory model with order-size dependent trade credit, in which the supplier provides not only a permissible delay but also a cash discount to the customers. Moreover, an efficient algorithm is provided to obtain the optimal solution, and then an empirical case is investigated to illustrate the theoretical results from both thesupplier and customer viewpoints. Key words: Inventory, deteriorating items, delay in payments, trade credit, cash discount.

This article derives an optimal ordering policy for non-instantaneously deteriorating items under successive price discounts with delay in payments. Here successive price discounts is a strategy to sell almost all the items before decomposition. The cause of implementing this concept in the model is the fact that about 25% of vegetables and fruits of India gets decayed before selling, due to lack of facilities and awareness of business strategies, although poverty is its vital factor. Thus we propose to offer successive price discounts of 20% and 40% after selling the stock up to 50% and 90% respectively to raise the customer’s inflow and so also rotate the cycle early to avoid more deterioration. This type of business not only reduces the factory of decomposability but also saves the holding cost partially. In addition to, the delay in payment is another business strategy of the wholesaler by which he keeps the retailers in track and so also reduces the holding cost. In this case the wholesaler offers an interest-free credit period to the retailers till the settlement of the accounts. The retailers earn interest on selling the revenue during this opportunity. Supplier charges interest on the outstanding balance after exceeding the period. Besides the above, again the inventory cost does not remaining constant due to various factors like inflation, salary, house rent etc. so a time varying holding cost has been well thought out instead of constant holding cost. Once more customers’ flow not only depends upon the price instigating but also on timings, hence we assume an exponential demand function which depends on these variables. The main idea of the task is to determine optimal selling price, optimal refill schedule and optimal ordering quantity such that the total profit is maximized under exponential constraints. The literal idea of the work is (a) to avoid the deterioration through successive price discounts, (b) to attract the customers through successive price discounts, (c) to sell all the items through successive price discounts, (d) to rotate the cycle early through successive price discounts, (e) to keep the retailers in track through delay in payment, (f) to keep variable holding cost instead of constant holding cost due to market inflation, (g) to get the optimum results under exponential constraints.

An inventory model under two levels of trade credit and limited storage space derived without derivatives

One of unrealistic assumptions in classical EOQ model is that the items received are all good quality. In real life, it is very difficult for all the products received to achieve a 100% qualified rate due to various imperfect production or transportation processes, which has effect on determining the order size and related inventory control parameters. In addition, nowadays trade credit is widespread and become an important form of company finance. Supplier realizes that retailers are interested to buy more items if they are offered some credit periods to pay the whole cost of items instead of paying immediately. This paper extends the work of Chung and Huang [29] by considering that shortages are allowed and occur as lost sales where the loss of stock out and the salvage of the residue are counted into the cost. An inventory model optimizing the retailer's expected profit per unit time is established under permissible delay in payments. Three theorems are developed to derive the optimal replenishment policy. Finally, sensitivity analysis on main parameters is given by numerical examples.