Optimal Ordering and Trade Credit Policy for EOQ Model

Trade credit is the most prevailing economic phenomena used by the suppliers for encouraging the retailers to increase their ordering quantity. In this article, an attempt is made to derive a mathematical model to find optimal credit policy and hence ordering quantity to minimize the cost. Even though, credit period is offered by the supplier, both parties (supplier and retailer) sit together to agree upon the permissible credit for settlement of the accounts by the retailer. A numerical example is given to support the analytical arguments.Trade Credit, Optimal ordering quantity, Lot-size

Optimal Inventory Policies for Weibull Deterioration under Trade Credit in Declining Market

The aim of this study is to develop mathematical model for Weibull deterioration of items in inventory in declining market when the supplier offers his retailers a credit period to settle the accounts against the dues. The computational steps are explored for a retailer to determine the optimal purchase units which minimize the total inventory cost per time unit. The numerical examples are given to demonstrate the retailer’s optimal decision. A sensitivity analysis is carried out to study the variations in the optimal solution.Weibull deterioration, trade credit, declining market

Trade Credit Policies for Supplier, Manufacturer, and Retailer: An Imperfect Production-Inventory System with Rework

In this study, we developed a trade credit policy for a three-layer supply chain consisting of a supplier, a manufacturer and a retailer. We propose an optimal production rate and selling price for the manufacturer and the retailer under an imperfect production system. The suggested coordination policy optimizes the profit of each supply chain member. Two models were formulated for two real-life strategies respectively. The first one is a collaborative (integrated) system and the second one is a Stackelberg leadership system. Both strategies were analyzed for various credit periods, respectively offered by the supplier to the manufacturer, by the manufacturer to the retailer, and by the retailer to the customers, by considering price-sensitive demand and a certain replenishment rate. Finally, we concluded which strategy will be better for inventory management under the given restrictions in the form of propositions. The concavity property for the net profit function was established with respect to the selling price and the production rate, which was also described graphically and analyzed by numerical examples

Inventory models for production systems with constant/linear demand, time value of money, and perishable/non-perishable items

This research considers inventory systems for economic production models where the objective is to find the optimal cycle time, which minimizes the total cost, and optimal amount of shortage if it is allowed. Several aspects such as time value of money, inflation, constant and linear demand rates, shortages, and deterioration are considered in developing different models. Closed formulas are obtained for the optimal policy in one model. For others, more complex models where closed formulas cannot be obtained, search techniques are used to find the optimal solution.;First, a deterministic inventory control problem is considered for determination of optimal production quantities for an item with constant demand rate, while considering the effect of time value of money. Closed formulas are obtained to calculate the optimal cycle time and corresponding production quantity for the model without shortage. However, search procedures are used to find the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed.;In the next inventory control problem, a deterministic model for items with linear demand rate over time, for a finite planning horizon, while considering the effect of time value of money, is considered. Search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage.;A deterministic inventory control problem is also considered for items with constant rate of demand and exponentially decaying inventory over an infinite planning horizon, while considering the effect of time value of money. Two different search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage

Trade Credit Policies for Supplier, Manufacturer, and Retailer: An Imperfect Production-Inventory System with Rework

In this study, we developed a trade credit policy for a three-layer supply chain consisting of a supplier, a manufacturer and a retailer. We propose an optimal production rate and selling price for the manufacturer and the retailer under an imperfect production system. The suggested coordination policy optimizes the profit of each supply chain member. Two models were formulated for two real-life strategies respectively. The first one is a collaborative (integrated) system and the second one is a Stackelberg leadership system. Both strategies were analyzed for various credit periods, respectively offered by the supplier to the manufacturer, by the manufacturer to the retailer, and by the retailer to the customers, by considering price-sensitive demand and a certain replenishment rate. Finally, we concluded which strategy will be better for inventory management under the given restrictions in the form of propositions. The concavity property for the net profit function was established with respect to the selling price and the production rate, which was also described graphically and analyzed by numerical examples

An EPQ Inventory Model with Allowable Shortages for Deteriorating Items under Trade Credit Policy

This paper attempts to obtain the replenishment policy of a manufacturer under EPQ inventory model with backorder. It is assumed here that the manufacturer delays paying for the received goods from the supplier and the items start deteriorating as soon as they are being produced. Based on these assumptions, the manufacturer’s inventory model is formulated, and cuckoo search algorithm is applied then to find the replenishment time, order quantity, and selling price with the objective of maximizing the manufacturer’s total net profit. Besides, the traditional inventory system is shown as a special case of the proposed model in this paper, and numerical examples are given to demonstrate better performance of trade credit. These examples are also used to compare the results of cuckoo search algorithm with genetic algorithm and investigate the effects of the model parameters on its variables and net profit

Coordinating Supply Chains with a Credit Mechanism

This paper studies the supply chain coordination with a trade credit under symmetric and asymmetric information, where the retailer has an individual profit target from the business and the vendor is the decision-maker of the supply chain. We propose a coordination mechanism through credit contracts and show that a win-win outcome is achieved by redistributing the cost savings from coordination mechanism under certain constraints. Numerical examples are given to illustrate our results

An EPLS model for a variable production rate with stock-price sensitive demand and deterioration

It is observed that large piles of consumer goods displayed in supermarkets lead consumers to buy more, which generates more profit to sellers. But a large number of on-hand display of stock leaves a negative impression on the buyer. Also, the amount of shelf or display space is limited. Due to this reason, we impose a restriction on the number of on-hand display of stock and also on initial and ending on-hand stock levels. We introduce an economic production lot size model, where production rate depends on stock and selling price per unit. A constant fraction deterioration rate is considered in this model. To illustrate the results of the model, four numerical examples are established. Sensitivity analysis of the changes of parameter values is also given