Optimal pricing and ordering policies for perishable commodities (original) (raw)
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International Journal of Production Economics, 2017
A contractor often requests a customer pay an advance payment when signing a contract to install a new roof. A cash payment to cover the contractor's materials cost is then required upon delivery of the materials to do the job. Then, the contractor grants the customer a credit payment to pay the remainder of the total cost after the work is completed and satisfactory. Hence, an advance-cash-credit (ACC) payment scheme is commonly used in real world business transactions. This paper develops a supplier-retailer-customer chain in which the retailer receives an upstream ACC payment from the supplier while in return offers a downstream cash-credit (some in cash and the rest in credit) payment to customers. Additionally, today's healthconscious consumers judge product freshness through its expiration date because the freshness of a perishable product degrades with time. As a result, the demand for perishable products is influenced by the combined effect of selling price and product freshness linked to expiration date. Taking time value of money into consideration, then an inventory model by using a discounted cash-flow analysis is developed. Furthermore, the present value of total annual profit is demonstrated that is strictly concave in unit price and strictly pseudo-concave in replenishment time, which simplifies the search for the global solution to a local maximum. Finally, a sensitivity analysis is conducted and several managerial insights are obtained.
International Journal of Systems Science: Operations & Logistics, 2017
For perishable products, the seller usually asks for the buyer to prepay a fraction of the purchasing cost as a good-faith deposit, to pay some cash upon the receipt of the order, and then to offer a short-term interest-free loan (also known as permissible delay or trade credit) on the remaining purchasing cost. In addition, it is evident that the deterioration rate ages to 100% as the expiration date is approaching. In this paper, we incorporate the above two important and relevant facts to find the optimal cycle time and the fraction of no shortages such that the total profit is maximised. Several managerial insights are presented. For instance, an increase in expiration date (or fraction of credit payment) induces higher values of no-shortage fraction and total profit, while giving a lower value of replenishment cycle. In contrast, an increase in fraction of advance payment causes lower values of no-shortage fraction and total profit, but a higher value of replenishment cycle. Notes on contributors Jiang Wu received an MS degree and a PhD degree in management science and engineering from Southwest Petroleum University and Southwest Jiaotong University in China, respectively. He joined the Department of Management Sciences, School of Statistics at Southwestern University of Finance and Economics of Chengdu, China, in 2004. His research interests include supply chain management and multi-attribute decision-making research. He has published articles in Inter
This study elaborates an inventory policy for perishable products where the products face exponential deterioration with time under the credit of trades. The demand rate is taken as a function of selling price and the delay in payment is permitted as per the order of quantity. Shortages are permitted and fully backlogged. The aim of the present study is to find the optimal ordering quantity of retailer and the optimal order cycle for optimizing the total profit. This study is also useful to find the optimal ordering scheme in the analysis of trade credit. A numerical example based on practical problems is presented which is helpful in the study of business decision making problems. A sensitivity analysis of the model is carried out for various parameters. The study concludes with a conclusion and an aspect at feasible future requirements.
International Journal of Operational Research, 2014
Achieving effective coordination among suppliers and retailers has become a pertinent research issue in supply chain management. A profitable decision policy between a supplier and the retailers can be characterised by an agreement on the trade credit scenario such as permissible delay in payments. Usually, in real life business, we observe that the demand depends on the selling price rather than the constant demand and supplier is willing to provide the retailer a full trade credit period for payments and the retailer just offers the partial trade credit period to his/her customers. In this paper, we develop an EPQ-based model for perishable items under retailer's partial trade credit policy and price dependent demand. The purpose of this paper is to maximise the profit by determining the optimal selling price and replenishment time. Mathematical theorems are developed to determine optimal inventory policy for the retailer and numerical examples are given to illustrate the theory. We also obtain a lot of managerial phenomena.
Engineering Science Letter
The inventory existence of the company is a waste but still needed to maintain service level. For drug industry companies, especially pharmaceutical installations, the expiration factor is a factor that needs to be considered because drugs have an expiration date. Previous research has an inventory model that considers product expiration factors, permissible payment delays, and price discounts. The developed study provides a solution to the loss of expiry costs by adding a return factor. This research aims to create an inventory model that considers expiration factors, permissible payment delays, discounts, and product returns. The result of the developed model can minimize the total cost of inventory by 3.37% with the predefined parameters compared to the previous model, which has not considered the return factor.
Foundations of Computing and Decision Sciences
Recently, utilizing appropriate inventory control policy and determining the optimal selling price for various goods has been the main topic of scientific and industrial research. Inventory management policy 1 by the seller is one solution that improves the chain’s performance by creating coordination between members of the supply chain. The current study attempts to devise an integrated model of inventory pricing and control under the inventory management policy by the seller for perishable goods with shortages is considered. The purpose of presenting the model is to determine the optimal price, the optimal repayment time, and the order size, in order to maximize the profit. To acquire those optimal values, the profit functions of the buyer and the seller are taken into account. Given the results acquired, it is demonstrated that at any cost, the repayment time is unique and optimal. It is concluded that with the optimal recovery time available, the objective function is a concave ...
Uncertain Supply Chain Management, 2013
This paper investigates the instantaneous economic order quantity model by allocating the percentage of units lost due to deterioration in an on-hand inventory by framing promotional effort cost and variable ordering cost. The objective is to maximize the net profit so as to determine the order quantity, promotional effort factor, the cycle length and number of units lost due to deterioration. For any given number of replenishment cycles the existence of a unique optimal replenishment schedule are proved and mathematical model is developed to find some important characteristics for the concavity of the net profit function. Numerical examples are provided to illustrate the results of proposed model, which benefit the retailer and this policy is important, especially for wasting of deteriorating items. Finally, sensitivity analyses of the optimal solution with respect to the major parameters are carried out.
Journal of Mathematical Modelling and Algorithms in Operations Research, 2015
In a supplier-retailer-customer supply chain, a credit-worthy retailer frequently receives a permissible delay on the entire purchase amount without collateral deposits from his/her supplier (i.e., an upstream full trade credit). By contrast, a retailer usually requests his/her credit-risk customers to pay a fraction of the purchase amount at the time of placing an order, and then grants a permissible delay on the remaining balance (i.e., a downstream partial trade credit). Also, in selecting an item for use, the selling price of that item is one of the decisive factors to the customers. It is well known that the higher selling price of item decreases the demand rate of that item where the lesser price has the reverse effect. Hence, the demand rate of an item is dependent on the selling price of that item. In addition, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. However, only a few researchers take the expiration date of a deteriorating item into consideration. This paper proposes an economic order quantity model to allow for: (a) the strategy that supplier offers retailer a full trade credit policy whereas the retailer offers their customers a partial trade credit policy, (b) selling price dependent demand rate, (c) a profit maximization objective and (d) deteriorating items not only deteriorate continuously but also have their expiration dates. For the 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.
An EOQ Model for Perishable Inventory under Credit Period Dependent Quadratic Demand
The supplier gives its customers a credit period to settle the account which attracts more customers and boosts market demand. Yet the present of credit period leads to default risk for the supplier. The default risk associated with sales revenue is taken into consideration in objective of profit maximization. Inventory system deals with quadratic demand which is function of permissible trade credit. Also products in the inventory are deteriorating at constant rate. The necessary condition to obtain the seller's optimal decision about setting the permissible credit period and purchase quantity is discussed. A process to determine the optimal solution is summarized. Lastly, the numerical example is given to show the theoretical results and sensitivity analysis is done to derive some managerial insights.