Optimal payment time with deteriorating items under inflation and permissible delay in payments

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. This article develops an inventory model under a situation in which the supplier provides the purchaser with a permissible delay of payments. Shortages are not allowed and the effect of the inflation rate, deterioration rate and delay in payment are discussed as well. As a result, in this article, we establish a mathematical model to determine the optimal payment period and replenishment cycle. Using Taylor series approximation, we characterise the optimal solution and provide an easy-to-use algorithm to find the optimal solution. Finally, the proposed models are illustrated through numerical examples and the sensitivity analysis is reported. 1. Introduction In real life, deterioration of many items during storage period is a fact, such as chemicals, IC chip, volatile liquids, blood banks, medicines, electronic components and so forth. In general, deterioration is defined as the decay, damage, spoilage, evaporation and obsolescence of stored items and it results in decreasing usefulness. Therefore, the control and maintenance of inventories of deteriorating items becomes an important issue for decision makers in modern organisations. Several researchers have studied deteriorating inventory in the past. Ghare and Schrader (1963) were the first proponents to establish a model for an exponentially decaying inventory. Covert and Philip (1973) extended Ghare and Schrader's constant deterioration rate to a two-parameter Weibull distribution. Goyal and Giri (2001) also provided a detailed review of deteriorating inventory literatures. Other interesting papers dealing with the same issue include Shah and Jaiswal In the conventional economic order quantity (EOQ) model, it is implicit that the purchaser must pay for the items as soon as the items are received. However, in practice, the supplier may offer his/her customers a certain credit period, that is, during the permissible delay time period, the customer …