Two storage inventory model of a deteriorating item with variable demand under partial credit period

In this paper, a two-warehouse inventory model for deteriorating item with stock and selling price dependent demand has been developed. Above a certain (fixed) ordered label, supplier provides full permissible delay in payment per order to attract more customers. But an interest is charged by the supplier if payment is made after the said delay period. The supplier also offers a partial permissible delay in payment even if the order quantity is less than the fixed ordered label. For display of goods, retailer has one warehouse of finite capacity at the heart of the market place and another warehouse of infinite capacity (that means capacity of second warehouse is sufficiently large) situated outside the market but near to first warehouse. Units are continuously transferred from second warehouse to first and sold from first warehouse. Combining the features of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) a hybrid heuristic (named Particle Swarm-Genetic Algorithm (PSGA)) is developed and used to find solution of the proposed model. To test the efficiency of the proposed algorithm, models are also solved using another two established heuristic techniques and results are compared with those obtained using proposed PSGA. Here order quantity, refilling point at first warehouse and mark-up of selling price of fresh units are decision variables. Models are formulated for both crisp and fuzzy inventory parameters and illustrated with numerical examples. © 2012 Elsevier B.V. All rights reserved. . Introduction The inventory model is based on the assumption that the retailer pays for the units of the item immediately after the units are received. ut, due to introduction of multinationals and their franchises, now-a-days, supplier frequently offers a permissible delay in payments o attract new customers and increase sale. Goyal [10] developed an economic ordered quantity (EOQ) model under the conditions of ermissible delay in payments. Aggarwal and Jaggi [2] extended Goyal’s [10] model considering deteriorating item. Chung and Liao [7] tudied a lot-sizing problem under supplier’s trade credit depending on the retailer’s order quantity. Huang [13] established an EOQ model n which the supplier offers a partially permissible delay in payment when the order quantity is smaller than a predetermined quantity. uyang et al. [29] developed an EOQ model for deteriorating items with partially permissible delay in payments linked to order quantity. n their model supplier gives full trade credit when retailer’s purchase quantity is more than or equal to certain amount and allows partial rade credit for less amount. Liang and Zhou [16] developed a two-warehouse inventory model for deteriorating items under conditionally ermissible delay in payment. Singh et al. [30] developed a two warehouse fuzzy inventory model under the conditions of permissible elay in payment. All of the above mention studies on permissible delay in payments are made considering single warehouse facility specially when partial rade credit period is offered to retailers. To avail the delay in payment facility retailer has to purchase a large amount of units for which ufficient warehouse space is required to store the item. But in present competitive market due to high rent and scarcity of space, it is ifficult to get an outlet having sufficient storage area at the heart of the market place. Due to limited capacity of outlet (viz., W1) at the arket place, purchase of large amount of units (to get facilities of permissible delay in payments, i.e., to maximize the profit) of an item eads to storage problem. As a result, normally excess units are stored in the second warehouse (W2) having sufficiently large capacity ∗ Corresponding author. Tel.: +91 9434385976. E-mail addresses: parthaguchhait@gmail.com (P. Guchhait), manasmaiti@yahoo.co.in (M.K. Maiti), mmaiti2005@yahoo.co.in (M. Maiti). 568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. ttp://dx.doi.org/10.1016/j.asoc.2012.07.028 w o o i o d o d a t w o i w i M c p • • •