A Collaborative Vendor – Buyer Deteriorating Inventory Model for Optimal Pricing, Shipment and Payment Policy with Two – Part Trade Credit

The classical economic order quantity model of Wilson’s was developed with the assumption that the buyer must pay off immediately on arrival of the goods in the inventory system. In fact, offering buyers to delays payment for goods received is considered as a sales promotional tool in the business world. With offer of trade credit, vendor increases sales, attracts more buyers and reduces on – hand stock level. Under this marketing strategy, the time of the buyer’s capital tied up in stock reduced which eventually reduces the buyer’s holding cost of finance. In addition, during this allowable credit period, the buyer can earn interest on the generated revenue. For the small – scale industries having a limited finance, the trade credit acts as a source of short – term funds. Goyal (1985) developed an economic order quantity model with a constant demand rate under the condition of permissible delay in payments. After that numbers of variants of the trade credit problem have been analyzed. For example Shah (1993a, 1993b), Aggarwal and Jaggi (1995), Kim et al. (1995), Jamal et al. (1997), Shinn (1997), Chu et al. (1998), Chen and Chung (1999), Chang and Dye (2001), Teng (2002), Chung and Huang (2003), Shinn and Hwang (2003), Chung and Liao (2004, 2006), Chung et al. (2005), Teng et al. (2005), Ouyang et al. (2005) and their cited references. For up – to day available literature on permissible delay period, refer to the article by Shah et al. (2010). The above cited references assume that the vendor offer the buyer a “one – part” trade credit, i.e. the vendor offers a permissible delay period. If the account is settled within this period, no interest is charged to the buyer. As a result, with no incentive for making early payments, and earning interest through generated revenue during the credit period, the buyer postpones payment up to the last day of the permissible period offered by the vendor. As an outset, from the vendor’s end, offering trade credit leads to delayed cash inflow and increases the risk of cash flow shortage and bad debt. To increase cash inflow and reduce the risk of a cash crisis and bad debt, the vendor may offer a cash discount to attract the buyer to pay for goods earlier. i.e. the vendor offers a “two – part” trade credit to the buyer to balance the trade off between delayed payment and cash discount. For example, under an agreement, the vendor agrees to a 2% discount to the buyer’s purchase price if payment is made within 10 days. Otherwise, full payment is to be settled within 30 days after the