Optimal Policies for Items With Quadratic Demand and Time-Dependent Deterioration Under Two Echelon Trade Credits

Optimal Policies for Items With Quadratic Demand and Time-Dependent Deterioration Under Two Echelon Trade Credits

Azharuddin Sarfuddin Shaikh (Institute of Infrastructure Technology Research and Management, India) and Poonam Prakash Mishra (Pandit Deendayal Petroleum University, India)
DOI: 10.4018/978-1-5225-3232-3.ch002

Abstract

In today's competitive and global business scenario there is always a race to boost demand of your product over others. This can be achieved by different means and allowing permissible delay in payments is one of them. Researchers have proposed number of inventory models with trade credit that actually help to understand effect of trade credit on total profit and overall demand. This paper proposes a two – echelon trade credit where retailer receives credit period from the manufacturer and offer it to end customers appropriately to raise demand. Proposed inventory model assumes quadratic demand and subjected to time dependent deterioration. Ordering cost is considered lot – size dependent whereas holding cost has been taken time dependent. In this model profit is maximized considering cycle time as a decision variable. Sensitivity analysis of crucial inventory parameters and numeric examples are discussed in detail. Outcome of this model can be applied to a huge range of products like readymade garments, fashion accessories, electronics, furniture and home furnishing products.
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Introduction

Offering credit to buyers is actually not new it is being practiced since a long time to accelerate demand positively. During this credit period, the retailer can sell the items and generate revenue, using this revenue retailer earns interest by depositing it in some interest bearing account or in some financial terms. Haley & Higgins (1973) proposed credit policy for classical EOQ and further explored its effect on inventory policy. Chapman et al. (1984) derived an EOQ model that allows payment delays to boost demand. Goyal (1985) discussed a lot size model with permissible delay that charge interest on the amount remain outstanding after the permissible period. Shah et al. (1988) extended Goyal’s paper by including shortages in the model. Mandal & Phaujdar (1989 a, 1989b) further extended Goyal’s paper by adding interest earned on sales revenue. Khouja & Mehrez (1996) developed vendor credit policy to determine optimum lot size policy when credit is lot size dependent. Huang (2003) established that the retailer gets benefited if the credit period which is received from the supplier is passed onto the customers. The economic order quantity is computed when the supplier offers the retailer a credit period 978-1-5225-3232-3.ch002.m01 and the retailer passes a credit period 978-1-5225-3232-3.ch002.m02 to the customers with 978-1-5225-3232-3.ch002.m03. This scenario is known as two-level trade credit. Teng and Chang (2009) analyzed the two-level trade credit by relaxing the assumption 978-1-5225-3232-3.ch002.m04. Chang et al. (2003, 2009) further developed inventory model with the effect of deterioration. Khanra et al. (2003) worked on the same line with the assumptions of time dependent quadratic demand. Later on, Chung & Liao (2004, 2006), Chung et al. (2005), Dye and Ouyang (2005) studied different ordering policy where trade credit remains lot size dependent. Shah et al. (2010) gave a complete review of trade credit in inventory system. Shah & Shukla (2010, 2011) studied the effect of trade credit in the scenario of decreasing demand due to inflation. Sarkar (2012) offered delay in payments for deteriorating inventory model. Sarkar & Sarkar (2013) developed better model for time – dependent deteriorating inventory when demand is stock dependent. Shah et al. (2014) presented a model for deteriorating items with fixed lifetime. Shah et al. (2014) also discussed order quantity linked credit policy to optimize joint profit of supplier and retailer.

Key Terms in this Chapter

Deterioration: Deterioration is defined as decay, evaporation, obsolescence, loss of utility or marginal value of the commodity that results into the reduction of usefulness from the original condition. e.g., medicines, bulbs, fashionable goods, dairy products, grocery, fruits, vegetables, crockery items, electronic items, fashion accessories etc.

Weibull Distribution: Two parameters Weibull distribution is defined as where is shape parameter and is scale parameter.

Trade Credit: Permissible time period offered to settle the accounts is known as trade credit. It helps in boosting the sale as customer do not have to pay the amount at the time of purchase.

Quadratic Demand: In the market when a product is launched its demand increases linearly for some time and with new substitute available demand decreases exponentially. So, this form of demand is quadratic demand.

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