In retail industries every ordered lot carry some fraction of imperfect quality items which can vary depending upon production and handling conditions. The situation is even more subtle when the items are prone to deterioration. However, an inspection process can spare us from such a criticality by bifurcating the defectives from the good quality lot. Thus, a screening process is mandatory. In the hyper-competitive market, trade-credit is well-known gimmick in order to boost the sales. Keeping in view, an inventory scenario of a retailer is investigated who has to deal with imperfect and “deteriorating items” under “permissible delay in payments”. The demand is assumed to be increasing exponentially. Shortages are permitted to occur and supposed to be “partially backlogged.” Rate of backlogging is assumed to have inverse relation with the waiting time for the subsequent replenishment. In this chapter, shortage point and length of cycle are jointly optimized. Numerical analysis and sensitivity analysis is performed to provide important insights for managerial persistence.
TopIntroduction
Efficient inventory management is the key aspect of todays’ business world which aims at minimizing the inventory holding cost and at the same time sustaining a desired service level. While managing the supply chain and inventory problems it is vital to expand the horizons for a realistic modeling so as to serve the decision-makers with solutions to real-time system. While talking about realistic inventory modeling phenomena of decay cannot be ignored because inventory items usually experience damage, spoilage, obsolescence, evaporation, pilferage etc. which results in diminishing the utility of the original product. The pioneer work in this category was contributed by Ghare and Schrader (1963), Covert and Philip (1973), Dave and Patel (1981), Sachan (1984) and Dave (1989) which was later summarized by Raafat et al. (1991). Later, Chung and Ting (1994), Hariga and Benkherouf (1994), Aggarwal and Jaggi (1995), Goyal and Giri (2001) etc.
Demand possesses pivotal role in manufacturing and sales industry. Fluctuations in demand pattern affects the market thoroughly. Therefore, it is not justified to assume the demand rate to be constant as a large number of commodities (viz., electrical and electronic items, products in fashion etc.) encounter with variable demand patterns which can be expressed through time-varying demand. Numerous products experience an inclining demand during their growth phase. The same phenomena are observed in the case of seasonal products, with the onset of a season the demand is higher for the respective product. Some remarkable work in this field was done by Wagner and Whitin (1958), Donaldson (1977), Silver (1979), Dave (1989), Reddy and Ranganatham (2012) etc.
One more factor which is quite unrealistic to assume is that all the units have perfect quality. However, despite all the efforts, it is difficult to manufacture or buy products with 100% perfect quality. It is therefore obligatory to perform screening of the lot. In the light of this fact several researchers explored the area of imperfect quality. Some of the instigators of this category were Porteus (1986) and Rosenblatt and Lee (1986) thereafter a number of researchers explored this area viz. Salameh and Jaber (2000), Papachristos and Konstantaras (2006), Maddah and Jaber (2008), Jaggi et al. (2013a), Aditi et al. (2016) and many more.
Further, Trade-Credit has become a renowned strategy which is now adopted by many supply chain players in order to uplift their business. It allows the customer to defer the payment up to the given limit of credit period allowed by the supplier so as to earn revenue and interest. Kingsman (1983), Goyal (1985), Davis and Gaither (1985), Chu et al. (1998) are the remarkable research of this area. Numerous research papers were published in this area which was later reviewed by Soni et al. (2010). Also, Shortages are unavoidable because of uncertainties in the process of demand and supply. Hariga (1995) presented a model for deteriorating items with shortages in which he considered demand to be time-varying. Followed by Chakrabarti and Chaudhari (1997), Wee et al. (2007), Chang and Ho (2010), Jaggi et al. (2013b) and many more.