Considering a single period inventory management problem used in the distribution channel to represent consumer demand for marketing/sales of a product, attempt is made to develop a deterministic inventory model with time-varying increasing demand that may be used to reflect sales in different phases of a product life cycle in the competitive market. We propose inventory model assuming replenishment cost is to be linearly dependent on lot size and purchasing cost per unit item is dependent on lead time. Lead time is taken as decision variable. Shortages are allowed to backlog and to lose partly. Our objective is to cumulatively evaluate optimal replenishment lot-size, order time and lead-time for maximization of total profit. Considering the complexities of the proposed model, we propose a heuristic solution approach by developing an ERCM Genetic Algorithm based on ranking section, elitism, whole arithmetic crossover and non-uniform mutation dependent on the age of the population. This heuristics are easy to compute and practical to implement, and perform well in numerical trials.
Top1. Introduction
Today’s global business environment force manufacturers to sustain a fierce competition among wholesalers and retailers within their distribution network. Business competition nowadays’ witness a sea change with service operation getting importance; force retailers to go for ‘more and more variety of buying’ as per end users choice of buying. Inventory management is one of the most relevant and challenging activities for any manufacturing organization and must be executed as efficiently as possible to achieve success in today's fierce competitive business world (Cárdenas-Barrón et al., 2014). In recent years, considerable attention is shown by many researchers on production-inventory problems with planning horizon and deterministic time varying demand pattern (Abad & Jaggi, 2003; Kun-Shan, 2000; Shah et al., 2012). This type of problem was first developed by Stanfel and Sivazalian, 1975, without highlighting / stating specific assumption about the nature of demand. Later on, Silver and Meal, 1973, developed a solution procedure heuristically to a deterministic inventory model with time varying demand.
Inventory problems considering with deterministic time - varying demand pattern have demonstrated a considerable more attention to many of the researchers (Ghare & Schrader, 1963; Giri et al., 1996). Donaldson, 1977, first developed an exact solution procedure for items with a linear trend in demand. Removing complexity, several researchers such as Mitra et al., 1984, Ritchie, 1984, Silver, 1984 etc. developed various other techniques to remove computational complexity of Donaldson’s model. However, all these models, shortages were not allowed to occur.
Inventory model with time independent demand pattern and incorporating finite shortage cost generally come under following two categories:
In the former, each of the first (n - 1) ordering cycle starts with a replenishment and inventory is built up for a certain period; followed by a period of shortages, but shortages are not permitted in the nth cycle. Academic research refers to Murdeshwar, 1988, Dave, 1989a, 1989b, Datta and Pal, 1992, etc.
In the second, every order cycle starts with shortages and after a period of shortage; replenishment is made. Significant works here refers to the seminal work of Goyal et al., 1992 and 1996. Model deals with time dependent demand assumed that the replenishment cost of items is constant in each replenishment cycle.
In controlling inventory, deterioration is considered as a deterrent factor; academic research refers to the famous work of Aggarwal, 1978, and Jaggi and Aggarwal, 1995, Shah and Jaiswal, 1997, Bhunia and Maiti, 1999 and Bhunia et al. 2001 etc. Recently, Chung et al., 2014, proposed and developed an Inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain under two levels of trade credit. They developed an Inventory model of deteriorating items under stock-dependent demand and two-level trade credit in the line of supply chain (Chung et al., 2014). Widyadana et al., 2011, proposed an Economic Order Quantity model for deteriorating items with planned back order level and with small deterioration rate. Lot size is taken as decision variable in controlling inventories; research work refers to Shah, 1993, Tersine and Barman, 1991 etc. Again, another factor which is predominant in controlling inventories is lead-time; is generally taken either as constant or stochastic. By shortening lead-time, we can lower safety stock, reduce stock-out loss and improve customer service level so as to gain competitive advantage in industry.