An inventory model of deteriorating seasonal products with Maximum Retail Price (MRP) for a wholesaler having showrooms at different places under a single management system is considered under random business periods with fuzzy resource constraints. The wholesaler replenishes the products instantaneously and earns commissions on MRP which vary with the ordered quantities following All Unit Discount (AUD), Incremental Quantity Discount (IQD) or IQD in AUD policy. Demand at showrooms are imprecise and related to selling prices by ‘verbal words’ following fuzzy logic. The wholesaler shares a part of commission with customers. The business periods follows normal distribution and converted to deterministic ones through chance constraint technique. The fuzzy space and budget constraints and fuzzy relations are defuzzified using possibility measures, surprise function and Mumdani fuzzy inference technique. The model is formulated as profit maximization for the wholesaler and solved using a real coded Genetic Algorithm (GA) and illustrated through some numerical examples and some sensitivity analysis. A real-life problem of a developing country is presented, solved using the above mentioned procedures and an appropriate inventory policy is suggested.
In the existing literature of inventory, most of the models are developed under infinite time horizon. As per Gurnani (1985), the life of a particular item is not infinite due to the change of design, technological development, variation of inventory costs, customers’ changing taste, etc. and this is very much true for the seasonal products in developing countries where preserving facilities are not available in plenty. For these seasonal products, even though the planning horizon is assumed as finite, in every season it fluctuates depending on some extraneous factors such as climatic conditions. This time period may be assumed to be random with a probability distribution. In the literature Maiti et al., 2006 and Roy et al., 2009 have solved some inventory problems with random planning horizon having exponential distribution. Also Moon and Lee (2000) have presented an EOQ model under inflation and discounting with a random product life cycle.
In an inventory system, deterioration is an usual phenomenon. Mandal and Phaujdar (1989) presented an inventory model with deteriorating items. Roy, Maiti, Kar, and Maiti (2009) have done a research work of deteriorating items with stock dependent demand over random planning horizon. Also Bhunia and Maiti, 1997 and Mahapatra and Maiti, 2006 presented some inventory models for deteriorating items with time dependent demand and imprecise production time respectively.
In the present competitive market, the demand depends on the stock directly and also inversely on the selling price. Recently Widyadana, Cardenas-Barron, and Wee (2011) presented a deteriorating inventory problem with constant demand via a simplified approach. Also Giri et al., 1996 and Mandal and Maiti, 2000 and others considered the demand as an indexed stock (i.e. D = dqβ, d and β are constants) dependent. But there are few research works with fuzzy demand depending on stock and selling price following fuzzy inference. Recently, some inventory models with rework for the defective products ( Jamal et al., 2004, Cardenas-Barron, 2007, Cardenas-Barron, 2008, Cardenas-Barron, 2009a, Cardenas-Barron, 2009b, Sarker et al., 2008 and Cardenas-Barron et al., 2012) have been presented in the literature.
Human knowledge is often represented imprecisely, vaguely and approximately. In our real life, some vague terms in the form of ‘words’ such as high, medium, and low, are used. The target of fuzzy inference process is to form it into natural language expressions of the type,
In this research paper, a realistic supply-chain/inventory model is depicted for a wholesaler with showrooms at different places selling multi-seasonal products and allowing different systems of discount on MRP, in which selling price and market demand are connected by fuzzy logic. Here, the time period of business is random having a distribution with mean and standard deviation. For the first time, randomness of the time horizon has been introduced in the from of a chance constraint and implemented in a supply chain/inventory problem. This analysis will help the practitioners of seasonal products such as fashional goods, warm cloths, and medicines. A methodology is presented to formulate the fuzzy data from some practical real-life survey data and this to solve the model following fuzzy rules and discounts The formulation and analysis presented here are quite general and can be extended to include different fuzzy logic relations connecting different parameters such as demand, price and exhibited quantity, etc. fully or partially backlogged shortages, fuzzy time period, etc.
