A deteriorating multi-item inventory model with price discount and variable demands via fuzzy logic under resource constraints

• Demands of the products very with selling price following some fuzzy rules.
• Fuzzy and crisp constraints expressed by possibility measures and surprise function.
• Three types of discounts – AUD, IQD and IQD in AUD on MRP are introduced.
• Business period is random with normal distribution.
• Mamdani technique is used and the problem is solved using Genetic Algorithm.

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.