A production-recycling model with variable demand, demand-dependent fuzzy return rate: A fuzzy differential equation approach

A two warehouse production-recycling system for a single item with stock-dependent demand is considered. Item is produced at a production plant situated at a market place having sufficiently large warehouse with a small decorated showroom. Units are continuously transformed from production center to a showroom at the market for sale and excess units are stored at the production center warehouse. Production is stopped at regular intervals and after some production cycles, recycling process is commissioned. Used units are collected from the customers (up to beginning of last recycling cycle) at a demand-dependent fuzzy rate and then repaired to new condition before being sold again. Model is formulated using fuzzy differential equation and α-cut of fuzzy average profit is obtained. In the first approach, Modified Graded Mean Integration Value (MGMIV) of the average profit is optimized to derive decisions for the decision maker (DM). A genetic algorithm with binary mode representation, Roulette wheel selection and random mutation process is used to solve the model. In the second approach, using fuzzy preference ordering of intervals (FPOIs), α-cut of fuzzy average profit is optimized using the above GA to derive optimum decisions for DM. The proposed models are illustrated with numerical examples.

► Both production and recycling are considered with their rates as decision variables.
► Production/recycling cost includes costs for labor force and wear and tear of tools.
► To push sale, display of products is considered and hence demand is stock-dependent.
► Returned-units amount depends on demand, price, initiative, etc. So its rate is fuzzy.
► Production-recycling model presented by a fuzzy differential equation is solved by GA.