A supply chain of a coastal biomass incorporating fuzzy deterioration and freshness under dynamic unit price

In this study, a wholesaler–retailer supply chain (SC) of a coastal biomass in an imprecise environment is developed incorporating the effect of the freshness of the units on the consumers’ demand under promotional cost sharing. Due to the imprecise nature of the rate of deterioration, the deterioration rate and the expiration time of the units are considered fuzzy numbers. As the freshness of the units depends on the expiration time, its nature is also imprecise and decreases with time. So, the seller normally decreases the unit selling price with time to boost the demand for biomass. The demand for the item is influenced by the unit selling price and freshness of the units, and hence its nature is also fuzzy. Due to the impreciseness of the rate of demand and deterioration, the model is mathematically formulated using fuzzy differential equations and fuzzy Riemann integration. The credibility measure of the fuzzy objective(average profit) with respect to a properly defined fuzzy goal is optimized for determining the marketing decision. Also, fuzzy simulation algorithms are presented for determining the said credibility measure. The models are studied in both the non-coordination scenario and the coordination scenario. In the non-coordination scenario, the retailer is the leader and the wholesaler is the follower, i.e., the retailer determines the marketing decision independently, and following the decision of the retailer the wholesaler determines his/her marketing strategy. In the coordination scenario, they make a joint decision for better performance by sharing the promotional cost incurred by the retailer by reducing the selling price to boost the demand. The model is illustrated using a set of test data and it is established that the individual profits as well as the channel profit improve if the decision is made jointly. In a particular case, the model is solved for the rough estimations of some problem parameters and an approach is proposed for the mathematical formulation and decision-making. The trust measure on a rough goal is defined for the formulation of the model and corresponding rough simulation algorithm is presented for the determination of the same. As the simulation approaches are used for the decision-making in imprecise environments, the basic particle swarm optimization algorithm is slightly modified, implemented, tested, and used for the determination of the marketing decision for the different models.