An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets

Graphical abstractDisplay Omitted HighlightsIt is an integrated production inventory model of a manufacturer and multiple markets which have different selling seasons.Raw-materials supplier offers a credit period to the manufacturer which may be crisp and fuzzy.The fuzziness of the credit period is analyzed in two different ways such as - triangular and trapezoidal fuzzy numbers.Raw-materials for production and finished item are both considered as deteriorating and nondeteriorating cases.Manufacturer allows a conditional part-payment to the markets and his selling price is assumed as an increasing function of production run time. The presence of multiple markets create profitable opportunities to the supply chain system. In this regard, this paper consists of the joint relationship between a manufacturer and multiple markets in which manufacturer offers part-payment to the markets due to their collection of finished products during the production run time. Here it is also considered that manufacturer is facilitated with credit period by raw material supplier where credit period has been presented as an interactive fuzzy fashion. In this paper, two types of deterioration have been assumed such as one for finished products and the other for raw materials. A solution algorithm is presented to get fuzzy optimal profit for the proposed integrated production inventory system optimizing production run time. A numerical example is used to illustrate the proposed model. Finally, sensitivity analysis has been carried out with respect to the major parameters to demonstrate the feasibility of the proposed model.

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