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This paper considers an imperfect manufacturing system with credit policies in fuzzy random environments. The supplier simultaneously offers the retailer either a permissible delay in payments or a cash discount and retailer in turn provides its customer a permissible delay period. We used an alternate approach – discount cash flow analysis to establish an inventory problem. It is assumed that the elapsed time until the machine shifts from 'in-control' state to 'out-of-control' state is characterized as a fuzzy random variable. As a function of this parameter, the profit function is also a random fuzzy variable. Based on the credibility measure of fuzzy event, the model with fuzzy random elapsed time can be transformed into a crisp model. We establish several theoretical results to obtain the solution that provides the largest present value of all future cash flows. Finally, numerical example is given to illustrate the results and obtain some managerial insights. [ABSTRACT FROM AUTHOR]

This paper considers the problem of dynamic decision-making for an inventory model for deteriorating items under price inflation and permissible delay in payment. In this paper, we adopt an iso-elastic and selling price dependent demand function to model the finite time horizon inventory for deteriorating items. The stocks deteriorate physically at a constant fraction of the on-hand inventory. The objective of this paper is to determine the optimal retail price, number of replenishments, and the cycle time under two different credit periods so that the net profit is maximized. We discuss the optimization properties and develop an algorithm for solving the problem based on dynamic programming techniques. Numerical examples are presented to illustrate the validity of the optimal control policy, and sensitivity analysis on major parameters is performed to provide more managerial insights into deteriorating items. [ABSTRACT FROM AUTHOR]