Multi-item inventory model with probabilistic demand function under permissible delay in payment and fuzzy-stochastic budget constraint: A signomial geometric programming method

This study proposes a new multi-item inventory model with hybrid cost parameters under a fuzzy-stochastic constraint and permissible delay in payment. The price and marketing expenditure dependent stochastic demand and the demand dependent the unit production cost are considered. Shortages are allowed and partially backordered. The main objective of this paper is to determine selling price, marketing expenditure, credit period, and variables of inventory control simultaneously for maximizing the total profit. To solve the problem, first some transformations are applied to convert the original problem into a multi-objective nonlinear programming problem, of which each objective has signomial terms. Then, the multi-objective nonlinear programming problem is solved by first converting it into a single objective problem and then by using global optimization of signomial geometric programming problems. At the end, several numerical examples and sensitivity analysis are done to test model and solution procedure and also obtain managerial insights.