Exploring the Dependency of Order Size in Integrated Inventory Model Under Partial Trade Credit and All Unit Discounts with Capacity Constraints

This study introduces an integrated inventory model with order size-dependent partial trade credit periods and all-unit discounts under capacity constraints, where the supplier accepts partial back-orders during the stock-out period. The model assumes that the manufacturer offers the supplier a partial trade credit period and all-unit discounts based on order size, and the supplier extends the partial trade credit to the retailer. The total profit function is developed by combining the profits of both the manufacturer and the supplier, and we proved the concavity of the total combined profit function. An algorithm is presented to determine the optimal number of shipments, ordering lot, and replenishment period. Numerical examples and sensitivity analyses on various parameters illustrate the suggested concept. We find that a higher interest-earning rate motivates the supplier to make more frequent, smaller orders, which boosts profits.