Effects of a quantity-based discount frame in inventory planning under time-dependent demand: A case study of mango businesses in Bangladesh

Abstract

This work studies an inventory planning problem for a practitioner selling a non-immediate perishable item after purchasing it from a supplier within a quantity-based discount frame and assesses the impact of the discount frame on the practitioner’s costs. Due to perishability, consumption behavior is directly interconnected with the storage time of the items. The foremost objective of this work is to provide, for the first time, proper inventory planning to minimize the practitioner’s total cost under a quantity-based discount frame when demand changes with the product’s storage time. To make this inventory planning problem more realistic, both zero-ending and stock-out situations are investigated. Under both scenarios, the optimal inventory plan for the practitioner is examined analytically, and then, integrating the analytical results, two solution algorithms are presented under the quantity-based discount frame. In order to verify the investigated inventory problem and scrutinize the efficiency of the algorithms as well, a real example of a mango business is inspected. Several insights are gained for the practitioner by running a sensitivity analysis on the optimal inventory plan against the system input parameters. The results suggest that the practitioner can take advantage of a reduced acquisition price by making a larger number of purchases under the order-based rebate program, greatly reducing its cost.

Keywords

• Quantity-based discount
• Deterioration
• Time-dependent demand
• Partial backordering