Models for Ordering Multiple Products Subject to Multiple Constraints, Quantity and Freight Discounts

Abstract

One of the most important responsibilities of a supply chain manager is to decide "how much" (or "many") of inventory items to order and how to transport them. This paper presents four mixed-integer linear programming models to help supply chain managers make these decisions for multiple products subject to multiple constraints when suppliers offer quantity discounts and shippers offer freight discounts. Each model deals with one of the possible combinations of all-units, incremental quantity discounts, all-weight and incremental freight discounts. The models are based on a piecewise linear approximation of the number of orders function. They allow any number of linear constraints and determine if independent or common (fixed) cycle ordering has a lower total cost. Results of computational experiments on an example problem are also presented.

Multiple Objective Fuzzy Sourcing Problem with Multiple Items in Discount Environments

“…According to the physical flow another discount scheme is freight rate discount scheme offered by shippers [13,14]. While quantity discount considers unit price, freight rate discount considers unit shipment and it can be offered according to all units (called all weights) or incremental strategies [15].…”

“…Step (4): considering lower bounds and upper bounds of demand levels, one at a time, the corresponding mathematical model defined with (1) to (15) in Section 3 is constructed and ideal solutions for each objective are found. Constructed payoff tables are Tables 5 and 6.…”

Development of multi-item EOQ when the constraints of investment and storage capacity are active

“…The order quantity which minimizes the cost is called Economic Order Quantity (EOQ). A four mixed integer linear programing models to support decision making of supply chain management for multi-item subject with multi-constraint when the supplier and shipper offer quantity and freight discount respectively showed by [3], they present possible collection of ascending quantity discount, ascending freight quantity discount, all-unit and all-weight in each mode. The models depend on the number of order function of piecewise linear approximation.…”