A Complicated Continuous Model of Supply Chain

Abstract

The issue of supply chain management has focused on practical operations and their theoretical applications for comparison with the traditional business aim, which merely pursues the maximal benefit. A business should simultaneously consider the benefits, resources and facilities for all stages in the supply chain system; i.e., consider the creation of an overall value for the system instead of the traditional goal of pursuing maximal benefits in certain focused stages.This study aims to provide a referenced decision-making tool for a decision-maker in the current complex environment and also function as a decision-making tool for focusing on the overall and real-time analyses of multi-interval planning for a supply chain system. This system will investigate the purchase, production, inventory, distribution, and product shortage to deal with customers' demands for pursuing the maximal profit under a constrained production/inventory and finite distribution capacity. This research not only considers the multi-product order, multi-factory production, multi-material purchase, multi-distribution transportation, quantity discounts, diverse-customer demand, product inventory cost and limited inventory space but also provides the punishment cost of the demand shortage to construct an Integer Nonlinear Programming (INLP) mathematical model for achieving the maximum profit. Moreover, the proposed mathematical model is constructed by using the syntax of Lingo 9.0, wherein the built-in ”global solver” is selected as the solution method. A numerical example then follows. This study creates a highly repetitive characteristic because of the application of the packaged software (Lingo 9.0); therefore, the proposed model and the solution method can be treated as valuable.