Suppose that an organization requires varying levels of resources at q geographical locations. Suppose, further, that changes
Question:
Suppose that an organization requires varying levels of resources at q geographical locations. Suppose, further, that changes in economic, political, social, or environmental conditions have brought about a sudden demand for the resources. For example, natural disasters such as floods might create a need for various types of rescue equipment at various flood locations. Or, the resources might be relief supplies such as food or medicines. This exercise studies a model that minimizes the combined cost of transportation and unfulfilled demands. Let djk denote the demand of resource k (in tons) at location j. The resources are available in limited quantities at different locations; let aik denote the amount of resource k available at location I. The cost of transporting 1 unit of the resource k from location I to location j is cijk. Due to technological constraints, at most ui tons of all resources can be transported from location I. As a result, it might not be possible to completely satisfy the demands for the resource. Let αjk denote the cost of unfulfilled demand of resource k at location j. Our objective is to identify the shipment of resources that minimizes the total of the transportation costs and the costs arising due to unfulfilled demand.
(a) Formulate this problem as a multi-commodity flow problem using arc variables.
(b) Formulate this problem as a multi-commodity flow problem using path variables.
The Legal Environment of Business
ISBN: 978-0538473996
11th Edition
Authors: Roger E Meiners, Al H. Ringleb, Frances L. Edwards