Case 36
Executive Summary
Overview
Agrifarm Company is in the business of buying and selling grain. The company wants to increase profitability by ensuring that shipping costs are kept low. All is shipments come from 3 rail cars origins. In addition, all shipments must be routed through either of two grain processing centers before sending them to the final customer. The object is to minimize the total shipping cost, therefore selecting the proper shipping route for each carload.
Problem
There is a total capacity (rail carloads) of 14 that is available to serve a total demand (rail carloads sold) of 15. With this mentioned, there is an unbalanced capacity and demand. To solve for the proper shipping route, we will have to include a dummy variable equal to 1, which is the difference between capacity and demand. This means one customer will receive a shortage of 1 rail car of grain. In addition, we need to meet certain requirements (constrains) that limit the capacity from origin (outbound) as well as (inbound) constraints at destinations. Not to mention, we also have two processing centers (hubs) constraints. There are a total of four rail cars of grain (outbound constraints) explained below. Muncie Farm Capacity | | | 3 | <= | 3 | | Outbound | Brazil Farm Capacity | | | 6 | <= | 6 | | Outbound | Xenia Farm Capacity | | | 5 | <= | 5 | | Outbound | Dummy | | | 1 | <= | 1 | | Outbound |
Also, there are two processing centers (hubs constraints) that need to be met. These are explained below. Louisville Proc Ctr Balance Constraint | | | 0 | = | 0 | | Hub | Cincinnati Proc Ctr Balance Constraint | | | 0 | = | 0 | | Hub |
In addition, we have four inbound constraints that need to be met. Macon Customer Demand | | | 2 | = | 2 | | Inbound | Greenwood Customer Demand | | | 5 | = | 5 | | Inbound | Concord Customer Demand | | | 3 | = | 3 | | Inbound | Chatham Customer Demand | | |
Overview
Agrifarm Company is in the business of buying and selling grain. The company wants to increase profitability by ensuring that shipping costs are kept low. All is shipments come from 3 rail cars origins. In addition, all shipments must be routed through either of two grain processing centers before sending them to the final customer. The object is to minimize the total shipping cost, therefore selecting the proper shipping route for each carload.
Problem
There is a total capacity (rail carloads) of 14 that is available to serve a total demand (rail carloads sold) of 15. With this mentioned, there is an unbalanced capacity and demand. To solve for the proper shipping route, we will have to include a dummy variable equal to 1, which is the difference between capacity and demand. This means one customer will receive a shortage of 1 rail car of grain. In addition, we need to meet certain requirements (constrains) that limit the capacity from origin (outbound) as well as (inbound) constraints at destinations. Not to mention, we also have two processing centers (hubs) constraints. There are a total of four rail cars of grain (outbound constraints) explained below. Muncie Farm Capacity | | | 3 | <= | 3 | | Outbound | Brazil Farm Capacity | | | 6 | <= | 6 | | Outbound | Xenia Farm Capacity | | | 5 | <= | 5 | | Outbound | Dummy | | | 1 | <= | 1 | | Outbound |
Also, there are two processing centers (hubs constraints) that need to be met. These are explained below. Louisville Proc Ctr Balance Constraint | | | 0 | = | 0 | | Hub | Cincinnati Proc Ctr Balance Constraint | | | 0 | = | 0 | | Hub |
In addition, we have four inbound constraints that need to be met. Macon Customer Demand | | | 2 | = | 2 | | Inbound | Greenwood Customer Demand | | | 5 | = | 5 | | Inbound | Concord Customer Demand | | | 3 | = | 3 | | Inbound | Chatham Customer Demand | | |