Mathematical Model of Transportaion Problem
Mathematical Model of a Transportation Problem
where m … number of sources n … number of destinations ai … capacity of i-th source (in tons, pounds, liters, etc) bj … demand of j-th destination (in tons, pounds, liters, etc.) cij … cost coefficients of material shipping (unit shipping cost) between i-th source and j-th destination (in $ or as a distance in kilometers, miles, etc.) xij … amount of material shipped between i-th source and j-th destination (in tons, pounds, liters etc.)
7. The Transportation Problem
There is a type of linear programming problem that may be solved using a simplified version of the simplex technique called transportation method. Because of its major application in solving problems involving several product sources and several destinations of products, this type of problem is frequently called the transportation problem. It gets its name from its application to problems involving transporting products from several sources to several destinations. Although the formation can be used to represent more general assignment and scheduling problems as well as transportation and distribution problems. The two common objectives of such problems are either (1) minimize the cost of shipping munits to n destinations or (2) maximize the profit of shipping m units to n destinations.
Let us assume there are m sources supplying n destinations. Source capacities, destinations requirements and costs of material shipping from each source to each destination are given constantly. The transportation problem can be described using following linear programming mathematical model and usually it appears in a transportation tableau.
There are three general steps in solving transportation problems.
We will now discuss each one in the context of a simple example. Suppose one company has four factories supplying four warehouses and its management wants to determine the minimum-cost shipping schedule for its weekly output of chests. Factory supply,
where m … number of sources n … number of destinations ai … capacity of i-th source (in tons, pounds, liters, etc) bj … demand of j-th destination (in tons, pounds, liters, etc.) cij … cost coefficients of material shipping (unit shipping cost) between i-th source and j-th destination (in $ or as a distance in kilometers, miles, etc.) xij … amount of material shipped between i-th source and j-th destination (in tons, pounds, liters etc.)
7. The Transportation Problem
There is a type of linear programming problem that may be solved using a simplified version of the simplex technique called transportation method. Because of its major application in solving problems involving several product sources and several destinations of products, this type of problem is frequently called the transportation problem. It gets its name from its application to problems involving transporting products from several sources to several destinations. Although the formation can be used to represent more general assignment and scheduling problems as well as transportation and distribution problems. The two common objectives of such problems are either (1) minimize the cost of shipping munits to n destinations or (2) maximize the profit of shipping m units to n destinations.
Let us assume there are m sources supplying n destinations. Source capacities, destinations requirements and costs of material shipping from each source to each destination are given constantly. The transportation problem can be described using following linear programming mathematical model and usually it appears in a transportation tableau.
There are three general steps in solving transportation problems.
We will now discuss each one in the context of a simple example. Suppose one company has four factories supplying four warehouses and its management wants to determine the minimum-cost shipping schedule for its weekly output of chests. Factory supply,