Least Time Model Or Schedule Of Transportation Model

Introduction:

It is well known fact that the transportation problem is cost minimization model, i.e. we have to find the least cost transportation schedule for the given problem. Some times the cost will become secondary factor when the time required for transportation is considered.

Time Minimisation model or least time model:

a)      This type of situation we see in military operation.

b)      When the army want to send weapons or food packets or medicine to the war front, then the time is important than the money.

c)       They have to think of what is the least time required to transport the goods than the least cost of transportation.

d)      matrix gives the time elements, i.e. time required to reach from one origin to a destination than the cost of transportation of one unit from one origin to a destination.

e)      A usual, we can get the basic feasible solution by Northwest corner method or by least time method or by VAM.

f)       To optimize the basic feasible solution, we have to identify the highest time element in the allocated cells, and try to eliminate it from the schedule by drawing loops and encouraging taking the cell, which is having the time element less than the highest one. Let us take a problem and work out the solution.

g)      Many a time, when we use VAM for basic feasible solution, the chance of getting an optimal solution is more.

h)      the basic feasible solution is obtained by Northwest corner method.

Example: The matrix given below shows the time required to shift a load from origins to destinations. Formulate a least time schedule.  Time given in hours. Roc: Row opportunity cost, Coc: Column opportunity cost, Avail: Availability, Req: Requirement.

Initial assignment by Northwest corner method: The Maximum time of allocated cell is 17 hours. Any cell having time element greater than 17 hours is cancelled, so that it will not in the programme.