# Assignment Problem In Operational Research

The row wise reduced matrix is shown in table below.Reduce the new matrix given in the following table by selecting the smallest value in each column and subtract from other values in that corresponding column.The second example illustrates a complex case where you need to proceed all the steps of the algorithm to get to an optimal solution.

In the first phase, row reductions and column reductions are carried out.

In the second phase, the solution is optimized on iterative basis.

We combine the above two objectives into one term: the total cost, a sum of the total dock operational cost and the penalty cost for all the unfulfilled shipments.

The problem is then formulated as an Integer Programming (IP) model.

Repeat the process until all the assignments have been made.

Write down the assignment results and find the minimum cost/time.

In this paper, we consider a truck dock assignment problem with operational time constraint in crossdocks where the number of trucks exceeds the number of docks available.

The objective is to find an optimal assignment of trucks that minimizes the operational cost of the cargo shipments and the total number of unfulfilled shipments.

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