Consider a situation where to make an item i (i = 1, ..., K), it first must be processed on machine 1, then machine 2, then machine 3, ..., and finally on machine M. Although the sequence of processing each item on the machines is fixed, namely, 1, 2, ..., M, the order of processing an item i at each machine is to be determined and may vary from machine to machine. Let tij be the processing time required by item i on machine j. Formulate the problem as an integer program where we wish to determine the order of processing the items at each machine so as to minimize the total time necessary to process all the items. List any assumptions