1 2 3 (ii) there are m machines, denoted by A, B, C, ..., K. f53 (11) each job is to be processed in the prescribed order, say ABCK. (iv) no passing of jobs is permitted (i.e., same order over each machine is maintained). (v) the actual or expected processing times A1, A2, ..., A, B1, B2, .., B.; C, C .... C.. K1, K2, ..., Kn are known and represented by a table of the type shown below. TABLE 5.18 Machine times for n jobs and m machines Job A B K 4 B C K B2 C, K A3 C K; : : : . c K : . B. K. The problem, as before, is to find the optimum sequence of jobs which minimizes T. CASEI Method of section 5.5 can be applied (extended) to cover the special cases where either one or both of the following conditions hold gold (if neither of the conditions holds good, the method fails) the minimum time on machine A is 2 maximum time on machines B, C,, K-1, (ii) the minimum time on machine K is 2 maximum time on machines B, C, ..., K-1. The method is to replace the m machine problem by an equivalent two machine problem. These two (fictitious) machines are denoted by a and b and their corresponding processing times are given by a = A + B + ... + (K-1). b;= B,+C, + ... + (K-1), + K, If this new problem with the prescribed order ab is solved by the method of section 5.5, the resulting optimal sequence will also be optimal for the original problem Further, if B + C + ... + (K - 1); = k, where k is a fixed positive constant for all jobs (i = 1, 2, 3.... n), then the given problem can be solved simply as n job two machine problem (where the two machines are A and K in the order AK) as per the method of section 5.4. EXAMPLE 5.7-1 Four jobs 1, 2, 3 and 4 are to be processed on each of the five machines A, B, C, D and E in the order ABCDE. Find the total minimum elapsed time if no passing of jobs is permitted. Also determine idle time for each machine. TABLE 5.19 MIC A B D E Job 1 B D 7 5 2 3 9 6 5 2 3 4 6 5 4 5 3 10 8 6 2 8 3 6