A Manufacturer of Semiconductor "Wafers" Has Been Attempting to Convert

A manufacturer of semiconductor "wafers" has been attempting to convert its operations to practices more in keeping with JIT principles. The firm is now paying much more attention to the transit time between one processing stage and the next. The plant has a somewhat haphazard pattern of machine locations, partly because the machines were purchased and installed at different times, partly from a shortage of floor space, and partly from previous experiments with work cells. The bottom line is this: there are four machines that perform a certain processing phase, and three machines that perform the next phase. All units of a large class of wafers go through these two phases. The table below displays the transit time, in minutes, from each machine of the first phase to each machine of the second. Machine 3 is not really 100 minutes away from machine B; the company has prohibited that combination because of quality problems associated with that specific pairing. Supply and demand quantities are in wafers processed per week. Develop a transit time minimizing solution for this firm. What is the total transit time of this solution? Which machines are fully utilized? Which machines have some capacity unused or requirements unfilled? Was the prohibition on the 3-B combination honored? $$\begin{array} { | l |r| r | r | r | } \hline \text { COSTS } & { \text { Phase 2, } } & \text { Phase 2, } & { \text { Phase 2, } } & \text { Supply } \\& \text { machine A } & \text { machine B } & \text { machine C } & \\\hline \text { Phase 1, machine 1 } & 7.5 & 2.5 & 4.0 & 700 \\\hline \text { Phase 1, machine 2 } & 3.0 & 6.0 & 6.5 & 600 \\\hline \text { Phase 1, machine 3 } & 2.5 & 100.0 & 8.0 & 1000 \\\hline \text { Phase 1, machine 4 } & 5.0 & 8.5 & 7.0 & 700 \\\hline\text { Demand } & 1200 & 800 & 1500 & 3500 \backslash 3000 \\\hline\end{array}$$