The production of tractors at the Jim Buck Company involves producing several subassemblies and then using an assembly line to assemble the subassemblies and other parts into finished tractors. Approximately three tractors per day are produced in this way. An in-process inspection station is used to inspect the subassemblies before they enter the assembly line. At present there are two inspectors at the station, and they work together to inspect each subassembly. The inspection time has an exponential distribution, with a mean of 15 minutes. The cost of providing this inspection system is $40 per hour.
A proposal has been made to streamline the inspection procedure so that it can be handled by only one inspector. This inspector would begin by visually inspecting the exterior of the subassembly, and she would then use new efficient equipment to complete the inspection. Although this processwith just one inspectorwould slightly increase the mean of the distribution of inspection times from 15 minutes to 16 minutes, it also would reduce the variance of this distribution to only 40 percent of its current value.
The subassemblies arrive at the inspection station according to a Poisson process at a mean rate of 3 per hour. The cost of having the subassemblies wait at the inspection station (thereby increasing in-process inventory and possibly disrupting subsequent production) is estimated to be $20 per hour for each subassembly.
Management now needs to make a decision about whether to continue the status quo or adopt the proposal.
(a) Find the main measures of performance—L, Lq, W, Wq—for the current queueing system.
(b) Repeat part (a) for the proposed queueing system.
(c) What conclusions can you draw about whatmanagement should do from the results in parts (a) and (b)?
(d) Determine and compare the expected total cost per hour for the status quo and the proposal.