Sterling Products Corporation (SPC), a local furniture manufacturer is considering automating its frame assembly operation by leasing a completely automated work station. Currently there is only a single employee, Willard Eggleston, doing the framing, and he is performing the assembly task by hand. Willard costs SPC a total of $8 per hour to maintain on their payroll. Frames ready for assembly arrive randomly at a rate of roughly one every 30 minutes on the average. It takes Willard an average of 25 minutes to assemble each of the frames, and his assembly times are fairly random. The automatic work station would replace Willard (who wants to go back to school anyway) and would cost SPC $10 per hour to lease. It would assemble frames at a constant rate of 3 per hour. Alternatively, SPC may simply hire an additional employee to work alongside Willard assembling the frames. Since this is a low skill operation, the new employee is expected to be essentially as productive as Willard, but will cost SPC only $7 per hour since Willard has earned some longevity raises along the way. Another possibility being considered by SPC is to lease a staple gun, which should improve Willard's productivity by around 50% but will cost SPC about $1 per hour. SPC has estimated that its inventory holding costs are quite high, at $2 per hour per frame unit held up in process. It is, therefore, important for SPC to choose an alternative which will minimize SPC's total costs, including the cost of work-in-process inventory. Which of the alternatives provides the lowest estimated total cost per hour for processing the frames? Note that "total cost" here includes wages, equipment rentals, and work-in-process inventory costs.

 

 -As described in the SPSF, a critical step in solving any problem is to define the decision involved. For the SPC situation, the decision variable being addressed is and the criterion of most importance is,

 -while the  pertaining to that criterion is to

 -The alternatives being considered in the SPC problem are -, and

 

 -Consider the existing situation from a queuing perspective, starting with the arrival process and then addressing the assembly process. The value for λ is  per , and the appropriate probability distribution for describing arrivals is the . In addition, the value for μ is  per  and the appropriate distribution for describing service times is the . On the other hand, if SPC were to equip Willard with a staple gun, the value of μ would instead be  per , and service times would be described by a(n)  distribution.

 -Again consider the existing situation. The number of service channels is , and the maximum allowable length of the queue (or queues) is . Similarly, the source population should be considered , so this can be considered a(n)  model per Kendall's notation. However, hiring an additional employee to work alongside Willard would mean that using a(n)  model would be the appropriate way to model the situation.

 - Now consider the alternative involving the automatic work station that would replace Willard. The value for λ is  per , and the appropriate probability distribution for describing arrivals is the . In addition, the value for μ is  per  and the appropriate distribution for describing service times is the . Finally, this would be considered a(n)  model per Kendall's notation.

 - If a cost analysis were to be performed, the tradeoff between waiting costs and service costs would need to be addressed. For each of the alternatives being considered by SPC, what are these two unit costs?

 -Waiting:  per , and service:  per 

 -Waiting:  per , and service:  per 

 -Waiting:  per , and service:  per 

 -Waiting:  per , and service:  per 

 -Extra Credit: Who is/was the "real" Willard Eggleston (no middle name or initial)?