Question

Exercise: Laundromat A laundromat has 5 washing machines. A typical machine breaks down once every 5 days. A repairer can repair a machine in an average of 2.5 days. Currently, three repairers are on duty. The owner of the laundromat has the option of replacing them with a superworker, who can repair a machine in an average of 5/6 day. The salary of the superworker equals the pay of the three regular employees. Breakdown and service times are exponential. Should the laundromat replace the three repairers with the superworker?

Answer 1

Notice we need to select a performance measure for comparison. Here the costs are the same. While a machine is in repair shop we are losing customers and money. Therefore, the best performance measure will be the average number in system (in repair shop). The system with smaller average number in the system is the better system. For 3 workers 21/5 machine/day u-.4 machines/day K 5,R 3,p 5 II2F 5

Notice that you need to use the other set of equation as i 4> R-3 0.54 41N 0431 *3(4-32)= = 0.4167 π。 0.55 5!n o (3! 3(5-3-0.0694 T 0 ΤΟ+25 πο+ 2.5 π0+1.25 πο+0.4167 πο T9=0.1293 0.0694 πο = 1 L j" j-0πο+1(2.5*0. 1293) +2(2.5*0.1293) + 3(1.25+0.1293) + 4(0.4167*0.1293)+50.0694*0.1293) 1.715 For 1/5 machine day u 1.2 machines/day K-5R 1 p 1/6 Notice that you need to use the other set of equation as 2R-1 пг .- 1 ; 1 (1/6) (21)110 / 313(2-1)-(2056)по П3-1 : 1 (1/6),(3 !jmo / 313(3-1)-(602 16)110 114-. I (1/6)4 (4!)m / 313(4-1)2 (554) Is =に! (1/6),(5 !jmo/ 313(5-1) = (201 296 по πο + 0.8265 πο 0.5465 πο +0.271 πο 0.0896 πο+ 0.0148 πο=1 TQ-03604 LJo 1.16 The best bet in this case would be for the owner of the Laundromat to get rid of the three repairmen and hire the superworker because there will be less broken washing machines at any point of time.

You may also argue that values of L in this problem are not much different and from practical point of view you prefer the system with 3 worker, because if one does not work there are two other repairers to work. But if supperworker does not work all repair jobs will be delayed.