Superior Customer Service Solutions (SCSS) Limited receives a contract from Filips, a personal care appliance producer, to provide after-sales services to Filips customers. SCSS needs to determine what service capacity is needed to support the service based on the following data.

During the eight opening hours each day, it is estimated that there are 120 customers on average. There are two machine models that can process the customer requests. The first one is an old model (called slow machine) that takes an average of 6 minutes to process a job. The second one is a new model (called fast machine) that takes an average of 3 minutes to process a job.

In analyzing the problem, assume Poisson arrival pattern and exponential service times.

(a) What is the average customer arrival rate per hour? What is the service rate per hour of a slow machine? What is the service rate per hour of a fast machine?

(b) SCSS limited considers two options. Option 1: use one fast machine.

Option 2: use two slow machines.

Compare these two options by calculating the performance measures summarized in the following table. Fill your numbers in the table and briefly comment on your comparison. (Hint: Lec-8, use Model 1 to analyze Option 1; use Model 3 with S=2 to analyze Option 2.)

(c) SCSS limited receives a lump sum payment from Filips each month for the services provided. But Filips keeps monitoring the service process by reviewing the system record and will deduct a certain amount of money depending on the service quality revealed by the service performance statistics.

Suppose that Filips imposes a penalty of $0.8 for every minute a customer waiting in the queue (not including the time when the customer is being served). The operating cost of each slow machine is $50 per hour; while that of a fast machine is $8X per hour, where X is the last numeric digit of your Student ID. (For example, if your Student ID is 21000006G, this cost is $86.)

Compare the total (i.e., penalty+operating) costs per hour for SCSS to use these two options. Which option would you suggest SCSS to use? Why?

(Hint: to calculate the penalty cost, ask yourself: What is the average time a random customer needs to wait in the queue? How many customers arrive in one hour?)

(d) Suppose SCSS adopts Option 1. In order to make most customers suffer less during waiting, the company wants to guarantee that there is at least 80% chance that an arriving customer gets service immediately or finds a waiting seat. In this case, how many waiting seats (not including the one for the customer being served) should SCSS provide in its waiting room? (Hint: The probability that an arriving customer sees n customers already in the system equals to .)

3. Superior Customer Service Solutions (SCSS) Limited receives a contract from Filips, personal care appliance producer, to provide after-sales services to Filips customers. SCSS nods to determine what service capacity is needed to support the service based on the following data During the cight opening hours each day, it is estimated that there are 120 customers on average There are two machine models that can process the customer requests. The first one is an old model called slow machine) that takes an average of 6 minutes to process a job. The second one is a new model (called fast machine) that takes an werage of 3 minutes to process a job In analyzing the problem, assume Poisson arrival pattem and exponential service times (a) What is the average customer arrival rate per hour? What is the service rate per hour of a slow machine! What is the service tale per hour of a fast machine (b) SCSS limited considers two options. Option 1: use one fast machine Option 2 use two slow machines Compare these two options by calculating the performance measures summarised in the following table. Fill your numbers in the table and briefly comment on your comparison (Lew Model M2) Performance measures server tiration Optie 1 Option 2 L L w w Po For Model I. 1- Note: For Model 3, server utilization - (SSCSS limited receives a lump sum payment from Filips cach month for the services provided. But Filips keeps monitoring the service process by reviewing the system record and will deduct a certain amount of money depending on the service quality revealed by the service performance statistics Suppose that Filips imposes a penalty of 50% for every minute a customer waiting in the queue (not including the time when the customer is being served). The operating cost of 3 each slow machine is $30 per hour, while that of a fast machine is SXX per hour, where X is the last numeric digit of your Student ID). (For example, if your Student ID - 210000066, this cost is $86) Compare the total de penalty operating costs per hour for SCSS to use these two options Which option would you suggest SCSS to use? Why? e o cabelos e pret and you are se manterne wille www.sew) (d) Suppose SCSS adopts Optica 1. In onder to make most customers suffer less during waiting, the company wants to guarantee that there is at least 80% chance that an arriving customer pots service immediately or find a waiting scat. In this case, how many waiting sets (not including the one for the customer being served) should SCSS provide in its waiting room? (int. They are in the Option 2 Performance Option 1 measures server utilization Po La Ls wa WS Pw Note: For Model 1, Pw = 1 - Po For Model 3, server utilization 2 Su 3. Superior Customer Service Solutions (SCSS) Limited receives a contract from Filips, personal care appliance producer, to provide after-sales services to Filips customers. SCSS nods to determine what service capacity is needed to support the service based on the following data During the cight opening hours each day, it is estimated that there are 120 customers on average There are two machine models that can process the customer requests. The first one is an old model called slow machine) that takes an average of 6 minutes to process a job. The second one is a new model (called fast machine) that takes an werage of 3 minutes to process a job In analyzing the problem, assume Poisson arrival pattem and exponential service times (a) What is the average customer arrival rate per hour? What is the service rate per hour of a slow machine! What is the service tale per hour of a fast machine (b) SCSS limited considers two options. Option 1: use one fast machine Option 2 use two slow machines Compare these two options by calculating the performance measures summarised in the following table. Fill your numbers in the table and briefly comment on your comparison (Lew Model M2) Performance measures server tiration Optie 1 Option 2 L L w w Po For Model I. 1- Note: For Model 3, server utilization - (SSCSS limited receives a lump sum payment from Filips cach month for the services provided. But Filips keeps monitoring the service process by reviewing the system record and will deduct a certain amount of money depending on the service quality revealed by the service performance statistics Suppose that Filips imposes a penalty of 50% for every minute a customer waiting in the queue (not including the time when the customer is being served). The operating cost of 3 each slow machine is $30 per hour, while that of a fast machine is SXX per hour, where X is the last numeric digit of your Student ID). (For example, if your Student ID - 210000066, this cost is $86) Compare the total de penalty operating costs per hour for SCSS to use these two options Which option would you suggest SCSS to use? Why? e o cabelos e pret and you are se manterne wille www.sew) (d) Suppose SCSS adopts Optica 1. In onder to make most customers suffer less during waiting, the company wants to guarantee that there is at least 80% chance that an arriving customer pots service immediately or find a waiting scat. In this case, how many waiting sets (not including the one for the customer being served) should SCSS provide in its waiting room? (int. They are in the Option 2 Performance Option 1 measures server utilization Po La Ls wa WS Pw Note: For Model 1, Pw = 1 - Po For Model 3, server utilization 2 Su