04 Jun DETERMINE THE AVERAGE LENGTH OF THE WAITING LINE AND THE AVERAGE TIME A CUSTOMER MUST WAIT.
1 Florida Institute of Technology, CIS 3315. Decision Support Systems Instructor: Nelson Garcia, garcian@fit.edu Week 4, Chapter 5 assignments (2 problems) Problem 1. Western Lithium produces a special type of material that is currently in short supply. Four of Western Lithium’s customers have already placed orders that together exceed the combined capacity of Western Lithium’s two plants. Western Lithium’s management faces the problem of deciding how many units it should supply to each customer. Since the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a “sell to the highest bidder” strategy unacceptable. After considering price, production costs, and transportation costs, Western Lithium has established the following profit per unit for each plantcustomer alternative. Plant Customer Panasonic Samsung Tesla Sony Reno $32 $34 $32 $40 Vancouver $34 $30 $28 $38 The plant capacities and customer orders are as follows: Plant Capacity (units) Reno 5000 Vancouver 3000 Distributor Orders (units) Panasonic 2000 Samsung 5000 Tesla 3000 Sony 2000 A. Develop an Excel layout and solver model to find a solution for this problem. B. How many units should each plant produce for each customer to maximize profits? 2 Problem 2 Anderson and Associates, Inc. is a software development firm that has three new clients. Project teams will be assigned to the three clients. Based on the different backgrounds and experiences of the teams, the various team-client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in weeks are: Project Team Client C1 C2 C3 Agile team 10 16 32 Spiral team 14 22 40 Waterfall team 22 24 34 A. Develop an Excel layout and solver model to find a solution to this problem. B. What team assignments will result in the minimum overall completion time?
CIS 3315 Week 7 Assignment Problems 1. The reference desk at a library receives requests for assistance. Assume that a Poisson probability distribution with a mean rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow the exponential probability distribution with a mean service rate of 12 requests per hour. a. What is the probability of no requests for assistance in the system? b. What is the average number of requests that will be waiting for service? c. What is the average waiting time in minutes before service begins? d. What is the average time at the reference desk in minutes (waiting time plus service time)? e. What is the probability that a new arrival has to wait for service? 2. ABC Design provides decorating assistance to its customers. In normal operations, an average of 2.5 customers arrive each hour. One design consultant is available to answer questions and make product recommendation. The consultant averages 10 minutes with each customer. a. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. b. Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal being met? If not, what action do you recommend? c. If the consultant can reduce the average time spent per customer to 8 minutes, what is the mean service rate? Will the service goal be met? 3. Mike’s television repair service receives an average of six TV sets per eight-hour day to be repaired. The service manager would like to be able to tell customers that they can expect oneday service. What average repair time per set will the repair shop have to achieve to provide oneday service on the average? (Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed). 4. A vending machine at a bus terminal dispenses hot coffee, hot chocolate, or hot tea, in a constant service time of 20 seconds. Customers arrive at the vending machine at a mean rate of 60 per hour (Poisson distributed). Determine the average length of the waiting line and the average time a customer must wait.
CIS 3315 Week 7 Assignment Problems 1. The reference desk at a library receives requests for assistance. Assume that a Poisson probability distribution with a mean rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow the exponential probability distribution with a mean service rate of 12 requests per hour. a. What is the probability of no requests for assistance in the system? b. What is the average number of requests that will be waiting for service? c. What is the average waiting time in minutes before service begins? d. What is the average time at the reference desk in minutes (waiting time plus service time)? e. What is the probability that a new arrival has to wait for service? 2. ABC Design provides decorating assistance to its customers. In normal operations, an average of 2.5 customers arrive each hour. One design consultant is available to answer questions and make product recommendation. The consultant averages 10 minutes with each customer. a. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. b. Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal being met? If not, what action do you recommend? c. If the consultant can reduce the average time spent per customer to 8 minutes, what is the mean service rate? Will the service goal be met? 3. Mike’s television repair service receives an average of six TV sets per eight-hour day to be repaired. The service manager would like to be able to tell customers that they can expect oneday service. What average repair time per set will the repair shop have to achieve to provide oneday service on the average? (Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed). 4. A vending machine at a bus terminal dispenses hot coffee, hot chocolate, or hot tea, in a constant service time of 20 seconds. Customers arrive at the vending machine at a mean rate of 60 per hour (Poisson distributed). Determine the average length of the waiting line and the average time a customer must wait.
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