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6 Lecture - Outline Lecture 6: Capacity Planning (Chapter 6) & Waiting Lines (Supplement C) Planning Long-Term Capacity Capacity Timing and Sizing Strategies A Systematic Approach to LT Capacity Decisions Why Waiting Lines Form Uses of Waiting-Line Theory Structure of Waiting-Line Problems Probability Distributions Using Waiting-Line Models to Analyze Operations Little's Law Decision Areas for Management Planning Capacity Capacity is the maximum rate of output of a process or system Accounting, finance, marketing, operations, purchasing, and human resources all need capacity information to make decisions Capacity planning is done in the long-term and the short-term Questions involve the amount of capacity cushion and expansion strategies Measures of Capacity Utilization Output measures of capacity Input measures of capacity Utilization 1 Lecture 6 - Outline Capacity and Scale Economies of scale o o o o Spreading fixed costs Reducing construction costs Cutting costs of purchased materials Finding process advantages Diseconomies of scale o o o Complexity Loss of focus Inefficiencies Capacity Timing and Sizing Sizing capacity cushions Capacity cushions are the amount of reserve capacity a process uses to handle sudden changes Capacity cushion = 100% Average Utilization rate (%) Expansionist strategies Wait-and-see strategies Combination of strategies 2 Lecture 6 - Outline Linking Capacity Capacity decisions should be linked to processes and supply chains throughout the organization Important issues are competitive priorities, quality, and process design Systematic Approach 1. Estimate future capacity requirements 2. Identify gaps by comparing requirements with available capacity 3. Develop alternative plans for reducing the gaps 4. Evaluate each alternative, both qualitatively and quantitatively, and make a final choice Step 1 is to determine the capacity required to meet future demand using an appropriate planning horizon Output measures based on rates of production Input measures may be used when Product variety and process divergence is high The product or service mix is changing Productivity rates are expected to change 3 Lecture 6 - Outline Significant learning effects are expected For one service or product processed at one operation with a one year time period, the capacity requirement, M, is Setup times may be required if multiple products are produced Problem 1 (EXAMPLE 6.1): A copy center in an office building prepares bound reports for two clients. The center makes multiple copies (the lot size) of each report. The processing time to run, collate, and bind each copy depends on, among other factors, the number of pages. The center operates 250 days per year, with one 8-hour shift. Management believes that a capacity cushion of 15 percent (beyond the allowance built into time standards) is best. It currently has three copy machines. Based on the following table of information, determine how many machines are needed at the copy center. Solution: 4 Lecture 6 - Outline 5 Lecture 6 - Outline Problem 2 (EXAMPLE 6.2): Grandmother's Chicken Restaurant is experiencing a boom in business. The owner expects to serve 80,000 meals this year. Although the kitchen is operating at 100 percent capacity, the dining room can handle 105,000 diners per year. Forecasted demand for the next five years is 90,000 meals for next year, followed by a 10,000-meal increase in each of the succeeding years. One alternative is to expand both the kitchen and the dining room now, bringing their capacities up to 130,000 meals per year. The initial investment would be $200,000, made at the end of this year (year 0). The average meal is priced at $10, and the before-tax profit margin is 20 percent. The 20 percent figure was arrived at by determining that, for each $10 meal, $8 covers variable costs and the remaining $2 goes to pretax profit. What are the pretax cash flows from this project for the next five years compared to those of the base case of doing nothing? 6 Lecture 6 - Outline Why Waiting Lines Form Define customers Waiting lines form Temporary imbalance between demand and capacity Can develop even if processing time is constant No waiting line if both demand and service rates are constant and service rate > than demand Affects process design, capacity planning, process performance, and ultimately, supply chain performance Uses of Waiting Line Theory Applies to many service or manufacturing situations Relating arrival and service-system processing characteristics to output Service is the act of processing a customer Hair cutting in a hair salon Satisfying customer complaints Processing production orders Theatergoers waiting to purchase tickets Trucks waiting to be unloaded at a warehouse Patients waiting to be examined by a physician Structure of Waiting Line Problems 1. An input, or customer population, that generates potential customers 2. A waiting line of customers 3. The service facility, consisting of a person (or crew), a machine (or group of machines), or both necessary to perform the service for the customer 4. A priority rule, which selects the next customer to be served by the service facility Customer Population: The source of input. Finite or infinite source Customers from a finite source reduce the chance of new arrivals Customers from an infinite source do not affect the probability of another arrival 7 Lecture 6 - Outline Customers are patient or impatient Patient customers wait until served Impatient customer either balk or join the line and renege The Service System Number of lines o A single-line keeps servers uniformly busy and levels waiting times among customers o A multiple-line arrangement is favored when servers provide a limited set of services Arrangement of service facilities o Single-channel, single-phase o Single-channel, multiple-phase o Multiple-channel, single-phase o Multiple-channel, multiple-phase o Mixed arrangement 8 Lecture 6 - Outline 9 Lecture 6 - Outline Priority Rule: First-come, first-served (FCFS)--used by most service systems Other rules Earliest due date (EDD) Shortest processing time (SPT) Preemptive discipline--allows a higher priority customer to interrupt the service of another customer or be served ahead of another who would have been served first Probability Distribution - The sources of variation in waiting-line problems come from the random of arrivals customers and the variation of service times - Arrival distribution Customer arrivals can often be described by the Poisson distribution with mean = T and variance also = T Arrival distribution is the probability of n arrivals in T time periods Interarrival times are the average time between arrivals Inter-arrival times 10 Lecture 6 - Outline Problem 3 (EXAMPLE C.1): Management is redesigning the customer service process in a large department store. Accommodating four customers is important. Customers arrive at the desk at the rate of two customers per hour. What is the probability that four customers will arrive during any hour? Service Time: - Service time distribution can be described by an exponential distribution with mean = 1/ and variance = (1/ )2 - Service time distribution: The probability that the service time will be no more than T time periods can be described by the exponential distribution Problem 4 (EXAMPLE C.2): The management of the large department store in Example C.1 must determine whether more training is needed for the customer service clerk. The clerk at the customer service desk can serve an average of three customers per hour. What is the probability that a customer will require less than 10 minutes of service? Using Waiting Line Models Balance costs against benefits Operating characteristics Line length Number of customers in system Waiting time in line 11 Lecture 6 - Outline Total time in system Service facility utilization Single Server Model Single-server, single line of customers, and only one phase Assumptions are 1. Customer population is infinite and patient 2. Customers arrive according to a Poisson distribution, with a mean arrival rate of 3. Service distribution is exponential with a mean service rate of 4. Mean service rate exceeds mean arrival rate 5. Customers are served FCFS 6. The length of the waiting line is unlimited Problem 5 (EXAMPLE C.3): The manager of a grocery store in the retirement community of Sunnyville is interested in providing good service to the senior citizens who shop in her store. Currently, the store has a separate checkout counter for senior citizens. On average, 30 senior citizens per hour arrive at the counter, according to a Poisson distribution, and are served at an average rate of 35 customers per hour, with exponential service times. Find the following operating characteristics: a. Probability of zero customers in the system b. Average utilization of the checkout clerk c. Average number of customers in the system d. Average number of customers in line e. Average time spent in the system f. Average waiting time in line Solution: The checkout counter can be modeled as a single-channel, single-phase system. Figure C.4 shows the results from the Waiting-Lines Solver from OM Explorer. 12 Lecture 6 - Outline Both the average waiting time in the system (W) and the average time spent waiting in line (Wq) are expressed in hours. To convert the results to minutes, simply multiply by 60 minutes/ hour. For example, W = 0.20(60) minutes, and Wq = 0.1714(60) = 10.28 minutes. Problem 6 (EXAMPLE C.4): The manager of the Sunnyville grocery in Example C.3 wants answers to the following questions: a. What service rate would be required so that customers average only 8 minutes in the system? b. For that service rate, what is the probability of having more than four customers in the system? c. What service rate would be required to have only a 10 percent chance of exceeding four customers in the system? 13 Lecture 6 - Outline Multiple-Server Model Service system has only one phase, multiple-channels Assumptions (in addition to single-server model) There are s identical servers The service distribution for each server is exponential The mean service time is 1/ s should always exceed 14 Lecture 6 - Outline Problem 7 (EXAMPLE C.5): The management of the American Parcel Service terminal in Verona, Wisconsin, is concerned about the amount of time the company's trucks are idle (not delivering on the road), which the company defines as waiting to be unloaded and being unloaded at the terminal. The terminal operates with four unloading bays. Each bay requires a crew of two employees, and each crew costs $30 per hour. The estimated cost of an idle truck is $50 per hour. Trucks arrive at an average rate of three per hour, according to a Poisson distribution. On average, a crew can unload a semitrailer rig in one hour, with exponential service times. What is the total hourly cost of operating the system? 15 Lecture 6 - Outline Little's Law Relates the number of customers in a waiting line system to the waiting time of customers Using the notation from the single-server and multiple-server models it is expressed as L = W or Lq = Wq Holds for a wide variety of arrival processes, service time distributions, and numbers of servers Only need to know two of the parameters Provides basis for measuring the effects of process improvements Is not applicable to situations where the customer population is finite Decision Areas for Management 1. Arrival rates 2. Number of service facilities 3. Number of phases 4. Number of servers per facility 5. Server efficiency 6. Priority rule 16 Lecture 6 - Outline 7. Line arrangement Additional Problems Additional Problem 1: Customers arrive at a checkout counter at an average 20 per hour, according to a Poisson distribution. They are served at an average rate of 25 per hour, with exponential service times. Use the single-server model to estimate the operating characteristics of this system. Find: a) Average utilization of the system b) Average number of customers in the service system c) Average number of customers in the waiting line d) Average time spent in the system, including service e) Average waiting time in line 17 Lecture 6 - Outline Additional Problem 2: In the checkout counter example, what service rate is required to have customers average only 10 minutes in the system? Additional Problem 3: Suppose the manager of the checkout system decides to add another counter. The arrival rate is still 20 customers per hour, but now each checkout counter will be designed to service customers at the rate of 12.5 per hour. Calcultate: a) Average utilization of the system b) Probability that zero customers are in the system c) Average number of customers in the waiting line d) Average waiting time of customers in line 18 ... View Full Document