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Queuing Theory

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1. Star Savings and Loan is planning to install a drive-through window. Transaction times at the drive-through are expected to average three minutes because customers would use it for simpler transactions. The arrival rate is expected to be ten customers per hour.
a. Compute the operating characteristics for the drive-through window queuing system.
b. The demand for drive-through services is expected to increase over the next several years. If you were the bank manager, how high would you let the average arrival rate increase before considering adding a second drive-through window?

2. A college office has one photocopier. Faculty and staff arrive according to a Poisson process at a rate of 5 per hour. Copying times average 8 minutes according to an exponential distribution. What are the operating characteristics for this system?

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Production Planning & Process

Scenario:
Manychip, Inc., is a specialty memory chip manufacturer located in Southern California with manufacturing plants located in the United States, Europe, Singapore, and Japan. Additionally, Manychip has branch sales offices located in major metropolitan areas across the globe. The market for Manychip's six key products included original equipment manufacturers of personal computers, cellular telephone manufacturers, electronics distributors, and government organizations. The market environment for Manychip's products is extremely volatile, with fluctuating demand and rapidly changing prices. The company uses short-term contracts (less than one month) and spot pricing for irregular customers. Internally, the operation is capital-intensive, with depreciation running approximately $1.2 million per day (depreciation has an impact on revenue streams). The six key products had further specialized components, making the possible line mix total 24 distinct products. Further, the manufacturing process required high manufacturing lead times and various product yields. In the high technology memory arena, product life cycles were dramatically shortened because of rapid obsolescence. To coordinate the manufacturing activity, Manychip has an established process and system that helped optimize resource utilization, improve shop floor efficiencies, and manage customer demand.

Manychip is experiencing 10-15% growth in revenues and volume, primarily tied to increased worldwide demand, product type, and market variables. Most significantly, the company received a major pre-order for a new cellular phone memory chip that's schedule to come out in three months. This pre-order is scaled for up to 10 million units and management is concerned the existing process and system may not be suitably optimized for this order. Additionally, the forecast in sales figures for all six key product lines is higher than it has been in the past.
As the company examines various methods to assess its performance and design processes, it is looking for an analysis of the existing workflow production process and the factors that most directly impact such measurements. As a review, the most common metrics for production processes are as follows:

? Quality: the number of defects associated with a given product
? Cost: material and labor costs
? Timeliness: how quickly products are manufactured and delivered
? Flexibility: the degree to which the production process can be adapted to produce other products or specific products more quickly
? Productivity: a ratio of outputs divided by inputs
? Efficiency: a ratio of actual outputs divided by standard (or expected) outputs, multiplied by 100% to give a total efficiency percentage
? Cycle Time: the total time it takes to complete a production process
? Theory of Constraints and Queuing Theory

Review the scenario above: (Answer the following)

1. Explain how each measure can be applied to Manychip's production planning process - can the company use each one? How?
2. Rank the criteria listed above in order of importance to Manychip's production planning strategy, detailing your rationale for such a ranking.
3. Identify other measures that might apply to Manychip and explain them.

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