Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 P.M. and 7:00 P.M., students arrive at the grill at a rate of 25 per hour (Poisson distributed) and service time takes an average of 2 minutes (negative exponential distribution). There is only 1 server, who can work on only $l$ order at a time.

What is the average number of students in line?

Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can "shoot" a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun's shooting times are negative exponentially distributed. Compute the following:

The average number of dogs being vaccinated and waiting to be vaccinated.

Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can "shoot" a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun's shooting times are negative exponentially distributed. Compute the following:

The proportion of the time that Tarun is busy.

Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are negative exponentially distributed.

What percentage of the time is the postal clerk busy?

Dwayne Cole, owner of a Florida firm that manufactures display cabinets, develops an 8-month aggregate plan. Demand and capacity (in units) are forecast as follows:

The cost of producing each unit is $\$ 1,000$ on regular time, $\$ 1,300$ on overtime, and $\$ 1,800$ on a subcontract. Inventory carrying cost is $\$ 200$ per unit per month. There is no beginning or ending inventory in stock, and no backorders are permitted from period to period. Let the production (workforce) vary by using regular time first, then overtime, and then subcontracting.

Set up a production plan that minimizes cost by producing exactly what the demand is each month. This plan allows no backorders or inventory. What is this plan's cost?

Southeast Soda Pop, Inc., has a new fruit drink for which it has high hopes. John Mittenthal, the production planner. has assembled the following cost data and demand forecast:

John's job is to develop an aggregate plan. The three initial options he wants to evaluate are:

• Plan A: a strategy that hires and fires personnel as necessary to meet the forecast.

• Plan B: a level strategy.

• Plan C: a level strategy that produces $1,200$ cases per quarter and meets the forecast demand with inventory and subcontracting.

If you are John's boss, the VP for operations, which plan do you implement and why?

Southeast Soda Pop, Inc., has a new fruit drink for which it has high hopes. John Mittenthal, the production planner. has assembled the following cost data and demand forecast:

John's job is to develop an aggregate plan. The three initial options he wants to evaluate are:

• Plan A: a strategy that hires and fires personnel as necessary to meet the forecast.

• Plan B: a level strategy.

• Plan C: a level strategy that produces $1,200$ cases per quarter and meets the forecast demand with inventory and subcontracting.

Which strategy is the lowest-cost plan?

Deb Bishop Health and Beauty Products has developed a new shampoo, and you need to develop its aggregate schedule. The cost accounting department has supplied you the costs relevant to the aggregate plan, and the marketing department has provided a four-quarter forecast. All are shown as follows:

Your job is to develop an aggregate plan for the next four quarters.

Which is the more economical plan for Deb Bishop Health and Beauty Products?

Deb Bishop Health and Beauty Products has developed a new shampoo, and you need to develop its aggregate schedule. The cost accounting department has supplied you the costs relevant to the aggregate plan, and the marketing department has provided a four-quarter forecast. All are shown as follows:

Your job is to develop an aggregate plan for the next four quarters.

Then try a plan that holds employment steady.

The S&OP team at Kansas Furniture, has received the following estimates of demand requirements:

a) Assuming one-time stock out costs for lost sales of $\$ 100$ per unit, inventory carrying costs of $\$ 25$ per unit per month, and zero beginning and ending inventory, evaluate these two plans on an incremental cost basis:

• Plan A: Produce at a steady rate (equal to minimum requirements) of $1,000$ units per month and subcontract additional units at a $\$ 60$ per unit premium cost.

• Plan B: Vary the workforce, to produce the prior month's demand. The firm produced $I,300$ units in June. The cost of hiring additional workers is $\$ 3,000$ per 100 units produced. The cost of layoffs is $\$ 6,000$ per 100 units cut back.

Note: Both hiring and layoff costs are incurred in the month of the change, (i.e. going from production of $1,300$ in July to $1,000$ in August requires a layoff (and related costs) of 300 units in August, just as going from production of $1,000$ in August to $1,200$ in September requires hiring (and related costs) of 200 units in September).

Consuelo Chua, Inc., is a disk drive manufacturer in need of an aggregate plan for July through December. The company has gathered the following data:

*No costs are incurred for unmet demand, but unmet demand (backorders) must be handled in the following period. If half or more of a worker is needed, round up.

** Note that there is no holding cost for June. What will each of the two following strategies cost?

Vary the workforce so that production meets demand. Chua had eight workers on board in June.

A technician monitors a group of 5 computers that run an automated manufacturing facility. It takes an average of 15 minutes (negative exponentially distributed) to adjust a computer that develops a problem. On average, one of the computers requires adjustment every 85 minutes. Determine the following:

The average number in the system

A technician monitors a group of 5 computers that run an automated manufacturing facility. It takes an average of 15 minutes (negative exponentially distributed) to adjust a computer that develops a problem. On average, one of the computers requires adjustment every 85 minutes. Determine the following:

The probability no computer needs adjustment

Debra Bishop's cabinet-making shop, in Des Moines, has five tools that automate the drilling of holes for the installation of hinges. Each machine needs an average of 3 "resettings" every 8-hour day, following the Poisson distribution. There is a single technician for setting these machines. Her service times are negative exponential, averaging 2 hours each.

What is the probability this system is empty?