A Capacity Planning Assignment 2014 Mustafa Senior Solution

Ain Shams UniversityFaculty of EngineeringCredit Hours Engineering ProgramSenior (MANF)

Industrial EngineeringSpring 2014

Capacity&Aggregate Planning

Question 1

A Manufacturing Corp. has the process displayed below. The drilling operation occurs separately from and simultaneously with the sawing and sanding operations. The product only needs to go through one of the three assembly operations (the assembly operations are “parallel”)

a) Which operation is the bottleneck?b) What is the system’s process time?c) What is the process cycle time for the overall system?d) If the firm operates 8 hours per day, 22 days per month, what is the monthly capacity of the

manufacturing process?e) Suppose that a second drilling machine is added, and it has the same process time as he original

drilling machine. What is the new pross time of the system?f) Suppose that a second drilling machine is added, and it has the same process time as the original

drilling machine. What is he new process cycle time?

Solutiona) The process time of a station: The time to produce a given number of units

at that single work station.The process time of Assembly station is 78 minutes / 3 operators= 26 minutes per unit, so the station with the longest process time, hence the bottleneck, is Drilling, at 27 minutes.

Sawing

Drilling

Sanding

Welding

Assembly

Assembly

Assembly

15 minues 15 minues

27 minues

25 minues

78 minues

78 minues

78 minues

Capacity Planning/ Aggregate Planning - 1/11

b) Process time of a system: The time of the longest (slowest) process, the bottleneck.The system’s process time 27 minutes per unit (the longest process, Drilling)

c) Process Cycle time: The time it takes for a product to go through the production process with no waiting: the longest path through the sysem.System process cycle time is the maximum of (15+15+25+78), (27+25+78) = maximum of (133,130) = 133 minutes

d) Monthly Capacity = (60 minutes)(8 hours) (22 days)/ 27 minutes per unit = 10,560 minutes per month / 27 minutes per unit = 391.11 units/ month

e) The bottleneck shifts to assembly, with a process time of 26 minutes per unitf) Redundancy does not affect process cycle time. It is still 133 minutes

Question 2

A manager has been asked to determine whether the $22.50 cost of tickets for the community dinner heater will allow the group to achieve break-even and whether 175 seating capacity is adequate. The cost for each performance of 10 performance run is $2,500. The facility rental cost for the entire 10 performance is $10,000. Drinks and parking are extra charges and have their own price and variable costs, as shown below:

Selling Price P$

Variable Cost V$

Estimated Quantity of sales Units

Tickets with Dinner 22.5 10.5 175Drinks 5.00 1.75 175Parking 5.00 2.00 100

Determine the break even sales and decide if the mix of costs and the forecasted revenue will breakeven together.Solution

Page 3341 2 3 4 5 6 7 8 9

P V

Percent Variable

Cost (V/P)

Contribution1- (V/P)

Estimated Quantity of sales Units

Sales*P

Percent of sales

Contribution weighted by percent sales(col.5*col.8)

Tickes and

Dinner22.5 10.50 0.467 0.533 175 3,938 0.741 0.395

Drinks 5.00 1.75 0.350 0.650 175 875 0.165 0.107Parking 5.00 2.00 0.400 0.600 100 500 0.094 0.056

450 5,313 1.000 0.558


(10∗2500 )+10,0000.558

=35,0000.558

= $ 62,724

Revenue for each performance (from col.7)= $5,313Total forecasted revenue for the 10 performances= 10*$5,313=$53,130Forecasted revenue with this mix of sales shows a break even of $62,724Thus given this mix of costs, sales, and capacity , the manager determines that the theatre will not break even

Question 3The president of Hill Enterprises, Terri Hill, projects the firm’s aggregate demand requirements over the next 8 months as follows

Period Demand1 14002 16003 18004 18005 22006 22007 18008 1400

Her operations manager is considering a new plan, which begins in January with 200 units on hand.

Stockout cost of lost sales is $100 per unit. Inventory holding cost is $20 per unit per month. Ignore any idle time costs. The plan is called plan A. Plan A : Vary the workforce level to execute a “chase” strategy by producing the quantity

demanded in the prior month . The December demand and rate of production are both 1600 units per month.

The cost of hiring additional workers is $5000 per 100 units. The cost of laying off workers is $7500 per 100 units.

It is required to:a) Evaluate the plan


b) Develop plan B : Produce at a consumer rate of 1400 units per month, which will meet minimum demands. Then use subcontracting, which additional units at a premium price of $75 er unit. Evaluate this plan by computing the costs for January through August

c) ) Develop plan C: Beginning inventory, stockout costs and holding costs as provided. Keep a “stable” workforce by maintaining a constant production rate equal to the average requirements and allow varying inventory levels. Plot the demand with a graph that also shows average requirements. Conduct your analysis for January through August


Question 4Planners for a company are about to prepare the aggregate plan that will cover six periods. They have assembled the following information:Period 1 2 3 4 5 6 TotalForecast 200 200 300 400 500 200 1800CostsOutputRegular time = $2 per unitOvertime = $3 per unitSubcontract =$6 per unitInventory =$1 per unit per period on average inventoryBack orders =$5 per unit per period

a) Prepare an aggregate plan and determine its cost knowing the following: They now want to evaluate a plan that calls for steady rate of regular time output,

mainly using inventory to absorb the uneven demand but allowing some backlog. They intend to start with zero inventory on hand in the first period. Assume a level output rate of 300 units per period with regular time (i.e., 1800/

6=300). The planned ending inventory is zero. There are 15 workers.

b) Planners have decided to develop an alternative plan. They have learned that one person is about to retire from the company. Rather than replace him, they would like to stay with the smaller workforce and use overtime to make up for the lost output. The reduced regular time output is 280 units per period . The maximum amount of overtime output per period is 40 units.Develop a plan and compare it to the previous one in (a)

c) Develop another plan in which you can use temporary workers to fill in during months of high demand. Suppose that it costs an additional $100 to hire and train a temporary worker, and that a temporary worker can produce at the rate of 15 units per period (compared wih 20 units per period for regular workers)


Solution of c)

Dividing the number of units needed (120) by the output rate of 15 per temporary worker, you find that eight worker periods are needed (e.g. two workers for four months each, four workers for two months each).Noting that Periods 4 and 5 have the heaviest demand, try using four temporary workers for two months each (i.e., Periods 4 and 5). The results are summarized in the following plan:

Period 1 2 3 4 5 6 TotalForecast 200 200 300 400 500 200 1800

Output Regular Overtime SubcontractOutput-ForecastInventory Beginning Ending AverageBacking

280------80

080400

280--------80

801601200

280------(20)

1601401500

340------(60)

140801100

340------(160)

8004080

280------80

0000

1800

0

46080

CostsOutput Regular Overtime Subcontract Hire/ FireInventoryBackorders

$560--------$ 0$ 40$ 0

560--------01200

560--------01500

680----------40040400

680--------40040400

560----------000

$3600

$ 800$ 460$ 400

Total $ 600 680 710 1190 1520 560 $5260

Question 5A manager is attempting to put together an aggregate plan for the coming year. She has obtained a forecast of expected demand for the planning horizon. The plan must deal with highly seasonal demand; demand is relatively high in periods 3 and 4 and again in period 8, as can be seen from the following forecasts:Period 1 2 3 4 5 6 7 8 9 TotalForecast 190 230 260 280 210 170 160 260 180 1,940

The department now has 20 full-time people, each of whom can produce10 units of output per period at a cost of $6 per unit. Inventory carrying cost is $5 per unit per period, and backlog cost is $10 per unit per period. The manager is considering a plan that would involve hiring


two people to start working in period 1, one on a temporary basis who would work only through period 5. This would cost $500 in addition to unit production costs.a) What is the rationale for this plan?b) Determine the total cost of the plan, including production, inventory, and backorder costs.

Solution


A Capacity Planning Assignment 2014 Mustafa Senior Solution

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