Lab 2 - Aggregate Planning

EPT 432 Production Management Laboratory Module

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A) Graphical Approaches

A manufacturer of roofing supplies has developed monthly forecasts for family of

products. Data for 6 moth period January to June are presented in Table below, The firm

would like to begin development of an aggregate plan.

Month Expected

Demand

Production

Days

January 900 22

February 700 18

March 800 21

April 1200 21

May 1500 22

June 1100 20

Solution:

Average requirement = Total expected demand = 6200 = 50 units / day

Number of production days 124

There is a few plan can be made:-


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1st plan is to maintain a constant workforce through out the whole year.

2nd

strategy is to maintain a constant workforce at level necessary to meet the lowest

demand and to meet all the balance demand and subcontracting.

Both plan 1 and 2 have a level production, so its called level strategies.

3rd

plan is to hire and layoff workers as needed to produce exact monthly requirements a chase strategy.

Table below provides cost information necessary for analyzing these three alternatives:

Inventory carrying cost $5 per unit / month

Subcontracting cost per unit $10 / unit

Average per rate $5 / hour ($40 / day)

Overtime per rate $7 / hour (above 8 hours /

day)

Labor hours to produce a unit 1.6 hours per unit

Cost of increasing daily production rate

(hiring and training)

$ 300 / unit

Cost of decreasing daily production rate

(layoffs)

$ 600 / unit

(i) Plan 1 - A constant workforce

Assume that 50 units are produced per day and that we have a constant workforce, no

overtime or idle time, no safety stock, and no subcontractors. The firm accumulates

inventory during the slack period of demand, January through March and depletes it

during the higher demand warm season, April through June. Assume beginning inventory

= 0 and planned ending inventory = 0

Solution:

(1) Find the production for 50 units/ day


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(2) Find the monthly inventory change

(3) Ending inventory


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Total units of inventory = 1850 units

(4) Find the total of man needed to produce 50 units / day

1 man who worker for 8 hours can produce 5 units. To produce 50 units a days, we need

10 men.


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(5) Find the total cost for the above figure

Inventory carrying = (1850 units in inventory x $5 per unit) = $9250

Regular time labor = (10 workers x $40 per day x 124 days) = $49600

Other cost (overtime, hiring, layoffs, subcontracting) =0 Total cost = $58,850

*Note the significant cost of carrying the inventory

(ii) Plan 2 Subcontractors and constant workforce

Although constant workforce is maintained, it is set low enough to meet demand only in

March, the lowest demand per day month. To produce 38 units per day in house, 7.6

workers are needed. (You can think of this as 7 full time workers and 1 part timer). All

other demand is met by subcontracting. Subcontracting is thus required in every other

month. No inventory holding costs are incurred in plan 2.

Solution:


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Because 6200 units are required during the aggregate plan period, we must compute how

many can be made by the firm and how must be subcontracted:

(1) Find the in house and subcontract total production

(1) In-House production = 38 units per day x 124 production days = 4,712 units

(2) Subcontract units = 6,200 4,712 = 1,488 units

(2) Find the total cost for regular time labor and subcontractor

Regular time labor = (7.6 workers x $40 per day x 124 days) = $37,696.00

Subcontracting = (1,488 units x $10 per unit) = $ 14,880.00 Total cost = $52,576.00

* Note the lower cost of regular labor but the added subcontracting cost


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(iii) Plan 3 Hiring and Firing

This plan involves varying the workforce size by hiring and firing as necessary. The

production rate will equal the demand, and there is no change in production from the

previous month, December

Solution:

Below show the calculations and total cost plan 3. Recall that it costs $600 per unit

produced to reduce production from the previous months daily level and $300 per unit change to increase the daily rate of production hiring.

Thus, the total cost, including production, hiring, and layoffs for plan 3 is $68, 200

* Note the substantial cost associated with changing (both increasing and decreasing) the

production levels.


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(iv) Final step in graphical method

The final step in the graphical method is to compare the costs of each proposed plan and

to select the approach with the least total cost. A summary analysis is provided below.

We can see that plan 2 has the lowest cost, it is the best of the 3 options.


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B) Mathematical Approaches

The transportation method of linear programming is not a trial-and-error method like

graphing but is rather produces an optimal plan for minimizing costs. Example below

shows the supply consists of on hand inventory and units produced by regular time,

overtime and subcontracting.

Farnsworth Tire Co. would like to develop an aggregate plan via the transportation

method. Data that relate to production, demand, capacity and cost at its West Virginia

Plant are shown in the table below:-

Sales Period

March April May

Demand Capacity: 800 1000 750

Regular 700 700 700

Overtime 50 50 50

Subcontracting 150 150 130

Beginning Inventory 100 tires

Costs

Regular time $40 per tire

Overtime $50 per tire

Subcontract $70 per tire

Carrying cost $2 per tire per month


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Illustration below showed the structure the transportation table and initial feasible

solution. However, the transportation method is flexible when costs are linear but does

not work when costs are non-linear.

The total cost for the initial solution is $105,900.


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EXERCISE

1. The president of Hill Enterprise, Terri Hill, projects the firms aggregate demand

requirements over the next 8 months as follows:

January 1400 May 2200

February 1600 June 2200

March 1800 July 1800

April 1800 August 1400

Her operations manager is considering a new plan, which begins in January with 200

units on hand and ends with zero inventories. Stock out cost of lost sales in $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 demand in the prior month. The December demand and rate of production

are both 1,600 units per month. The cost of hiring additional workers is $5000 per

100 units. The cost laying off workers is $7500 per 100 units. Evaluate the plan.

2. Haifa Instruments, an Israeli producer of portable kidney dialysis units and other medical products, develops a 4 months aggregate plan. Demand and capacity in

units are forecasts as follows:

Capacity

Source Month 1 Month 2 Month 3 Month 4

Labor

Regular time 235 255 290 300

Overtime 20 24 26 24

Subcontract 12 15 15 17

Demand 255 294 321 301

The cost of producing each dialysis units is $985 on regular time, $1319 on overtime and

$1500 on a subcontract. Inventory carrying cost is $100 per unit per month. There is to be

no beginning or ending inventory in stock and backorders are not permitted. Set up a

production plan that minimizes cost using the transportation method.


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LAB 2

AGGREGATE PLANNING

Lab Result

SCHOOL / PROGRAMME OF :___________________________

DATE OF LABORATORY :___________________________

GROUP MEMBERS NAME : (Reminder: Do not accept your group member to sign if his/her contribution is not satisfy)

1)_______________________________signature:__________

2)_______________________________signature:___________

3)_______________________________signature:__________

Marks:

Lab 2 - Aggregate Planning

Documents

total units of inventory

units day ept

unit cost

inventory ept

demand production days

level production

total cost

inventory x