Lab 2 - Aggregate Planning

April 25, 2018 | Author: litrakhan | Category: Inventory, Labour Economics, Linear Programming, Overtime, Business Economics
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EPT 432 Production Management

Laboratory Module

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.


January February March April May June

Expected Demand 900 700 800 1200 1500 1100

Production Days 22 18 21 21 22 20


Average requirement =

Total expected demand  Number of production days

There is a few plan can be made:-

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= 6200 = 50 units / day 124

EPT 432 Production Management

Laboratory Module

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 it’s 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 Subcontracting cost per unit Average per rate Overtime per rate

$5 per unit / month $10 / unit $5 / hour ($40 / day) $7 / hour (above 8 hours / day) 1.6 hours per unit $ 300 / unit

Labor hours to produce a unit Cost of increasing daily production rate (hiring and training) Cost of decreasing daily production rate $ 600 / unit (layoffs)

(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


(1) Find the production for 50 units/ day

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EPT 432 Production Management

Laboratory Module

(2) Find the monthly inventory change

(3) Ending inventory

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EPT 432 Production Management

Laboratory Module

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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EPT 432 Production Management

Laboratory Module

(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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EPT 432 Production Management

Laboratory Module

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 Subcontracting

= (7.6 workers x $40 per day x 124 days) = (1,488 units x $10 per unit) Total cost

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

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= $37,696.00 = $ 14,880.00 = $52,576.00

EPT 432 Production Management

Laboratory Module

(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 month’s 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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EPT 432 Production Management

Laboratory Module

(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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EPT 432 Production Management

Laboratory Module

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 Demand Capacity: 800 1000 Regular 700 700 Overtime 50 50 Subcontracting 150 150 Beginning Inventory 100 tires

Regular time Overtime Subcontract Carrying cost

May 750 700 50 130

Costs $40 per tire $50 per tire $70 per tire $2 per tire per month

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EPT 432 Production Management

Laboratory Module

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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EPT 432 Production Management

Laboratory Module

EXERCISE 1. The president of Hill Enterprise, Terri Hill, projects the firm’s aggregate demand requirements over the next 8 months as follows:

January February March April

1400 1600 1800 1800

May June July August

2200 2200 1800 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 Labor Regular time Overtime Subcontract Demand

Month 1

Month 2

Month 3

Month 4

235 20 12 255

255 24 15 294

290 26 15 321

300 24 17 301

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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EPT 432 Production Management

Laboratory Module


Lab Result







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