Lecture No 11

Held on: Wednesday, September 1, 2000

 

Frequency of Replanning:

Although plans are made over a fairly long planning horizon, replanning occurs frequently and the plans are used in a rolling mode.

Graphical Representation of a Production Plan.

Clearly plan 2 is better because of:

  1. Lower inventory.
  2. Lower change in production rate.

Earlier change (firing of workers) is better than waiting till end, where it will have to be more drastic.

 

 

Production planners use many methods in the face of seasonal demand.
    1. Inventory, varying production rate (overtime, hiring, firing).
    2. Demand management through promotions, pricing etc. to reduce fluctuations.
    3. Vacation planning of employees allows production to fluctuate without seasonal layoffs or overtime.
    4. Focus effort on training, experiment with new production methods, during low demand intervals.
    5. Divide workforce into permanent and seasonal.

When the demand is increasing, the key issue is when to increase capacity and by how much?

When demand is highly uncertain, buffer stocks have to be maintained.

Now we consider some solved production planning examples and some L.P. formulations. We begin with using Transportation L.P. method for solving some production planning facilities.

EXAMPLE:

Salico corporation must determine how many sailboats should be produced in the next 4 quarters.

The demand for the 4 quarters is as following:

Q1 Q2 Q3 Q4

Demand 40 60 75 25

The supply points are as follows:

Initial inventory = 10.

Q1RT = 40(the maximum which we can produce in

regular time in a quarter).

Q1OT = 150(we can keep a very large number at this position, but

over the 4 quarters the total demand is 200, hence our

purpose of including all possible feasible solutions

would be served if we keep the number as

200-40-10 = 150.

Q2RT = 40.

Q2OT = 150.

Q3RT = 40.

Q3OT = 150.

Q4RT = 40.

Q4OT = 150.

The demand points are:

D1 = 40.

D2 = 60.

D3 = 75.

D4 = 25.

Ddummy = (10+40+150+40+150+40+150+40+150) - (40+60+75+25)

= 570.

 

 

1

2

3

4

Dummy

Supply

Initial

10(0)

(20)

(40)

(60)

(0)

10

Q1RT

30(400)

10(420)

(440)

(460)

(0)

40

Q1OT

(450)

(470)

(490)

(510)

(0)

150

Q2RT

(M)

40(400)

(420)

(440)

(0)

40

Q2OT

(M)

10(450)

(470)

(490)

(0)

150

Q3RT

(M)

(M)

40(400)

(420)

(0)

40

Q3OT

(M)

(M)

35(450)

(470)

(0)

150

Q4RT

(M)

(M)

(M)

25(400)

(0)

40

Q4OT

(M)

(M)

(M)

(450)

(0)

150

Demand

40

60

75

25

570

770

* RT - regular time.

* OT - over time.

* M is a very large number.

* The number in the bracket ( ) indicates the cost for taking a particular path.

Thus ,

Q1 demand is met by: 10 units initial production.

30 units Q1 RT production.

Q2 demand is met by: 10 units Q1 RT production.

40 units Q2 RT production.

10 units Q2 OT production.

Q3 demand is met by: 40 units Q3 RT production.

35 units Q3 OT production.

Q4 demand is met by: 25 units Q4 RT production.

 

Points to ponder:

Will optimal solution change if:

  1. Demand could be backlogged at cost of $30/sailboat/month.
  2. If demand is not met on time, the sale is lost and an opportunity cost of $450 is incurred.
  3. Sailboats can be held in inventory for a maximum of 2 months.
  4. At a cost of $440/boat, Salico can purchase upto 10 sailboats from sub-contractors.
  5. Total production in Q1 and Q2 cannot exceed 75 units.

 

 

 

 

Hosted by www.Geocities.ws

1