Work-force Planning Models Example 1 Suppose that each American can be classifie

Question

Work-force Planning Models Example 1 Suppose that each American can be classified into one of three groups: children, working adults, or retired people. During a one-year period, .959 of all children remain children, .04 of all children become working adults, and.001 of all children die. During any given year, .96 of all working adults remain working adults, .03 of all working adults retired, and .01 of all working adults die. Also, .95 of all retired people remain retired and.05 of all retired people die. One thousand children are born each year.

Explanation / Answer

Transition Matrix will be:

At Markovian steady state:

The steady-state census exists if the no. people entering each group is equal to the no. of people leaving each group. So,

For children: 1,000 = (0.04+0.001)*N1 or, N1 = 1000/(0.041) = 24,390
For the adults: 0.04*N1 = (0.01+0.03)*N2 or, N2 = 0.04*24,390/0.04 = 24,390
For the retired: 0.03*N2 = 0.05N3 or, N3 = 0.03*24,390/0.05 = 14,634

---------------

Total fund required at steady state = $5000 x 14,634.14 = $73170731.7

Contribution of each adult = $73170731.7 / 24,390 = $3,000

Child Adult Dead Retired Child 0.959 0.04 0.001 0 Adult 0 0.96 0.01 0.03 Retired 0 0 0.05 0.95 Dead 0 0 1.00 0

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.