Question

In a hotel renovation project, some air ducts and furnaces for the new centralized air conditioning system are required. The material cost is USD 250,000. Transportation cost is USD 3,850. Administrative (order) cost is USD 1,000. A nearby storage area is available and can be rented for a cost of 65 cents/cu yd/day (knowing that the purchased material will take 2,500 cubic yards of storage). For every day of project delay, the contractor is charged a fine of USD 1,800. The activity of installing the materials has an Early Start and Late Start of 95 and 99 respectively. The probabilities of delivery for the materials are shown in the table below.

t (days)	P(t)
15	0.07
16	0.10
17	0.18
18	0.20
19	0.25
20	0.15
21	0.05

Calculate:

1. The expected delivery time for the required materials.
2. The total costs in case the material arrives at day 97
3. The total costs in case the material arrives at day 102
4. If the material is ordered on day 80, what is the probability of paying unavailability cost?
5. If the material is ordered on day 77, what is the probability of paying holding cost?
6. Which of these project days is more suitable to order the pipes? Day 78, 79 or 80? (prove with calculations)

Answer 1

A. Expected delivery time is

15*0.07+16*0.1+17*0.18+18*0.2+19*.25+20*0.15+21*0.05= 18.11 days

B. Total costs in case material arrives at day 97

=250,000+3,850+1000+2500*0.65 = USD 256,475

Assuming the activity of installation for a normal start is 97 days ((95+99)/2)

C. Total costs in case material arrives at 102 day

=250,000+3,850+1000+2500*0.65+1800*5= USD 265,475

D. (1-.07-.1-.18)=0.65

E. Expected days = 77+18.11=95.11

Extra days = 97-95.11=1.89 equivalent to 2

If arrived on 92 day 0.07+0.1+0.18=0.35