Assignment 1.pdf - Assignment #1 INDU6141 Logistic Network...

Assignment #1 INDU6141 Logistic Network Models
Due date: Oct. 21, 2019
Hard copy submitted at the beginning of the class and before 6 pm. No submission through email is
accepted.
Problem 1. Assume that, for a certain company, the estimated annual sales to service level curve r(x) has
been determined by means of a simulation method. The resulting equation is r(x) = 950000x - 328000x 2 ,
where x denotes the percentage of customers served within 24 hours (e.g. if x=0.7, 70% of customers are
served within 24 hours); r(x) is expressed in $. The annual logistics costs (in $) are estimated as 280,000,
320,000, 380,000, 410,000, 460,000 and 510,000, with respect to the following values of service level
offered to customers: 50%, 60%, 70%, 80%, 90% and 100%, respectively. Determine the service level at
which the maximum estimated annual profit is achieved.
Problem 2: Your company has to close 20 of its 125 warehouses. Suppose the CPL hypotheses hold. How
would you define V
1
? What is the value of p?
Problem 3: Modify the CPL model to take into account that a subset of already existing facilities V
1
’ ⊆ V
cannot be closed (but can be upgraded). Indicate the current fixed cost and capacity of facility i ϵ V
1
’ as f
i
’
and q
i
’ , respectively. Moreover, let f
i
’’ and q
i
’’ be the fixed cost and capacity if facility i ϵ V
1
’ is upgraded,
respectively.
The original CPL model is:
Problem 4: Consider the following discrete location problem
Min ෍ ෍ c
୧୨
∗ x
୧୨
୨∈୚
మ
୧∈୚
భ
+ ෍ f
୧
∗ y
1