Solu�on File Open Ques�ons
BT2110 Resit, 7 July 2023, On campus
• 31
o A Dutch manufacturer called “Cuppie” is producing circular cups for companies.
The company has 16 decentralized (local) warehouses which are delivering the
cups. Currently, Cuppie is planning to switch to a centralized warehouse. Each
local warehouse faces a monthly demand of 100 units and a monthly standard
deviation of 25 units. The demand between warehouses is independent. The
lead time for each decentral local warehouse is 1 week, and 4 weeks for the
(new) centralized warehouse. The CSL is 95% and a continuous (R,Q) policy is
used. Assume a month consists of 4 weeks
o a
Calculate the total safety stock for the (current) decentralized setting with 16
local warehouses.
z = 1.65
o b
Calculate the safety stock for the centralized setting, i.e., switching to a single
central warehouse. Assume that the demand of the warehouses is independent
and all warehouses are aggregated in this central warehouse.
z = 1.65
o c
What would happen to the amount of safety stock for the centralized case when
the demand of all the local warehouses is negatively correlated? Motivate your
answer.
The safety stock decreases: Proper explanation, e.g. referring to pooling
benefits when demand is negatively corelated
Copyright: Erasmus University Roterdam
, Solu�on File Open Ques�ons
• 32
Network
7.5 points · 3 questions
o Heineken wants to open a new distribution center to cut delivery cost to its retail
locations in Zuid-Holland. Each location requires a different number of deliveries
each week, with each delivery being exactly one full truckload. The table shows
the coordinates and the weekly deliveries for each retail location.
Retail X- Y-
Weekly deliveries
location Coordinate Coordinate
A 3 6 200
B 14 2 300
C 7 16 100
D 9 10 160
E 4 13 240
o a
Determine the optimal location of the new distribution center if you want to
minimize the total load-distance using rectilinear distances
Sum weekly deliveries is 1000. 1000/2 = 500
X: Cumulative sum larger or equal than 500 when x-coordinate is 7
(location C)
Y: Cumulative sum larger or equal than 500 when y-coordinate is 6
(location A) or 10 (location D) if sorted descending
o b
Determine the optimal location of the new distribution center if you want to
minimize the total load-distance using Euclidean distances
X* = (3*200+14*300+7*100+9*160+4*240)/1000 = 7.9
Y* = (6*200+2*300+16*100+10*160+13*240)/1000 = 8.12
o c
When comparing to the result of question a., how does the solution change if the
coordinates of retail location B are changed to (20, 0.5)? Explain the answer.
Copyright: Erasmus University Roterdam
BT2110 Resit, 7 July 2023, On campus
• 31
o A Dutch manufacturer called “Cuppie” is producing circular cups for companies.
The company has 16 decentralized (local) warehouses which are delivering the
cups. Currently, Cuppie is planning to switch to a centralized warehouse. Each
local warehouse faces a monthly demand of 100 units and a monthly standard
deviation of 25 units. The demand between warehouses is independent. The
lead time for each decentral local warehouse is 1 week, and 4 weeks for the
(new) centralized warehouse. The CSL is 95% and a continuous (R,Q) policy is
used. Assume a month consists of 4 weeks
o a
Calculate the total safety stock for the (current) decentralized setting with 16
local warehouses.
z = 1.65
o b
Calculate the safety stock for the centralized setting, i.e., switching to a single
central warehouse. Assume that the demand of the warehouses is independent
and all warehouses are aggregated in this central warehouse.
z = 1.65
o c
What would happen to the amount of safety stock for the centralized case when
the demand of all the local warehouses is negatively correlated? Motivate your
answer.
The safety stock decreases: Proper explanation, e.g. referring to pooling
benefits when demand is negatively corelated
Copyright: Erasmus University Roterdam
, Solu�on File Open Ques�ons
• 32
Network
7.5 points · 3 questions
o Heineken wants to open a new distribution center to cut delivery cost to its retail
locations in Zuid-Holland. Each location requires a different number of deliveries
each week, with each delivery being exactly one full truckload. The table shows
the coordinates and the weekly deliveries for each retail location.
Retail X- Y-
Weekly deliveries
location Coordinate Coordinate
A 3 6 200
B 14 2 300
C 7 16 100
D 9 10 160
E 4 13 240
o a
Determine the optimal location of the new distribution center if you want to
minimize the total load-distance using rectilinear distances
Sum weekly deliveries is 1000. 1000/2 = 500
X: Cumulative sum larger or equal than 500 when x-coordinate is 7
(location C)
Y: Cumulative sum larger or equal than 500 when y-coordinate is 6
(location A) or 10 (location D) if sorted descending
o b
Determine the optimal location of the new distribution center if you want to
minimize the total load-distance using Euclidean distances
X* = (3*200+14*300+7*100+9*160+4*240)/1000 = 7.9
Y* = (6*200+2*300+16*100+10*160+13*240)/1000 = 8.12
o c
When comparing to the result of question a., how does the solution change if the
coordinates of retail location B are changed to (20, 0.5)? Explain the answer.
Copyright: Erasmus University Roterdam
