The purpose of this assignment is to enable students to investigate, analyze and critique a process that allows decision making for optimizing logistics supply chain design at the tactical level which includes global logistics and distribution and warehousing design features. This may include utilizing linear programming techniques for optimizing supply chain networks.
Assessment 1consists of
three
parts
Assessment 1- Part A- Case study-1- Supply chain design of X & Co.
Designing the Production Network at X & Co.
Mr. Johnson, vice president of supply chain at x & co. thought that his current production and distribution network was not appropriate given the significant increase in Transportation costs over the past few years. Compared to when the company had set up its production facility in
Chicago
, Transportation costs had increased by a factor of More than four and were expected to continue growing in the next few years. A quick decision on building one or more new plants could save the company significant Amounts in Transportation expenses in the future.
X & Co.
X & was founded in the late 19
70
s and produced baby wipes and diaper ointment. The demand for the two products was as shown in
Table 1
. The company currently had one factory in Chicago that produced both Products for the entire country. The wipes line in the Chicago facility had a capacity of 5 million units, an annualized fixed cost of $5 million a year, and a variable cost of $10 per unit. The ointment line in the Chicago facility had a capacity of 1 million units, an annualized fixed cost of $1.5 million a year, and a variable cost of $20 per unit, the current transportation costs per unit (for both wipes and ointment) are shown in
Table 2
.
| Table 1 | |||||||
|
Table 1: Regional Demand at X & Com (in ‘000s) |
|||||||
|
Zone |
Wipes Demand |
Ointment Demand |
|||||
|
Northwest |
50 0 |
50 |
Lower Midwest |
800 |
65 |
||
|
Southwest |
700 |
90 |
Northest |
1,000 |
120 |
||
|
Upper Midwest |
900 |
southeast |
600 |
70 |
| Table 2 | ||||||||||||
|
Table 2 Transportation Costs per Unit |
||||||||||||
|
Northeast |
Southeast |
|||||||||||
| Chicago |
$6.32 |
$3.68 |
$4.04 |
$5.76 |
$5.96 |
|||||||
|
Princeton |
$6.60 |
$5.92 |
$4.08 |
|||||||||
|
Atlanta |
$6.72 |
$6.48 |
$3.64 |
|||||||||
|
Los Angeles |
$4.36 |
New Network Options
Johnson had identified Princeton, Chicago; Atlanta; and Los Angeles as potential sites for new plants. Each new plant could have a wipes line, an ointment line, or both. A new wipes line had a capacity of 2 million units, an annual fixed cost of $2.2 million, and a variable production cost of $10 per unit. A new ointment line had a capacity of 1 million units. An annual fixed cost of $1.5 million, and a variable cost of $20 per unit. The current transportation cost per unit is shown in Table 3. Johnson had to decide whether to build a new plant and if so, which production lines to put into the new plant.
Question
1. What is the annual cost of serving the entire nation from Chicago?
2. Do you recommend adding any plant(S)? if so, where should the plant(S) be build and what lines should be included? Assume that the Chicago plant will be maintained at its current capacity but could be run at lower utilization. Would your decision be different if transportation costs are half of their current value? What if they were double their current value?
3. If Johnson could design a new network from scratch (assume he did not have the Chicago plant but could build it at the cost and capacity specified in the case). What production network would you recommend? Assume that any new plants built beside Chicago would be at the cost and capacity specified under the new network options. Would your decision be different in transportation costs were half of their current value? What if they were double their current value?
The purpose of this assignment is to enable students to investigate, analyze and critique a process that allows decision making for optimizing logistics supply chain design at the tactical level which includes global logistics and distribution and warehousing design features. This may include utilizing linear programming techniques for optimizing supply chain networks.
Assessment 1 consists of
three
parts
Assessment 1- Part B- Case Study-2- Managing Growth at Y & Co.
In December 2008, Mr. Thomson and his management team were busy in evaluating the performance at Y & co. over the previous year. Demand had grown by 80 percent. This growth, however, was a mixed blessing. The venture capitalists supporting the company were very pleased with the growth in sales and the resulting increase in revenue. Thomson and his team, however, could clearly see that costs would grow faster than revenues if demand continued to grow and the supply chain network was not redesigned. They decided to analyze the performance of the current network to see how it could be redesigned to best cope with the rapid growth anticipated over the next three years.
Y & Co.
Thomson founded Y &Co. in 2004 with a mission of supplying parents with more affordable sports equipment for their children. Parents complained about having to discard expensive skates, skis, jackets, and shoes because children outgrew them rapidly. Thomson’s initial plan was for the company to purchase used equipment and
Jackets from families and any surplus equipment from manufacturers and retailers and sell these over the Internet. The idea was well received in the marketplace, demand grew rapidly, and by the end of 2004, the company had sales of $0.8 million. By this time, a variety of new and used products were being sold, and the company received significant venture capital support.
In June 2004, Thomson leased part of a warehouse in the outskirts of
St. Louis
to manage a large amount of product being sold. Suppliers sent their product to the warehouse. Customer orders were packed and shipped by UPS from there. As demand grew, Y & Co. leased more space within the warehouse. By 2007, Y & Co. leased the entire warehouse and orders were being shipped to customers all over the United states. Management divided the United States into six customer zones for planning purposes. The demand from each customer zone in 2007 was as shown in Table 1. Thomson estimated that the next three years would see a growth rate of about 80 percent per year, after which demand would level off.
|
Table 1: Regional Demand at Y & Co. for 2007 |
|||||
|
Zone |
Demand in 2007 |
||||
|
Northwest |
320,000 |
Lower Midwest |
220,000 |
||
|
Southwest |
200,000 |
Northeast |
350,000 |
||
|
Upper Midwest |
160,000 |
Southeast |
175,000 |
The Network Options
Thomson and his management team could see that they needed more warehouse space to cope with the anticipated growth. One option was to lease more warehouse space in St. Louis itself. Other options included leasing warehouses all over the country. Leasing a warehouse involved fixed costs based on the size of the warehouse and variable costs that depended on the quantity shipped through the warehouse. Four potential locations for warehouses were identified in
Denver
,
Seattle
,
Atlanta
, and
Philadelphia
, warehouses. Leased could be either small (about 100,000 sq. ft.) or large (200,000 sq. ft). Small warehouses could handle a flow of up to 2 million units per year, whereas large warehouses could handle a flow of up to 4 million units per year. The current warehouse in St. Louis was small. The fixed and variable costs of small and large warehouses in different locations are shown in Table 2.
homson estimated that the inventory holding costs at a warehouse (excluding warehouse expense) was about $600, where F is the number of units flowing through the warehouse per year. This relationship is based on the theoretical observation that the inventory held at a facility (not across the network) is proportional to the square root the throughput through the facility. As a result, aggregating throughput through a few facilities reduces the inventory held as compared with disaggregating throughput through many facilities. Thus, a warehouse handling I million units per year incurred an inventory holding cost of $600,000 in the course of the year. If your version of Excel has problems solving the nonlinear objective function, use the following inventory costs:
|
Inventory Cost |
|
|
Range of F |
Inventory Cost |
|
0-2 million |
$ 250,000 Y + 0.310F |
|
2-4 million |
$530,000Y + 0.170F |
|
4-6 million |
$678,000Y + 0.133F |
|
More than 6 million |
$798,000Y + 0.113F |
If you can handle only a single linear inventory cost, you should use $475,000Y + 0.165F. For each facility, Y=1 if the facility is used, 0 otherwise.
Y & Co. charged a flat fee of $3 per shipment sent to a customer. An average customer order contained four units. Y & Co. in turn contracted with UPS to handle all its outbound shipments. UPS charges were based on both the origin and the destination of the shipment and are shown in Table 3.
Table 2: Fixed and
Variable Cost
s of Potential Warehouses
Small Warehouse
Large Warehouse
Location
Fixed Cost
($/year)
($/Unit Flow)
($/year)
Variable Cost
($/Unit Flow)
300,000
0.20
500,000
0.20
0.20
420,000
0.20
220,000
0.20
375,000
0.20
220,000
0.20
375,000
0.20
240,000
0.20
400,000
0.20
Management estimated that inbound transportation costs for shipments from suppliers were likely to remain unchanged, no matter what warehouse configuration was selected.
|
Table 3: UPS Charges per Shipment (Four Units) |
||||||||||||||||||||||
|
Northwest |
Southwest |
Upper Midwest |
Lower Midwest |
Northeast |
Southeast |
|||||||||||||||||
|
$2.00 |
$2.50 |
$3.50 |
$4.00 |
$5.00 |
$5.50 |
|||||||||||||||||
|
$3.00 |
$4.50 |
|||||||||||||||||||||
|
St. Luis |
||||||||||||||||||||||
Questions
1. What is the cost Y & Co. incurs if all warehouses leased are in St. Louis?
2. What supply chain network configuration do you recommend for Y & Co.? Why?
3. How would your recommendation change if transportation costs were twice those shown in Table 3?
Supply Chain Management Analytics (21946)
Lecture 7
Logistics, distribution and warehousing network optimization part-2
AGENDA FOR TODAY
Topic – Logistics, distribution and warehousing network optimization part-2
Discussion on Assessment 1 and 3.
Feedback on assessment 2.
Scheduling Thought leadership discussion- Presentation
Study material available on UTS online
Related readings: See UTS online
Last lecture recap
Introduction to LP
Introduction to ILP
Introduction to MILP
Introduction to GP
Practice exercises
Network Optimization- Models for facility location & capacity allocation
Deciding regional facility & capacity (based on demand & supply) – Phase (ii)- Capacitated plant location model
Deciding plant location in each region- Phase (iii)- Gravity location model
Allocating capacity- Phase (iv)- Allocating demand to production facilities
Which plants to establish? How to configure the network?
Key Costs:
Fixed facility cost
Transportation cost
Production cost
Inventory cost
Coordination cost
5-5
Notes:
Capacitated Plant Location- with Multiple Sourcing
Which market is served by which plant?
Which supply sources are used by a plant?
None of the plants are open, a cost of fi is paid to open plant i
At most k plants will be opened
yi = 1 if plant is located at site i, 0 otherwise
xij = Quantity shipped from plant site i to customer j
5-6
Notes:
Plant Location with Single Sourcing (each customer has exactly one supplier)
Which market is served by which plant?
Which supply sources are used by a plant?
None of the plants are open, a cost of fi is paid to open plant i
yi = 1 if plant is located at site i,
0 otherwise
xij = 1 if market j is supplied by factory i,
0 otherwise
5-7
Notes:
Network optimization Models-
Gravity Methods for Location
Ton Mile-Center Solution
x,y: Warehouse Coordinates
xn, yn : Coordinates of delivery location n
dn : Distance to delivery location n
Fn : Annual tonnage to delivery location n ($/ton mile)
D.n – Demand
Min
5-8
Notes:
Demand Allocation Model
Which market is served by which plant?
Which supply sources are used by a plant?
xij = Quantity shipped from plant site i to customer j
5-9
Network optimization problem (Capacitated plant location- multiple sourcing)
The Vice President of Supply Chain for SunOil is considering where to build new production facilities. There are five options: North and South America, Europe, Asia, and Africa. The total costs of production and transportation for each possible pair of “Supply” and “Demand” regions are given in the following table: 1. In addition, there is a fixed cost to constructing a plant that does not depend on the production volume. There are two possible plant types: low capacity that can produce up to 10 million units a year at a fixed cost that depends on the region and is given in cells G4:G8 of table 1, and high capacity that can produce up to 20 million units a year at a 50% higher fixed cost (thus exhibiting economies of scale). The associated cost and maximum capacity are given in cells I4:J8 of table 1. Total demand in each region (in millions of units) is given in cells B9:F9. We need to decide: (i) How many, and what type of plants we should build in each region (ii) How to allocate production between them (iii) What markets should each plant supply
Fig-1
Table 1
Gravity location model
After deciding regional configurations a manager must identify potential locations in each region where the company has decided to locate a plant. As a preliminary step, the manager needs to identify the geographical location where potential sites may be considered. Gravity location models can be useful when identifying suitable geographic allocations within a region. Gravity models are used to find locations that minimize the cost of transporting raw materials from suppliers and finished goods to the market served.
-Consider, for example, Steel Appliances (SA), a manufacturer of high-quality refrigerators and cooking ranges. SA has one assembly factory located near Denver from which it has supplied the entire United States. Demand has grown rapidly and the CEC of SA has decided to set up another factory to serve its eastern markets. The supply chair manager is asked to find a suitable location for the new factory. Three parts plants located in Buffalo, Memphis, and St. Louis will supply parts to the new factory, which will serve markets in Atlanta, Boston, Jacksonville, Philadelphia, and New York. The coordinate location, the demand in each market, the required supply from each parts plant, and the shipping cost for each supply source or market are shown in Table 5.l.
-Gravity models assume that both the markets and the supply sources can be located as grid points on a plane. All distances are calculated as the geometric distance between two points on the plane. These models also assume that the transportation cost grows linearly with the quantity shipped. We discuss a gravity model for locating ( single facility that receives raw material from supply sources and ships finished product to markets.
-Find the best location.
Table 5.1
Coordinates
Sources/market $/ton mile (Fn) Tons (Dn) Xn Yn dn
Sources Buffalo 0.9 500 700 1200 1389
Memphis 0.95 300 250 600 650
St. Louis 0.85 700 225 825 855
Markets Atlanta 1.5 225 600 500 781
Boston 1.5 150 1050 1200 1595
Jacksonvile 1.5 250 800 300 854
Philadelphia 1.5 175 925 975 1344
New York 1.5 300 1000 1080 1472
Allocating Demand to Production Facilities – Example
TelecomOne has a total production capacity of 71,000 units per month and a total demand of 30,000 units per month whereas HighOptic has a production capacity of 51,000 units per month and a demand of 24,000 units per month. Each year, managers in both companies must decide how to allocate the demand to their production facilities. This decision will be revisited every year as demand and costs change. Both TelecomOne and HighOptic are manufacturers of the latest generation of telecommunication equipment. TelecomOne has focused on the eastern half of the United States. It has manufacturing plants located in Baltimore, Memphis, and Wichita, and serves markets in Atlanta, Boston, and Chicago. HighOptic has targeted the western half of the United States and serves markets in Denver, Omaha, and Portland. HighOptic has plant located in Cheyenne and Salt Lake City. Capacity, demand and cost data are below:
Inputs – Costs, Capacities, Demands data for Telecomone and HighOptic (TelecomOne)
Demand City
Production and Transportation Cost per 1000 Units Fixed Capa-
Supply City Atlanta Boston Chicago Denver Omaha Portland Cost ($) city
Baltimore 1,675 400 685 1,630 1,160 2,800 7,650 18
Cheyenne 1,460 1,940 970 100 495 1,200 3,500 24
Salt Lake 1,925 2,400 1,425 500 950 800 5,000 27
Memphis 380 1,355 543 1,045 665 2,321 4,100 22
Wichita 922 1,646 700 508 311 1,797 2,200 31
Demand 10 8 14 6 7 11
Continued
Management at both TelecomOne and HighOptic has decided to merge the two companies into a single entity to be called TelecomOptic. Management feels that significant benefits will result if the two networks are merged appropriately. TelecomOptic will have five factories from which to serve six markets. Management is debating whether all five factories are needed. They have assigned a supply chain team to study the network for the combined company and identify the plants that should be shut down.
Find optimal sol for Telecome one
Find opt sol for High Optic
Find total cost when merged (all plants are Open)
Find Opt sol after merge
Find opt sol after merge considering single sourcing option (not needed).
Assessment 1- Part B
Managing growth at company Y
Assessment 1- Part A
Supply chain design of X & Co
Assessment 3
Report on supply chain design
Thank You
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Supply Chain Management Analytics (21946)
Lecture 7
Logistics, distribution and warehousing network optimization part-2
AGENDA FOR TODAY
Topic – Logistics, distribution and warehousing network optimization part-2
Discussion on Assessment 1 and 3.
Feedback on assessment 2.
Scheduling Thought leadership discussion- Presentation
Study material available on UTS online
Related readings: See UTS online
Last lecture recap
Introduction to LP
Introduction to ILP
Introduction to MILP
Introduction to GP
Practice exercises
Network Optimization- Models for facility location & capacity allocation
Deciding regional facility & capacity (based on demand & supply) – Phase (ii)- Capacitated plant location model
Deciding plant location in each region- Phase (iii)- Gravity location model
Allocating capacity- Phase (iv)- Allocating demand to production facilities
Which plants to establish? How to configure the network?
Key Costs:
Fixed facility cost
Transportation cost
Production cost
Inventory cost
Coordination cost
5-5
Notes:
Capacitated Plant Location- with Multiple Sourcing
Which market is served by which plant?
Which supply sources are used by a plant?
None of the plants are open, a cost of fi is paid to open plant i
At most k plants will be opened
yi = 1 if plant is located at site i, 0 otherwise
xij = Quantity shipped from plant site i to customer j
5-6
Notes:
Plant Location with Single Sourcing (each customer has exactly one supplier)
Which market is served by which plant?
Which supply sources are used by a plant?
None of the plants are open, a cost of fi is paid to open plant i
yi = 1 if plant is located at site i,
0 otherwise
xij = 1 if market j is supplied by factory i,
0 otherwise
5-7
Notes:
Network optimization Models-
Gravity Methods for Location
Ton Mile-Center Solution
x,y: Warehouse Coordinates
xn, yn : Coordinates of delivery location n
dn : Distance to delivery location n
Fn : Annual tonnage to delivery location n ($/ton mile)
D.n – Demand
Min
5-8
Notes:
Demand Allocation Model
Which market is served by which plant?
Which supply sources are used by a plant?
xij = Quantity shipped from plant site i to customer j
5-9
Network optimization problem (Capacitated plant location- multiple sourcing)
The Vice President of Supply Chain for SunOil is considering where to build new production facilities. There are five options: North and South America, Europe, Asia, and Africa. The total costs of production and transportation for each possible pair of “Supply” and “Demand” regions are given in the following table: 1. In addition, there is a fixed cost to constructing a plant that does not depend on the production volume. There are two possible plant types: low capacity that can produce up to 10 million units a year at a fixed cost that depends on the region and is given in cells G4:G8 of table 1, and high capacity that can produce up to 20 million units a year at a 50% higher fixed cost (thus exhibiting economies of scale). The associated cost and maximum capacity are given in cells I4:J8 of table 1. Total demand in each region (in millions of units) is given in cells B9:F9. We need to decide: (i) How many, and what type of plants we should build in each region (ii) How to allocate production between them (iii) What markets should each plant supply
Fig-1
Table 1
Gravity location model
After deciding regional configurations a manager must identify potential locations in each region where the company has decided to locate a plant. As a preliminary step, the manager needs to identify the geographical location where potential sites may be considered. Gravity location models can be useful when identifying suitable geographic allocations within a region. Gravity models are used to find locations that minimize the cost of transporting raw materials from suppliers and finished goods to the market served.
-Consider, for example, Steel Appliances (SA), a manufacturer of high-quality refrigerators and cooking ranges. SA has one assembly factory located near Denver from which it has supplied the entire United States. Demand has grown rapidly and the CEC of SA has decided to set up another factory to serve its eastern markets. The supply chair manager is asked to find a suitable location for the new factory. Three parts plants located in Buffalo, Memphis, and St. Louis will supply parts to the new factory, which will serve markets in Atlanta, Boston, Jacksonville, Philadelphia, and New York. The coordinate location, the demand in each market, the required supply from each parts plant, and the shipping cost for each supply source or market are shown in Table 5.l.
-Gravity models assume that both the markets and the supply sources can be located as grid points on a plane. All distances are calculated as the geometric distance between two points on the plane. These models also assume that the transportation cost grows linearly with the quantity shipped. We discuss a gravity model for locating ( single facility that receives raw material from supply sources and ships finished product to markets.
-Find the best location.
Table 5.1
Coordinates
Sources/market $/ton mile (Fn) Tons (Dn) Xn Yn dn
Sources Buffalo 0.9 500 700 1200 1389
Memphis 0.95 300 250 600 650
St. Louis 0.85 700 225 825 855
Markets Atlanta 1.5 225 600 500 781
Boston 1.5 150 1050 1200 1595
Jacksonvile 1.5 250 800 300 854
Philadelphia 1.5 175 925 975 1344
New York 1.5 300 1000 1080 1472
Allocating Demand to Production Facilities – Example
TelecomOne has a total production capacity of 71,000 units per month and a total demand of 30,000 units per month whereas HighOptic has a production capacity of 51,000 units per month and a demand of 24,000 units per month. Each year, managers in both companies must decide how to allocate the demand to their production facilities. This decision will be revisited every year as demand and costs change. Both TelecomOne and HighOptic are manufacturers of the latest generation of telecommunication equipment. TelecomOne has focused on the eastern half of the United States. It has manufacturing plants located in Baltimore, Memphis, and Wichita, and serves markets in Atlanta, Boston, and Chicago. HighOptic has targeted the western half of the United States and serves markets in Denver, Omaha, and Portland. HighOptic has plant located in Cheyenne and Salt Lake City. Capacity, demand and cost data are below:
Inputs – Costs, Capacities, Demands data for Telecomone and HighOptic (TelecomOne)
Demand City
Production and Transportation Cost per 1000 Units Fixed Capa-
Supply City Atlanta Boston Chicago Denver Omaha Portland Cost ($) city
Baltimore 1,675 400 685 1,630 1,160 2,800 7,650 18
Cheyenne 1,460 1,940 970 100 495 1,200 3,500 24
Salt Lake 1,925 2,400 1,425 500 950 800 5,000 27
Memphis 380 1,355 543 1,045 665 2,321 4,100 22
Wichita 922 1,646 700 508 311 1,797 2,200 31
Demand 10 8 14 6 7 11
Continued
Management at both TelecomOne and HighOptic has decided to merge the two companies into a single entity to be called TelecomOptic. Management feels that significant benefits will result if the two networks are merged appropriately. TelecomOptic will have five factories from which to serve six markets. Management is debating whether all five factories are needed. They have assigned a supply chain team to study the network for the combined company and identify the plants that should be shut down.
Find optimal sol for Telecome one
Find opt sol for High Optic
Find total cost when merged (all plants are Open)
Find Opt sol after merge
Find opt sol after merge considering single sourcing option (not needed).
Assessment 1- Part B
Managing growth at company Y
Assessment 1- Part A
Supply chain design of X & Co
Assessment 3
Report on supply chain design
Thank You
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