Capacitated plant location model supply chain

Supply Chain Management Analytics

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

https://www.youtube.com/watch?v=fQwAZsH_OP4

https://www.youtube.com/watch?v=N7TJa9W47HY&t=363s

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

https://www.youtube.com/watch?v=0urjPqJHoZc&t=43s

https://www.youtube.com/watch?v=0urjPqJHoZc

https://www.youtube.com/watch?v=fFo1MBg0hG4&t=400s

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

https://www.youtube.com/watch?v=sDwM5kDVG58&t=968s

https://www.youtube.com/watch?v=BuGbHaAfKuo

https://www.youtube.com/watch?v=avjYKKwAIwA

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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