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Facility Location Facility location is the determination of the geographical site(s) in which to locate a firm’s operations. Globalisation Factors to consider Quantitative tools for analysis locating a single facility locating within a network of facilities Location decisions must be co-ordinated with production planning and distribution strategies

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**Location Theory - Early History**

Weber’s classification of industries (1909) Weight-losing process locate close to raw materials e.g. steel making Weight-gaining process incorporate “ubiquitous” raw materials e.g. air, water locate near markets Hoover’s (1957) tapered transportation rates tapered transportation rates minimum costs at either production point or market point

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**Factors - Location Related**

Facility Location Factors - Location Related Land/Construction costs Community receptivity Local business climate Quality of life Government incentives tax breaks free trade zone Government barriers currency controls trading blocs local content environmental regulations Political Risks Janny Leung

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**Factors - Resource/Cost Related**

Proximity to suppliers Quality/Availability of labour Transportation/Energy infrastructure Proximity to customers Inbound/Outbound distribution costs Other (company-owned) facilities Competitive Advantage

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**Quantitative Tools Center of Gravity Method Mixed Integer Programming**

Simulation Heuristics Other methods Single facility location Multi-facility location Supply chain network design Dynamic location models

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**Single Facility Location**

Given a set of demand points, each located at (xi,yi) with a specified volume Vi to be moved to a facility (at transportation rate Ri ), locate a single facility to minimise total transportation costs. Find (X,Y) to Minimise Vi Ri di where di = [(Xi - X)2 + (Yi - Y)2]1/2

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**Centre of Gravity Method**

Grid method centroid method Locate facility at:

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**Concerns/Assumptions of Centre-of-Gravity Model**

continuous demand concentrated at a point transportation costs proportional to Euclidean distance fixed cost of establishing facility ignored static simple useful “first-cut” solution

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**Multi-Facility Location**

How many sites? Where to locate each? Capacities? Which customers assigned to each site? Which products to stock/produce at each site?

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**Multiple Centre-of-Gravity Approach**

Pre-assign demand points to each facility (i.e. cluster customers that are closest together). For each cluster, locate one facility at centre of gravity. With facility locations fixed, re-assign customers to closest facility. Find centres of gravity for new clusters. Repeat cluster-assign until no further change.

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**Linear and Mixed Integer Programming**

LP useful in calculating distribution costs Mixed Integer Programming can `optimize’ site selection and distribution plan simultaneously Detailed cost estimates needed

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p-median Problem Locate p facilities so as to minimise the sum of fixed cost for establishing facilities and transportation costs from demand points to assigned facility. Ballou (Logware): demand point co-ordinates given assume out-and-back along Euclidean distance

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**p-median problem -- MIP formulation**

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**Heuristic Methods = Rules of Thumb**

Kuehn & Hamburger (1963) ADD No facilities open initially For each facility not currently used: evaluate the savings in total cost if opened (reduced transportation costs less fixed cost) Add facility that gives maximum (positive) savings DROP All (Selected set of) facilities open initially For each facility currently used: evaluate the savings in total cost if closed (fixed cost less increased transportation costs) Drop facility that gives maximum savings

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**Multi-Facility Multi-Product Location-Allocation Problem**

Find the number and location of the facilities to minimise the total (fixed and variable) costs of moving all products through the logistics network, subject to: available supply at each plant cannot be exceeded for each product demand for all products met throughput of each facility cannot exceed its capacity minimum throughput of a facility must be achieved before it can be opened all products from same customers must be met from one facility.

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**MIP formulation FIGURE 13.5 A small Multiproduct Warehouse Location**

Customer C1 50,000 cwt. $4/cwt. Plant P1 Production = $4/cwt. Capacity = 60,000 cwt. $0/cwt. Handling = $2/cwt. Warehouse W1 $2/cwt. $5/cwt. $3/cwt. Customer C2 100,000 cwt. $1/cwt. $4/cwt. Handling = $1/cwt. Warehouse W2 Plant P2 Production = $4/cwt. Capacity = unrestricted $2/cwt. $2/cwt. $5/cwt. Customer C3 50,000 cwt. Fixed = $100,000 Capacity = 110,000 cwt. Fixed = $500,000 Capacity = unrestricted Product 2 Customer C1 20,000 cwt. $3/cwt. Plant P1 Production = $3/cwt. Capacity = 50,000 cwt. $0/cwt. Handling = $2/cwt. Warehouse W1 $3/cwt. $5/cwt. $2/cwt. Customer C2 30,000 cwt. $2/cwt. $4/cwt. Handling = $1/cwt. Warehouse W2 Plant P2 Production = $2/cwt. Capacity = unrestricted $2/cwt. $3/cwt. $4/cwt. Customer C3 60,000 cwt. FIGURE 13.5 A small Multiproduct Warehouse Location Problem for Mixed Integer Linear Programming

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**Sum of demand for customer l**

Technical Supplement Fixed costs Handling rate Inbound and outbound transport rates Sum of demand for customer l across all products Plant capacity

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**Minimum warehouse throughput**

Customer demand Minimum warehouse throughput Warehouse capacity

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**Relevant Costs for Location Decision**

production/purchase costs warehouse storage and handling warehouse fixed costs cost for carrying inventory stock order and customer ordering costs warehouse inbound and outbound transportation costs Tradeoffs? (Figure 13-8, Ballou)

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Facility Location Selective Evaluation Modified multiple centre-of-gravity to include inventory and fixed costs form clusters of `markets’ find centres of gravity re-assign `markets’ evaluate total costs (including transportation, inventory and fixed costs) Can be used to determine the number of warehouses that best tradeoffs transportation, inventory and fixed costs (See Ballou, p ) Janny Leung

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**Guided Linear Programming**

Relevant costs include both fixed and variable costs Accurate model requires a mixed-integer program Computationally intensive Approximation: distribute the fixed cost over the throughput (unknown until problem solved) Problem then becomes a linear programming which is much easier to solve Allocate fixed costs according to approximate throughput, solve LP, re-adjust fixed cost allocation, re-solve LP, etc. (See Ballou, p )

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Simulation Methods Optimisation models are often “approximation” of “real-world” problems accurate problem description incorporate time-related aspects integrate inventory and geographical concerns only evaluative candidate solutions must be provided no optimality guarantee Sub-optimal solution to accurately described problem

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**Appraisal of Multi-Location Methods**

Mathematical Programming based methods gaining popularity inexpensive and robust decision support tool Extensions: non-linear cost structure discontinuous cost structure integrated inventory and transportation issues revenue effects

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**Other methods Regression analysis Factor rating system**

Analytic Hierarchy Process (AHP) Covering models Game theory Location-allocation models goal programming mixed integer programming

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**Logistics Network (Supply Chain) Planning**

(Multi) product flow from source to demand points number, size and location of production facilities number, size and location of distribution centres assignment of products and customers to DC’s assignment of DC’s to production sites choice of transportation modes inventory policies: frequency of replenishment order size

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**Complexities Spatial and temporal aspects**

Data collection and aggregation Costs allocation and approximation fixed storage (related to inventory levels) handling (related to throughput) transportation cost non-linear inventory-throughput relationship non-linear

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**Integrated Decisions Iterative approach Location**

Transportation (Allocation) Inventory Iterative approach Solve approximations of each problem in sequence Update approximations and iterate

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Facility Location Decisions

Facility Location Decisions

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