Facility Location

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

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

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

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

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

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

Centre of Gravity Method • Grid method • centroid method Locate facility at:

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

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?

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.

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

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

p-median problem --MIP formulation

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

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.

MIP formulation Product 1 Customer C1 50,000 cwt. $4/cwt. $0/cwt. Handling = $2/cwt. Warehouse W1 Plant P1 Production = $4/cwt. Capacity = 60,000 cwt. $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 $5/cwt. $2/cwt. $2/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. $0/cwt. Handling = $2/cwt. Warehouse W1 Plant P1 Production = $3/cwt. Capacity = 50,000 cwt. $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 $4/cwt. $2/cwt. $3/cwt. Customer C3 60,000 cwt. FIGURE 13.5 A small Multiproduct Warehouse Location Problem for Mixed Integer Linear Programming

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

Customer demand Minimum warehouse throughput Warehouse capacity

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)

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. 506-507)

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. 508-510 )

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

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

Other methods • Regression analysis • Factor rating system • Analytic Hierarchy Process (AHP) • Covering models • Game theory • Location-allocation models • goal programming • mixed integer programming

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

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

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

Facility Location