Topic No. 9 Facility Location Planning and Environment Thorsten Noss Ulrich Lindner

1. Facility Location Planning Topic No. 9 Facility Location Planning and Environment Thorsten Noss Ulrich Lindner

2. Facility Location Planning and Environment • Contents • Introduction and Overview • Model: Uncapacitated Facility Location Problem and Environment • Model: Airline Networks and Environment • Transportation Planning and Environment • Summary

3. Facility Location Planning and Environment • Introduction and Overview • Model: Uncapacitated Facility Location Problem and Environment • Model: Airline Networks and Environment • Transportation Planning and Environment • Summary

4. Introduction and Overview Introduction: • Only a small proportion of the location literature deals with environmental problems • Environmental problems often include uncertainty • Complexity • Multi-objective models • Not only minimization of cost

5. Introduction and Overview Hazardous Materials: • Hazardous materials ... • include toxic ingredients (explosives,radioactive materials) • require special treatment • include a considerable risk for accidents • can cause significant damage to humans and environment • Multitude of objectives • asymmetrically distributed risks • equity as an objective • different viewpoints and priorities of stakeholders

6. Introduction and Overview Planning Hazardous Facilities (1): • Hazardous facilities • Nuclear power plants • disposal sites • chemical processing plants • Single objective models • focus on distance between facility and population centers • maximization of the sum of distances • maximization of minimum distance

7. Introduction and Overview Planning Hazardous Facilities (2): • Multi objective models • minimization of costs • minimization of public opposition against facility • minimization of risks • maximization of equity • models can include new ways of technology • tradeoffs between objectives

8. Introduction and Overview Planning Hazardous Materials Transport: • Transport mode and vehicle selection problems • solved with risk assessment studies • no best mode for all settings • Route planning problems • minimization of risks, lenghts, costs etc • again multi-objective problems • Integrated models • include location and transport problems • e.g. management of hazardous waste

9. Introduction and Overview Reservation Sites: • Selection of natural area reserves • 1980s: - Simple scoring and ranking procedures • - highest ranked site not always the best • 1990s: - Integer optimization models • - based on formulations from location science • - identify and evaluate entire sets of sites • - include uncertainty • - not always possible to predict species occurrence

10. Introduction and Overview Oil Spills: • Locating capability to respond to disasters / oil spills • Problem of locating levels and types of cleanup capability • Allocation problem (points of high spill potential) • Occurrence of oil spills is uncertain (place, time) • Large variability in volumes of these spills • Different cleanup technologies • Efficiency of the equipment • Costs of damage to the environment

11. Facility Location Planning and Environment • Introduction and Overview • Model: Uncapacitated Faclity Location Problem and Environment • Model: Airline Networks and Environment • Transportation Planning and Environment • Summary

12. Model: UFLP and Environment The Uncapacitated Facility Location Problem - discrete location problem (the number of potential sites isfinite). - related to the field of networks. - a set of nodes is considered, which are connected to each other. - the nodes represent given locations of customers on the one hand, on the other hand potential facility sites.

13. Model: UFLP and Environment - the sets of nodes share no elements underneath the other. - the transportation costs of supplying customer i (i  I) with a demand of bn units with shipments from an established facility at a potential site j (j  J) are cIJ money-units. - If a facility is located at a potential site (j  J), fixed costs of fj units (measured in terms of money) arise.

14. Model: UFLP and Environment Assumptions of the model: - every located facility is of unlimited capacity - the customer demand can be satisfied by any potentially established facility Single-assignment property: Existence of an optimal solution in which no customer is serviced by more than one faciltiy Decision variables are of binary type, only able to take on values 0 or 1

15. Model: UFLP and Environment Type of Problem: How many facilities have to be established and where should they be located, when by satisfying total customer demand the summation of fixed and transportation costs are to be minimised. c11 f1 b1 potential facility sites customers fJ bi cIJ

16. Model: UFLP and Environment Decision Variables Other constituents of the model: fJ is recognised as fixed cost for locating facility j, for all j  J cIJ represent transportation cost to supply customer i with shipments for each pair of (i,j)

17. Model: UFLP and Environment

18. Model: UFLP and Environment An extension of the model: The UFLP with additive noxious effects - the terms obnoxious and noxious describe detrimental effects caused by operations of a facility - a differentiation of objectives is made in 'pull' and 'push' objectives pull-objectives apply to the attractiveness of a facility push- objectives to their undesirable counterpart

19. Model: UFLP and Environment -the undesirable part of a facility will be expressed in a set of K subjects, which push the facilities away from, for example population centers. - these subjects are affected negatively by the work of a facility Negative effects could be noise, heat, unpleasant odours, pollution of air and water etc. -to express beside attractions also possible repulsions of a facilitiy`s activities, the term ‘semi-obnoxious‘ is introduced

20. Model: UFLP and Environment -semi-obnoxious facilities can have an attraction as well as a repulsion to both the customers I and the subjects K - the set of customers and subjects are not disjoint and may coincidide Therefore the term individual isintroduced being of one or both sets This leads to a finite set I K of individuals

21. Model: UFLP and Environment -the objective-function is added by the term -the coefficient aKJexpresses the (ob)noxious effect on an individual caused by a facility It is a nonnegative number equaling zero if the negative effect is below a certain distance - for additive reasons, it is measured in units of money, to become compatible to the transportation costs cIJ

22. Model: UFLP and Environment - the push-pull version of the UFLP assumes that each individual is affected by each facility and that these effects are expressed as costs - also the assumptions of the UFLP in its original form continue to exist

23. Model: UFLP and Environment

24. Model: UFLP and Environment -It is possible to include the (ob)noxious effect of facility j in the fixed costs of this facility Defining leads to the objective-function in its original form

25. Model: UFLP and Environment

26. Model: UFLP and Environment

27. Model: UFLP and Environment

28. Model: UFLP and Environment The UFLP with minimal covering - the previous version of the UFLP assumes that the (ob)noxious effects are additive - perhaps costs arising from polluting facilities are constant? - this leads to the question if this assumption is reasonable - do the negative effects depend on the number of facilities located closely to a subject (individual), or more on the fact whether a facility is sufficiently close to affect an individual?

29. Model: UFLP and Environment

30. Model: UFLP and Environment -the new binary variable zkexpresses whether individual/subject k is affected by any facility - the coefficient ak denotes the costs of the concerned subject - the set Ck includes all facilities located close enough to affect subject k If a facility j  Ckis located, zk takes on the value 1 and ak is included to the objective If xJ equals 0 for all j  Ck, the constraint is redundant

31. Model: UFLP and Environment

32. Facility Location Planning and Environment • Introduction and Overview • Model: Uncapacitated Facility Location Problem and Environment • Model: Airline Networks and Environment • Transportation Planning and Environment • Summary

33. Model: Airline Networks and Environment Airline Networks (1): • International Airlines (Global Player) • Extensive network • Destinations all over the world • Hub-and-spoke system • Extension of some airports to big hubs • Reduction of non-profitable point-to-point connections • More transfer-connections • Higher load factors • Lower unit cost

34. Model: Airline Networks and Environment Airline Networks (2): • Example: normal Network • Example: Hub-Network

35. Model: Airline Networks and Environment Hub-Location and Environment (1): • Trade-Off for the Airline: • Environmental aspect: • Maximize distance between hub and population center • Reduction of negative impacts on population (noise etc) • Lower airport fees • Economical aspect: • Minimize distance between hub and population center • More direct passengers, who pay more for a ticket • Higher airport fees

36. Model: Airline Networks and Environment Hub-Location and Environment (2): • Distance between Hub and other Cities: • On routes to destinations which are relatively close to the hub it is hardly possible for an airline to operate these routes profitabily (e.g. FRA-CGN, FRA-STR) • Introduction of high-speed railroad links: • Increasing profits for the airline • Better for the environment

37. Model: Airline Networks and Environment The Model – Assumptions (1): • Assumptions: • Airline with a big network: - long-haul network • - feeder network • Amount of pax for long-haul network is fixed • Set of potential hub-locations within an area (country) • Airline has to decide where to locate its hub • Dependig on chosen location airline has to operate feeder-connections to other locations to transport pax to hub • When rail-link exists, no air-connection is necessary

38. Model: Airline Networks and Environment The Model – Assumptions (2): Potential Hubs and train-links: Long-Haul Destinations: HAM BER TYO AMS ORD CGN BRU HUB DEL FRA NYC PRG STR SIN VIE PAR MUC RIO ZRH JNB

39. Model: Airline Networks and Environment The Model – Assumptions (3): Hub FRA: train-and air-links: Long-Haul Destinations: HAM CGN BER TYO AMS ORD BRU FRA FRA DEL NYC PRG SIN PAR STR VIE MUC RIO ZRH JNB Train Link Air Link

40. Model: Airline Networks and Environment The Model – Assumptions (4): • Notations (1): • Pi = Population at location i • xi = No. of total pax at hub i • xL = No. of total pax for long-haul network (fix) • xDi = No. of direct pax for long-haul-network at hub i • xTi = No. of transfer-pax for long-haul-network at hub i • xAi = No. of pax on feeder network (air travel) at hub i • xRi = Number of pax on feeder network (railway) at hub i

41. Model: Airline Networks and Environment The Model – Assumptions (5): • Notations (2): • fi= Fixed cost for establishing hub at location i • mD = Contribution margin per direct pax on long-haul network (average) • mT = Contribution margin per transfer pax on long-haul network (average) • mA = Contribution margin per air travel-pax on feeder network (average) • ci = airport fee per pax at hub i

42. Model: Airline Networks and Environment The Model – Assumptions (6): • Decision variable: • zi = 1, if hub is established at site i, 0 otherwise • Relations: • Airport fee is positively related to no. of population at site i: • ci := ci (Pi) = α Pi, α > 0 • No. of direct pax is positively related to population around the airport: • xDi := xDi (Pi) = β Pi , β > 0 • Direct pax pays more than an tranfer pax: mD> mT • Losses on flights within feeder network: mA <0

43. Model: Airline Networks and Environment The Model (1): subject to: 1. 2. 3.

44. Model: Airline Networks and Environment The Model (2): 4. 5. 6. 7. 8. 9.

45. Model: Airline Networks and Environment Example (1): • Potential hubs i= 1,2,3,4 • Given: - margin per direct pax (long h.): mD = 150 EUR - margin per transfer pax (long h.): mT = 120 EUR - margin per air-feeder-pax: mA = - 50 EUR - Total pax for long-haul network: xL = 300.000 i=1 (DUS) i=2 (CGN) i=3 (FRA) i=4 (MUC) Train Link

46. Model: Airline Networks and Environment Example (2):

47. Model: Airline Networks and Environment Example (3): i=1 (DUS) • Hub: i= 2 (CGN) 100.000 i=2 (CGN) xA2 80.000 + xR2 160.000 = xT2 240.000 + xD2 60.000 = xL 300.000 + xA2 80.000 = x2 380.000 Long Haul Network i=3 (FRA) 60.000 300.000 80.000 i=4 (MUC) Train Link Air Link

48. Model: Airline Networks and Environment Example (4): • Hub: i= 2 (CGN) – Calculation of Profit in TEUR: Profit Direct Pax Long Haul mD * xD2 9.000 + Profit Transfer Pax Long Haul mT * xT2 28.800 + Profit Feeder Pax Air-Connection mA * xA2 - 4.000 + Profit Feeder Pax Railroad 0 * xR2 0 - Cost Airport Fees c2 * x2 - 5.700 - Fixed Cost Airport Fees f2 - 5.000 = Profit Hub at Location 2 (CGN) 23.100

49. Model: Airline Networks and Environment The Model – Conclusions: • The model optimizes both objectives: • Maximization of profits for the airline • Minimization of negative effects on population & evironment • Possible modifiations to the model: • Include distances between potential hubs • Possibility to allow new railroad-links to be established • Include public opposition against the growth of an airport as an uncertainty parameter •  higher costs or capacity cap

50. Facility Location Planning and Environment • Introduction and Overview • Model: Uncapacitated Facility Location Problem and Environment • Model: Airline Networks and Environment • Transportation Planning and Environment • Summary