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

2. Contents 1.Introduction and Overview 2.Model: Uncapacitated Facility Location Problem and Environment 3.Model: Airline Networks and Environment 4.Transportation Planning and Environment 5.Summary Facility Location Planning and Environment

4. Introduction: Introduction and Overview  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. Hazardous Materials: Introduction and Overview  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. Planning Hazardous Facilities (1): Introduction and Overview  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. Planning Hazardous Facilities (2): Introduction and Overview  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. Planning Hazardous Materials Transport: Introduction and Overview  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. Reservation Sites: Introduction and Overview  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. Oil Spills: Introduction and Overview  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

12. The Uncapacitated Facility Location Problem - discrete location problem (the number of potential sites is finite ). - 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. Model: UFLP and Environment

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

14. 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 Model: UFLP and Environment

15. c 11 c IJ potential facility sitescustomers f1f1 fJfJ b1b1 bibi 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. Model: UFLP and Environment

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

18. 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 Model: UFLP and Environment

19. - 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 Model: UFLP and Environment

20. - 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 is introduced being of one or both sets This leads to a finite set I  K of individuals Model: UFLP and Environment

21. - the objective-function is added by the term - the coefficient a KJ expresses 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 c IJ Model: UFLP and Environment

22. - 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 Model: UFLP and Environment

24. - 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 Model: UFLP and Environment

28. - 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? The UFLP with minimal covering Model: UFLP and Environment

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

32. Facility Location Planning and Environment

33. Airline Networks (1): Model: Airline Networks and Environment  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. Airline Networks (2): Model: Airline Networks and Environment  Example: normal Network  Example: Hub-Network

35. Hub-Location and Environment (1): Model: Airline Networks and Environment  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. Hub-Location and Environment (2): Model: Airline Networks and Environment  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. The Model – Assumptions (1): Model: Airline Networks and Environment  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. The Model – Assumptions (2): Model: Airline Networks and Environment Potential Hubs and train-links: HAM ZRH STR CGN BER MUC BRU VIE FRA AMS PRG Long-Haul Destinations: PAR ORD JNB TYO NYC DEL SIN RIO HUB

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

40. The Model – Assumptions (4): Model: Airline Networks and Environment Notations (1): P i = Population at location i x i =No. of total pax at hub i x L =No. of total pax for long-haul network (fix) x D i =No. of direct pax for long-haul-network at hub i x T i =No. of transfer-pax for long-haul-network at hub i x A i =No. of pax on feeder network (air travel) at hub i x R i =Number of pax on feeder network (railway) at hub i

41. The Model – Assumptions (5): Model: Airline Networks and Environment  Notations (2): f i =Fixed cost for establishing hub at location i m D =Contribution margin per direct pax on long-haul network (average) m T =Contribution margin per transfer pax on long-haul network (average) m A =Contribution margin per air travel-pax on feeder network (average) c i =airport fee per pax at hub i

42. The Model – Assumptions (6): Model: Airline Networks and Environment  Decision variable: z i =1, if hub is established at site i, 0 otherwise  Relations: Airport fee is positively related to no. of population at site i: c i := c i (P i ) = α P i, α > 0 No. of direct pax is positively related to population around the airport: x D i := x D i (P i ) = β P i, β > 0 Direct pax pays more than an tranfer pax:m D > m T Losses on flights within feeder network:m A <0

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

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

45. Example (1): Model: Airline Networks and Environment  Potential hubs i= 1,2,3,4 i=1 (DUS) Train Link i=2 (CGN)i=3 (FRA) i=4 (MUC)  Given: - margin per direct pax (long h.): m D =150 EUR - margin per transfer pax (long h.): m T =120 EUR - margin per air-feeder-pax: m A =- 50 EUR - Total pax for long-haul network: x L =300.000

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

47. Example (3): Model: Airline Networks and Environment  Hub: i= 2 (CGN) i=1 (DUS) i=2 (CGN) i=3 (FRA) Air LinkTrain Link i=4 (MUC) 100.000 60.000 80.000 x A 2 80.000 +x R 2 160.000 =x T 2 240.000 +x D 2 60.000 =x L 300.000 +x A 2 80.000 = x 2 380.000 Long Haul Network 300.000

48. Example (4): Model: Airline Networks and Environment  Hub: i= 2 (CGN) – Calculation of Profit in TEUR: Profit Direct Pax Long Haulm D * x D 2 9.000 +Profit Transfer Pax Long Haul m T * x T 2 28.800 +Profit Feeder Pax Air-Connectionm A * x A 2 - 4.000 +Profit Feeder Pax Railroad0 * x R 2 0 -Cost Airport Feesc 2 * x 2 - 5.700 -Fixed Cost Airport Feesf 2 - 5.000 = Profit Hub at Location 2 (CGN)23.100

49. The Model – Conclusions: Model: Airline Networks and Environment  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

51. Aspects and influences in the field of transport planning - emissions (exhaust gases) of trucks  Co 2 -emissions are one aspect contributing to the change of climate - decision is to be made: which means of transport is considered for the transportation?  are there alternatives for the transportation of shipments? Transportation Planning and Environment

52. - also the shipments carried by a means of transport have to be taken into account  differentiation between harmless and hazardous materials - in a 'normal' transport planning model, the objective is to move products from origins to destinations at minimal costs  these cost apply pricipally to the length of the route Transportation Planning and Environment

53. - what happens in the case of an accidental release of hazardous material?  locating optimal routes for the transport of hazardous material has to deal with risks related to a possible release - the aim is to minimize the exposure to the environment in case of an accident - also new costs emerge  costs of compensation, costs related to the emission of pollutants Transportation Planning and Environment

54. Facility Location Planning and Environment