Location Problems in Supply Chain Management

Transcription

1 Location Problems in SCM Location Problems in Supply Chain Management Stefan Nickel Suppliers Plants Distribution Centers Institute for Operations Research Karlsruhe Institute of Technology (KIT) Customers Contents A Supply Chain Design Problem with facility location, production and transportation activities The real problem: Multi-Period Relocation Problems Heuristic Solution Procedures (Applications and Software) Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Location Problems in SCM Location Problems in SCM Contents Strategic Planning of Supply Chains A Supply Chain Design Problem with facility location, production and transportation activities Strategic planning MIP formulation Numerical results procurement: set of suppliers to select & amount of raw materials to acquire? production: which products to manufacture, where and in which amount? facility location: number, location, capacity of new service facilities to open? Number, location of existing service facilities to keep? transportation: which transportation channels to use to ship products between facilities? customer allocation: which customers to serve by which facility? Suppliers Plants Distribution Centers Customers 3 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 4 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

2 Characteristics of Strategic Planning Facility Location Models in SCM Highly aggregated data High uncertainty in data or even no data Decisions involve the upper management Specialized and well trained users Running time of algorithms is non-critical No classical fixed costs Operational decisions (like make or buy ) should not be modeled Typical features found in the literature Specific network: categorization of facilities into levels, usually maximum 3 levels product flow from one level to the next (e.g. plants DCs customers) strategic decisions focus on facility location and allocation facility location restricted to one or two levels (e.g. locate new DCs; locate new plants and DCs) demand occurs in the lowest level of the network location level typical network structure 5 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 6 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Facility Location Models in SCM Supply Chain Networks Practical needs general network: no echelon structure required, no restriction on the type of facilities product flow allowed between any type of facility and in any direction (e.g. Interdepot transportation, recycling) additional strategic planning possible, e.g. production, procurement no restrictions on the type of facilities to open/close demand can occur in any type of facility general network structure Practical needs Different types of facilities 7 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 8 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

3 Supply Chain Networks Practical needs Different types of facilities Multiple facility layers Supply Chain Networks Practical needs Different types of facilities Multiple facility layers Flow between facilities in the same layer 9 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 0 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Supply Chain Networks Practical needs Different types of facilities Multiple facility layers Flow between facilities in the same layer Direct shipments Location Problems in SCM Contents A Supply Chain Design Problem with facility location, production and transportation activities Strategic planning MIP formulation Numerical results 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

4 A General Supply Chain Design Model A General Supply Chain Design Model non-selectable facility selectable facility decision: operate a selectable facility (y/n)? fixed costs selectable closing opening facilities existing X - potential - X Activities Decision Variables (product p, facility i ) procurement production P P P7 P3 b i,p amount of p bought by facility i h i,p amount of p produced by facility i transportation v i,j,p amount of p shipped from facility i to facility j facility operation capacity expansion unsatisfied demand P4 P8 P9 δ i modelling production processes if selectable facility i operates 0 otherwise x r, y r amount of additional production /handling resource r used z i,p amount of p not delivered to facility i 3 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 4 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Capacity Modelling A Mixed Integer Program resource consumption in production, e.g. equipment, number of working shifts handling of goods, e.g. pallet loader for incoming/outgoing goods in a facility i, ) (, r, p i, r, p resource facility combination one to many same resource used in several facilities one to one many to one resources have limited availability resource extension, e.g. through overtime work additional costs charged ( i, r, p same resource used by all products in a facility different resources used by several products in a facility ) Objective function capacity expansion costs min procurement costs ii p rr ii pp is ji, pp j i i,p i,p ii pp ii pp OC BC EPC i r PDC δ opening costs new facilities i b TC x r i,p i,j,p h rr z production costs v i,p i,j,p is EHC HC i r y i,p r h i,p CC ( δ ) closing costs existing facilities i transportation costs penalty demand costs 5 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 6 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

5 A Mixed Integer Program Constraints I general flow conservation for every product p, in every facility i A Mixed Integer Program Constraints II resource consumption and capacity expansion outbound flow b i transport out of i production of other products demand unsatisfied demand i, p v j,i,p hi,p vi,k,p ai,p,qhi,q di,p zi,p ji ki qp j i k i production resources handling resources ii pp ii r 0 y ji, pp j i r μ i,r,p h λ i,p 0 x PK r, i,r,p HK r PK λ, j,r,p r x, v r i, j,p available capacity λ i,r,p ii pp b i,p HK r y r, r R r R h r R p r R h p procurement transport into i production of p inbound flow 7 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 8 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management A Mixed Integer Program Constraints III activities in selectable facilities b h v v i,p i,p i,j,p i,j,p M M i,p i,p M M δ, δ, i,j,p i,j,p i i δ, δ i j, i S, p P i S, p P i S, j I (j i), p P i I \ S, j S, p P (M: upper bound depending on material requirements & resource availability) integrality and non-negativity conditions bi,p 0,h vi,j,p 0 δ {0,} i i,p 0,0 z i,p d i,p i I,p P i, j I,(i i S procurement production transportation out of a selectable facility i transportation into a selectable facility j j), p P Choosing suitable upper bounds M Taking material requirements into account raw materials P P intermediate products 3 P3 3 P4 final product P5 MD p max. amount of product p required in the network Taking resource availability in each selectable facility into account v M selectable facility i non-selectable v facility i, j, p j M i, j, p i, j, p i, j, p i capacity r in i capacity r in j minmdp,min,min r consumption r consumption 9 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 0 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

6 Location Problems in Supply Chain Management Numerical Tests Contents 7 test problems randomly generated A Supply Chain Design Problem with facility location, production and transportation activities Strategic planning MIP formulation Numerical results structure of distribution network customers 5, 0, 5 product types one-level: 30 selectable DCs (0 existing + 0 potential) two-level: 5 plants, 30 selectable DCs (0 existing + 0 potential) dense transportation network (70-80%) all costs randomly generated (production, transportation, capacity expansion) (uniform dist.) incapacitated & capacitated instances Plants Distribution Centers Customers 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Numerical Results Location Problems in SCM problem type uncap. large cap. medium cap. #var #const root LP CPU root feas. CPU #B&B total CPU gap(%) (sec.) sol gap(%) (sec.) nodes (sec.) min average max min average max min average max Contents A Supply Chain Design Problem with facility location, production and transportation activities The real problem: Multi-Period Relocation Problems Heuristic Solution Procedures (Applications and Software) Problems modeled with ILOG Concert (C++ interface) and solved optimally with CPLEX 7.5 in a Pentium III, 850 MHz, GB RAM 3 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 4 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

7 Supply Chain Networks Dynamic relocation of facilities Practical needs Different types of facilities Multiple facility layers Flow between facilities in the same layer Direct shipments Network redesign Multi-period process... Flexibility! Motivation Facility location Long-term project Melo, Nickel, Saldanha da Gama, 006, COR Robust facilities cope with current and future system conditions Large investment capital financial strain on the company Time-consuming activities new infrastructure, equipment supply, employee training, Gradual setup of new facilities and phase-out of existing facilities Coordination of all operational aspects supply chain activities cannot be disrupted Practical situation: relocation of production facilities, new target markets gradual location / relocation of facilities through capacity shifts 5 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 6 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Model features Model features Facility relocation through capacity shifts (Gradual) capacity transfers from existing to new facilities during the planning horizon (Gradual) capacity transfers from existing to new facilities during the planning horizon Existing Facilities New Facilities Existing Facilities New Facilities total cap. relocation end of period t end of period t+ 7 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 8 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

8 Model features Model features (Gradual) capacity transfers from existing to new facilities during the planning horizon (Gradual) capacity transfers from existing to new facilities during the planning horizon Existing Facilities New Facilities Existing Facilities New Facilities total cap. relocation total cap. relocation no cap. relocation partial cap. relocation partial cap. relocation end of period t+ end of period t+ 9 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 30 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Model features Financial budget Availability of investment capital in each period for opening new facilities, moving capacity and closing existing facilities Model features General Supply Chain Structure Suppliers Plants Distribution Centers Customers existing facilities new facilities t t+ t+ variable capacity moving costs variable capacity moving costs, fixed closing costs t t+ t+ fixed opening costs variable capacity moving costs variable capacity moving costs no shutdown at the end of last period first operation period is 3 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 3 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

9 Model features not restricted to an echelon structure shipping lanes in any direction, e.g. inter-facility transportation, reverse logistics fixed facility, e.g. plant fixed facility, e.g. customer existing facility new facility commodity flow capacity transfers Model features Additional Aspects Available budget per period: use non-invested capital in previous periods subject to interest rate External supply of products through procurement / production (supply nodes) Facilities with limited capacity Min. throughput at facilities Inventory opportunities for goods in each period (availability of stocks at the beginning of the planning horizon) 33 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 34 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Dynamic relocation of facilities Decisions Supply Amount of product p purchased by facility i in period t? Transportation Amount of product p shipped from facility i to facility j in period t? Inventory Amount of product p held in stock in facility i at the end of period t? Facility operation Should facility i be operated in period t? Relocation Amount of capacity to shift from the existing facility i to a new facility j at the beginning of period t? Capital investment Capital available at the end of period t? Dynamic relocation of facilities Model Objective function Minimize total costs external supply, transportation, inventory holding costs fixed facility operating costs Constraints general conservation of flow per facility, product, period feasible capacity transfers from existing to new facilities capacity limits per facility, period min. throughput per facility, period open / close a facility at most once during planning horizon budget limitations for investments on opening & closing facilities and capacity shifts per period Large MIP model NP-hard: reduction to dynamic model of Van Roy & Erlenkotter (MS, 98) 35 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 36 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

10 Location Problems in SCM Contents A Supply Chain Design Problem with facility location, production and transportation activities The real problem: Multi-Period Relocation Problems Heuristic Solution Procedures (Applications and Software) The facilities modeled in the supply chain do not necessarily have to be part of the own organization. E.g. external supplier. Notation L Set of all facilities S S o Set of all selectable facilities Set of all selectable facilities, which could be opened S c Set of all selectable facilities, which could be closed S = S o S c. Set of all products Set of all time periods 37 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 38 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Location decisions Open Close OC t l CC t l Opening Costs for the facility l S o at the beginning of period t and for its operation for the rest of the planning period Costs for closure of the facility l S c at the end of period t and their operation until then. Demand Facilities can have demand for products. Forecast future demands. If the forecasts are not exact enough, then consider the problem several times for different scenarios of demand trends pessimistic (worst-case) normal (average-case) optimistic Notation D t l,p Demand in quantity units for product p at facility l in period t /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 40 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

11 Satisfaction of customer demands It may be that the demand can/shall not be (completely) satisfied. Example: Costs for the satisfaction of demand is too high (compared to profit) Supply within the given service time is not possible, or just with very high efforts Capacities are not sufficient Unsatisfied demand incurs penalty costs. However, they are difficult to quantify. Possibility: lost profits, service level which has to be satisfied z t l,p PDC t l,p Number of quantity units of demand at facility l for product p in period t, which were not delivered. Penalty costs per quantity unit of product p, which were not delivered to facility l in period t to satisfy the demand. Procurement Facilities can buy products from external, i.e. from external suppliers. Example: raw material or semi-finished goods, which cannot be produced at their own facilities products, that are cheaper to buy than to produce them (Out-Sourcing) Notation b t l,p Amount of product p, which is procured at facility l in period t. BC t l,p Costs for procurement of one unit of product p at facility l in period t. 4 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 4 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Production Manufacturing of finished goods from different inputs. Example: classical manufacturing of finished goods in factories from raw material and intermediate goods packaging or picking products in distribution centers. E.g. drill machine from factory A with boring head from factory B packed together. Manufacturing processes are specified by bills of materials. Example: Intermediate product Z is manufactured by raw material R and R. The numbers on the arcs indicate the related material consumption factors. The production of one unit of Z needs and.5 R units of raw materials Z and Z, respectively Z.5 R Simplify multi-stage lists of material to single-stage ones. R Notation 3 Z P R Z.5 R 3 a l,p,q Number of units of product q, needed to manufacture one unit of product p in facility l. h t l,p Amount of product p, produced in facility l in period t. HC t l,p Costs for manufacturing one unit of product p in facility l in period t. Includes costs for material, machine utilization,. P R R R /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 44 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

12 Storage Products (raw material, intermediate products, finished goods) can be d in facilities from one period to the next. Notation inv t l,p Amount of product p d at facility l in period t. IC t l,p Costs for storing one unit of product p at facility l in period t. Include costs for inventory, stock ground, Distribution Transportation links between all facilities possible. Notation x t l,l,p Amount of product p transported from facility l to l in period t. TC t l,l,p Transportation costs for one unit of product p from facility l to l in period t. The transportation costs depend on the distance, but also on the product and the means of transportation. Include often costs for goods issue (e.g. order picking, shipment) at the starting facility and for incoming goods (warehousing) at the destination facility. Sometimes costs for storage (within a period) at the starting location, too /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 46 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Capacities Displayed via resources. Example: machine, stockyard storage, order picking system staff, shift Resources characterized by Base capacity (e.g. production capacity of a machine, maximal throughput of the picking system per period). Consumption factor states for each product the consumption of resources in resource units per quantity unit of a product. Expansible capacity of the resource (e.g. overtime, leasable storage or production capacity). Penalty costs per unit, that extend (overload) the base capacity. Relations between facilities and resources one to many The same resource can be used on several facilities. Example: executive producer, which is responsible for several production lines one to one The same resource is used by all products of one facility. Example: flexible configurable machine many to one Several resources attached in the same facility. Example: facilities correspond to production lines and resources to executive producers Consider resources for production and incoming goods and goods issue (handling) 47 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 48 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

13 Notation R p R h μ l,r,p Set of production resources Set of handling resources Consumption factor of production resource r R p per unit of product p at facility l. λ i l,r,p, Consumption factor of production resource r R h per λ o l,r,p unit of product p at goods receipt respectively issue atfacility l. v t r Number of units, the resource r R p R h has been extended in period t. RK t r Base capacity of resource r R p R h in period t. ERK t r RC t r Maximally allowed extension of the capacity of the resource r R p R h in period t. Penalty costs per extended resource unit of resource r R p R h in period t. Mixed integer linear program Objective function procurement and production distribution resource extension unsatisfied demand inventory costs location decisions 49 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 50 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Constraints Flow conservation incoming transports procurement production inventory last period incoming goods outgoing goods Resources Production Handling outgoing transports consumption to production inventory this period demand unsatisfied demand Incoming goods and goods issue, respectively, by transports Feasibility of extension goods issue by procurement 5 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 5 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

14 Location decisions Selectable facilities can be opened and closed, respectively, only once and Production Inventory Define Outgoing distribution Activities at selectable facilities Procurement Incoming distribution 53 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 54 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Integer and non-negativity constraints Example 0 periods 0 products 5 plants 50 customers existing facilities: 0 DCs Plants new facilities: 0 potential sites for DCs 0 70 constraints non-negative variables (dense network) 70 binary variables status of facilities Distribution Centers Customers 55 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 56 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

15 Numerical tests Numerical tests Class Class Class 3 DCs Customers Plants DCs Customers Plants Central DCs Regional DCs Customers 57 Periods: 3, 4, 5, 6 Products: 5, 0, 5 Customers: 50, 75 DCs: 0 existing location level 0 new Periods: 4 Products: 5, 0 Plants: 5 Customers: 50, 75, 00, 50 DCs: 0 existing 0 new Periods: 3, 4, 5 Products: 5 Plants: 5 Customers: 50, 75 DCs: 0 existing new location level 95 randomly generated problems solved optimally with CPLEX 7. (Pentium III, 850 MHz, GB RAM) 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 58 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Numerical tests Impact of budget constraints 700 Numerical tests Facility relocation vs pure open / close facilities average CPU (s) with budget const. no budget const. average CPU (s) with relocation only open/close Class Class Class 3 0 Class Class Class /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 60 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

16 Numerical tests Facility relocation vs pure open / close facilities & no budget constraints average CPU (s) with relocation open/close, no budget Location Problems in SCM Contents A Supply Chain Design Problem with facility location, production and transportation activities The real problem: Multi-Period Relocation Problems Heuristic Solution Procedures (Applications and Software) 00 0 Class Class Class /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 6 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Problem characteristics Heuristics Approach Two types of decision variables: existing facility new facilities Non-negative continuous capacity transfers, transportation, inventory, investments Binary Status change of a facility in a period periods for given status matrix the resulting problem is a LP! LP-based heuristic Phase : (Fast) Construction All status variables are fixed to 0 or Phase : Repair / Improvement Some fixing decisions made in phase are changed 0 no status change status change open closed 63 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 64 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

17 Heuristics Approach Heuristics Approach Phase : Construction Rounding Variable Fixing Feasible solution with good quality STOPP Feasible solution with bad quality Infeasible solution Phase : Construction Rounding Variable Fixing Phase : Repair / Improvement 4 Strategies for variable fixing: S Use lower threshold Fixing variables to 0 S Select an existing facility 0 Fixing variables to S3 Use upper threshold S4 Select a potential facility 65 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 66 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Heuristics approach Heuristics approach Phase : Construction Start by solving LP-relaxation considering all facility status variables in [0,] Phase : Construction Variable fixing strategy = (facility, period) 67 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 68 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

18 Heuristics approach Heuristics approach Phase : Construction Solve LP considering all non-fixed facility status variables in [0,] Phase : Construction Variable fixing strategy /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 70 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Heuristics approach Heuristics approach Phase : Construction Solve LP considering all non-fixed facility status variables in [0,] Phase : Construction Variable fixing strategy /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 7 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

19 Heuristics approach Heuristics approach Phase : Construction Variable fixing strategy 4 Phase : Repair / Improvement One or more variables are randomly selected to change from to 0 One or more variables are randomly selected to change from 0 to 73 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 74 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Heuristics approach Heuristic approach Phase : Repair / Improvement Tuning the heuristic: Phase : How many variables should be fixed to 0 before a variable is fixed to? Values for the upper & lower thresholds: should they change during the procedure? Phase : How to choose variables for repair / improvement? Phases & : Many degrees of freedom! A set of preliminary computational experiments were performed 75 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 76 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

20 Computational experience Computational Experience DCs customers plants DCs customers plants central DCs regional DCs customers 5 randomly generated instances: Periods: 3, 4, 5, 6, 8 Products: 5, 0, 5, 0, 50 Plants:, 5 Customers: 50, 75, 00, 50, 00 Set 45 instances Set 5 instances Set 3 45 instances Existing New Relocation Central DCs 4, 8, 0 8,, 0 Levels Regional DCs 0, 0 0, 30 From Melo, Nickel and Saldanha-da-Gama (006) Newly generated instances Continuous variables: Binary variables: Constraints: /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 78 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Computational experience Heuristic Phase Phase Computational experience Phase Heuristic Phase 00% 90% 80% 70% 7 Feasible bad quality solutions % 90% 80% 70% 7 Feasible bad quality solutions 34 No solution improvement 0 60% 50% 40% 30% 0% Feasible good quality solutions Non-feasible solutions 54 Feasible solutions 60% 50% 40% 30% 0% Feasible good quality solutions Non-feasible solutions 54 7 Improved solutions 0% 0% 0% 0% 79 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 80 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

21 Computational experience cpu heuristic / cpu CPLEX Execution time and solution quality 0 Instances UB heuristic / UB CPLEX CPLEX used as a heuristic (% gap or time limit 5h) Computational experience cpu heuristic / cpu CPLEX Execution time and solution quality UB heuristic / UB CPLEX Heuristic: - solution quality as good as CPLEX - much less cpu time than CPLEX 8 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 8 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Further Model Enhancements Solution Approach for a special Multiperiod Case Include uncertainties Stochastic Programming Include Nonlinearities Location-Routing (from a location perspective) Lagrangian Relaxation Assumptions Two-echelon structure inventory is allowed in the warehouses location decisions are final: if a facility is opened/closed once it can never be closed/reopened again Constraints on the minimum number of open facilities at the beginning and the end of the planning horizon Relax the demand satisfaction and the flow conservation between the planning periods /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 84 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

22 Lagrangian Relaxation Solution Approach for a special Multiperiod Case Problem Types Determined Values Reference: Hinojosa, Kalcsics, Nickel, Puerto, Velten, 008, COR 85 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 86 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Solution Approach for a special Multiperiod Case Solution Approach for a special Multiperiod Case Summary of Computational Results (Average over 5 Instances / Problem Type and Time Periods) Summary of Computational Results 6 5 H-Gap 4 3 T=4 T=5 T=8 0 P P P3 P /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 88 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

23 Solution Approach for a special Multiperiod Case Solution Approach for a special Multiperiod Case Summary of Computational Results Summary of Computational Results,4, E-Gap CPU-E ,8 0,6 T=4 T=5 T= T=4 T=5 T=8 0, , P P P3 P4 0 P P P3 P /3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 90 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Solution Approach for a special Multiperiod Case Solution Approach for a special Multiperiod Case Summary of Computational Results Summary of Computational Results CPU-H N T=4 T=5 T= T=4 T=5 T= P P P3 P4 0 P P P3 P4 9 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 9 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

24 Location Problems in SCM Contents A Supply Chain Design Problem with facility location, production and transportation activities The real problem: Dynamic Relocation Problems Heuristic Solution Procedures Applications and Software Take Over Scenario in the Steel Industry Problem Description Nickel, Velten, Weimerskirch, 005 and 007 Steel company is a merger of 3 huge steel companies Multiple synergy effects are expected World leader in steel production p.a. but less than 5 % market share no monopoly Entering new markets is an ultimate strategic objective Possibility to take over another steel company Where and when should capacity be shifted? Which facilities should be opened and closed, respectively? How should the capacity be shifted from existing facilities to new ones without interrupting the supply chain activities or without breaking the budget and capacity restrictions? Is it profitable to take over the foreign company in order to use its additional capacities and to include its supply chain? 93 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 94 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Take Over Scenario in the Steel Industry Supply Chain Steel company SC: 63 operating facilities Potential new facilities: 3 locations Take over candidate SC: 3 operating facilities Analytical Approach for WEEE Network Design Problem Description Nickel, Velten, Verter, Weimerskirch, 008 WEEE Directive (Waste Electrical and Electronic Equipment) is setting collection, recycling and recovery targets for all types of electrical goods Existing infrastructure incorporating collection points, inspection and recycling facilities needs to be redesigned The responsibility of the WEEE is imposed on the producers The municipalities are responsible for the drop off centers Do we need more or less, bigger or smaller inspection centers? Is it economically reasonable to operate a demanufacturing facility? Where and when should capacity be shifted? Which facilities should be opened and closed, respectively? 95 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 96 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

25 Analytical Approach for WEEE Network Design Location Planning for Petrol Stations Min. objective function (disposal / treatment + collecting + inventory + operating costs) Constraints categories: a)flow conservation e) econ. reasonable minimum throughput b) quotas for secondary markets f) facility location c) capacity relocation g) budget restrictions d) capacity restriction h) non-negativity and integrality Drop-Off Centers Demanufacturing Center Inspection Centers Recycler/ Disposal Secondary Markets Consideration of Geo-Data Questions Which data may support location planning and how can we integrate these data in existing location models? Which geographic and demographic data are usually available? Where can we get these data from? How can we govern the huge amount of geographic and demographic data? Horstmann, Nickel, van Bonn, Ziegler 007 For how far into the past do we need the data and how far into the future is our location planning reliable? 97 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 98 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management Location Planning for Petrol Stations Location Planning for Petrol Stations Advantages Some geographic and demographic data are widely available, all over the world. These data provide a wider data base, if the classical database is unsatisfyingly. They allow better forecasts of the expected trends, since they were elevated and safed for years. The additional information may help the user to come to more reliable and safer decisions. Classical database Running charges Costs for opening or closing stations Geographic and demographic data Position of crossroads Number of vehicles Length of streets Position of existing gas stations Location Model for Petrol Stations Average gas consumption 99 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 00 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management

26 Case Study - Gas Stations Before Optimization After Optimization References T. Bender, H. Hennes, J. Kalcsics, T. Melo and S. Nickel, Location Software and Interface with GIS and Supply Chain Management, Facility Location: Applications and Theory, Springer, (00). S. Nickel, S. Velten, G. Weimerskirch, Strategische Supply-Chain Entscheidungen in der Stahlindustrie - Eine Fallstudie, in H.O. Günther, D. C. Mattfeld and L. Suhl (editors): Supply Chain Management and Logistik, Physica- Verlag (005). M.T. Melo, S. Nickel and F. Saldanha da Gama, Dynamic multi-commodity capacitated facility location: A mathematical modeling framework for strategic supply chain planning, Computers and Operations Research 33: 8-08 (006). Y. Hinojosa, J. Kalcsics, S. Nickel, J. Puerto and S. Velten, Dynamic Supply Chain Design with Inventory, Computers and Operations Research 35: (008). M.T. Melo, S. Nickel and F. Saldanha da Gama, Facility Location and Supply Chain Management A Review, European Journal of Operational Research 96:40-4 (009). 0 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management 0 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management ANT E D 03 05/3/00 Professor Dr. Stefan Nickel - Location Problems in Supply Chain Management