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Process and Facility Planning for Mobile Phone Remanufacturing
Process and Facility Planning for Mobile Phone Remanufacturing G. Seliger ( I ) , C. Franke, M. Ciupek, B. Bagdere Institute for Machine Tools and Factory Management, Technical University Berlin, Dept. of Assembly Technology and Factory Management, Berlin, Germany.
Abstract Successful remanufacturing of electric and electronic products must meet the challenges of continuously falling prices for new products, short life cycles, disassembly of unfriendly designs and prohibiting costs in high-wage countries. Mobile phones are identified as suitable products for profitable remanufacturing. A generic remanufacturing plan for mobile phones is developed. For the planning of remanufacturing capacities and production programs a linear optimization model is introduced. In order to analyze the performance of the remanufacturing facilities under consideration of uncertainties regarding quantity and conditions of mobile phones, reliability of capacities, processing times, and demand, discrete-event simulation is applied. The simulation model is generated by an algorithm using results from the linear optimization approach. The introduced method allows the continuous adaptation of remanufacturing facilities under quickly changing product, process, and market constraints. Keywords: Mobile phone remanufacturing, linear optimization, discrete-event simulation
1 INTRODUCTION Today, the remanufacturing of expensive, long living investment goods, e.g. machine tools, jet fans, military equipment or automobile engines, is extended to a large number of consumer goods with short life cycles and relatively low values. Reuse is an alternative to material recycling to comply with recovery rates and quantities as well as special treatment requirements as prescribed by European legislation with the directive on Waste of Electrical and Electronic Equipment (WEEE) [ I ] . Market studies regarding offer and demand for mobile phones with GSM standard [2] show the worldwide potential for mobile phone remanufacturing. The studies revealed that with a total quantity of over 200 Mio. unutilized mobile phones, Europe can serve as a supply market whereas demand markets can be found in Asia and Latin America, e.g. China and Brasil where market penetration is as low as 20% and - in the case of Brasil where the old TDMA mobile communication standard is replaced by the GSM standard. By means of low cost remanufactured phones, one cannot only serve communication demands of lower income classes in those regions, but it is possible to recycle phones complying with WEEE requirements and thus provide services for OEMs within the scope of the directive. In order to evolve mobile phone remanufacturing into a profitable business segment, it is necessary to provide remanufacturers with efficient planning methods and tools, capable to deal with the special procurement, remanufacturing and distribution processes. The tools and methods should allow to determine the cost minimal adaptation of remanufacturing facilities under consideration of the fast changing product, process and market situation. The most frequently changing input parameters are the type and quantity of mobile phones offered at the market. In Western Europe, with the average replacement cycle of phones being less than 18 months and more than 100 new phone models every year it is feasible to assume that the remanufacturing program
requires adaptation several times during a year. In this paper, an approach is presented to support the remanufacturing program planning under the above stated framework. The remanufacturing program and required capacities are determined by means of combinatorial optimization. Based on the results, the planner is enabled to adapt and evaluate the existing remanufacturing facility using discrete-event simulation.
2
CONSTRAINTS FOR PLANNING OF MOBILE PHONE REMANUFACTURING In the following, the process chain of mobile phone remanufacturing is analyzed to identify aspects that need to be considered in the planning of a remanufacturing facility. The procurement of phones can be realized in cooperation with OEMs, e.g. by acquisition of overproduction, or in cooperation with net providers, supermarkets or other private and public organizations who have frequent and close contact to phone users, in so-called take backs. Experience has shown, that consumers are willing to either turn in their used phones as a charitable donation or trade them in for benefits such as free phone minutes [3]. After the take back, phones need to be separated, e.g. from chargers or earphones, and identified. Experience of remanufacturers shows that about 70 percent of phones recovered in Europe and the USA are considered beyond economic reuse, i.e. that either remanufacturing costs are to high or demand is too low for these phones, and they are consequently sent to material recycling. The remaining phones need to be tested to determine optical or functional faults that can be ascribed to the main elements housing, printed circuit board (PCB), display, microphone and speaker. The combination of faults results in different process times for disassembly and reassembly [3,4]. Replacement components are supplied either by external procurement or internal retrieval of components from used phones.
Experience of mobile phone remanufacturing in the USA has shown, that customers are willing to remunerate value adding upgrades of phones, e.g. software update or surface treatment by polishing. Offering different quality classes for the same phone model is an approach to meet the market demand. Customers show more flexibility in accepting alternative phone models as substitutes, as long as they offer comparable features, such as software updates. A more elastic demand for mobile phones simplifies the handling of the high variability on the phone procurement side. Future demand could also come from OEMs or independent service entities procuring retrieved phone components to cope with post production supply, i.e. the supply of spare parts to customers and service networks beyond the time of the production of the product. Recovering components could help to reduce warehousing of large quantities of spare parts over long periods of time, respectively to reduce the extend of the continuing production of spare parts.
3 GENERIC REMANUFACTURING PROCESS CHAIN To enable meeting a cost efficient treatment decision for each phone, a generic remanufacturing process was modeled (figure 1). Options for phone utilization are reuse, components retrieval and material recycling. In case of reuse, three different quality classes are differentiated, according to the extent of remanufacturing. Upon arrival phones are separated from accessories and identified. Accessories, e.g. chargers or earphones, are identified and tested to assign them to reuse or recycling. Following identification, phones can be sent directly to recycling or can be tested. Faultless mobile phones are assigned to either reuse (ReMobile Class 1) or software update. Updated phones can be assigned to either reuse (ReMobile Class 2) or polishing (ReMobile Class 3). Defective phones are assigned to alternatively manual or automated disassembly, cleaning and reassembly. Hereafter, phones can undergo additional value adding processes, i.e. software update or polishing, or be sent directly to reuse. When deciding which phones are to be assigned to which process, certain constraints, e.g. the availability of, and demand for phones and components, the condition of available phones or the cost for and number of remanufacturing resources need to be considered. The problem of assigning each phone to a cost optimal treatment belongs to the class of combinatorial optimization. Combinatorial optimization deals with models and methods to find the best solution for problems with discrete choices, and is well established in disassembly planning [5]. In the described problem the discrete choices are related to the discrete amount of required capacities for remanufacturing processes and the discrete number of mobile phones which are assigned to every remanufacturing process.
4
MODEL FOR CAPACITY AND PROGRAM PLANNING Based on the generic remanufacturing process, a mathematical model was developed to determine the required process capacities for identification, testing, manual or automated disassembly, reassembly, software update, and polishing for a given number of offered and demanded mobile phones. Available product, process and market data are considered regarding product structure and condition of used phones, operating times for remanufacturing processes, capacities of resources, offer for used phones and demand and revenues for sold phones and components as well as costs for assigned process capacities.
Figure 1 represents all assignment options for products, and all types of remanufacturing resources considered in this model. For example, the decision variable HT, describes the quantity of the mobile phone type m with the condition z that is assigned to the process testing after being identified, whereas HY, represents the quantity of the mobile phone type m with the condition z that is assigned to recycling. All assigned mobile phone quantities are defined as non-negative integers.
Figure 1: Optional phone treatment. The following sets are used in the model: . . . , i}; index m E M Set of mobile phones: M; M = {I,
Set of components: C;
C = {I, ... ,j}; index c
E
C
Set of conditions: 2;
2 = {I, ... ,k}; index z
E
2.
Set of resources: R;
R = {I, ... ,I}; index r E R.
Set of processes: P;
P = {I, ... ,n}; index p E P
Analysed phones can have different conditions regarding the functionality of the five basic mobile phone components, i.e. housing, PCB, display, speaker, and microphone. In this model, only two conditions for each component - functional and non-functional - are considered resulting in 32 (=Z5) possible phone conditions. Data about the failure probability of mobile phone components is available from market surveys.
The objective in this approach is to maximize the profit margin considering revenues for material recycling RYm, components reuse RCU, and phone reuse, i.e. ReMobile Classes 1-111 RUI, RUII,, RUIII,, as well as costs CR, for installed resources RQ,.
B,, with B,=l indicating that automation is possible. Constraints 10 and 11 guarantee that no phones are assigned to automated disassembly if B,=O. xHDA,=
~HCA,=
0
z
z
(10)
VrnlB,,,= 0
o (11)
VrnlB,,,= 0
Constraint 12 assures the required reassembly capacity, considering the time required for reassembly RMT,,.
xxHR,
XRMT,,
g RQ, xRC,
m z
Vr=3
MAX
Constraints 13-17 guarantee resource capacities for identification (13), testing (14), cleaning (15), software update (16), and polishing (17). The process time PT, depends on the phone type m, not on the condition z.
The solution is being derived under consideration of constraints for material flow continuity, available resource capacity, and the demand and offer for phones and components. According to figure 1, the constraints 2-7 guarantee material flow continuity for the remanufacturing program.
K,
HT,
=
+ HY,
Vm,Vz HT,
=
HTY,,
HTU,
+ HCM,+HCA,,
+ HTS,
+ HDM,,
HDM,,
+ HDA,
+
+ FDA,
(3)
Vm,Vz
HR,
=
(4)
Vm,Vz
HR,
=
HRS,
+ HRU,
Vm,Vz HTS,
+ HRS,,
=
HSU,,
+ HPU,,
Vm,Vz HTS,+HTU,=
0
(7)
Vm,Vz t 2
Resources required to perform remanufacturing processes are assigned under consideration of the previously stated requirements of the remanufacturing program. Decision variables for resource capacities need to be defined as non-negative integers as only whole resources can be assigned. Constraint 8 guarantees that the capacity RC, of all assigned automated disassembly stations RQ, is sufficient for the disassembly of all phones assigned to these stations. The disassembly time DAT,, required for the automated disassembly of the mobile phone type m with a certain condition z is derived by test disassemblies.
~ ~ ( H D A +HCA,)XDAT, , ~ m z
~ R QXRC, , (8)
Vr=l
~ ~ ( H c M , +, HCA,,)XBCO,,,=
,n\
(31
Vr=2 Whether or not a disassembly process of a phone can be automated or not is described by the binary variable
CY,+CU, (18)
m z
vc
CU,
< DCO,
vc Constraints 20-22 assure that the quantity of phones assigned to ReMobile Classes 1-111 are smaller than the demand for these classes DUI, DUII, and DUIII,.
x
(HTU,, +HRU,
Z
Analogical, constraint 9 guarantees the required resource capacity for manual disassembly, with DMT,, being the disassembly time required for the manual disassembly of a phone with a certain condition. r n z
The market driven demands for phones and components are being considered in constraints 18-22. Constraint 18 determines the type and quantity of components that can be obtained by manual and automated disassembly of phones assigned to component recovery, and assigns components to material recycling CY, or to the components for reuse class Recover CU,. BCO,,, is the binary variable describing which functional component c can be obtained from phone type m with a certain condition z. Constraints 19 guarantees that the quantity of sold components CU, is not higher than the corresponding demand DCO,.
Vrn XHSU,
< DUII,
Z
Vrn
xHPU, Z
Vm
< DUIII,
) g DUI,
5 IMPLEMENTATION The developed capacity and program planning model is described as a combinatorial optimization problem. To solve this type of problem two classes of methods can be distinguished: exact methods, that guarantee an optimal solution and heuristic methods, without any a priori guarantee in terms of solution quality. Exact methods apply mainly tree search technique with complete enumeration and bounded enumeration. For bounded enumeration the branch 8, bound algorithm has been proved to find the optimal solution, yet with non polynomial running time behavior [6]. In recent years efficient meta heuristic search methods, e.g. Genetic Algorithms, Evolutionary Strategies, Simulated Annealing, Threshold Accepting and Tabu Search for formulation and solution of complex, reality-based problems have been developed. These heuristics are mainly applied for problems, where enumeration methods would require extremely long computation time, to find the optimal solution. The selection of an adequate method deals with the trade off between solution quality and computation time. Also, the selection of a method depends on the time available for the implementation of the model, and the necessity of adapting the model due to frequently changing decision variables or constraints in the decision problem. In this approach, modifications of the described problem like remanufacturing technologies or possible material flow alternatives are very probable. If the problem complexity, described by number of decision variables and constraints allows the application of enumeration methods it is advantageous to use standard solvers, e.g. CPLEX, GAMS or LINGO. These solvers are using branch 8, bound algorithms to find the optimal solution, according to the applied data. Solvers provide a modeling language for a fast implementation of the developed mathematical model. The developed Integer Linear Programming (ILP) model was implemented using the solver LINGO. 6 FACILITY PLANNING AND EVALUATION To support the planner in the periodic adaptation of an existing remanufacturing system he needs to be enabled to apply the results from the capacity and program planning model efficiently. Simulation models allow the planner to model and test systems under consideration of relevant factory elements, e.g. storage, transport and processing resources. In order to increase the efficiency, simulation models need to be generated automatically under consideration of the results derived by the ILP model. For this purpose the object oriented simulation tool eM-Plant was selected. The software allows to generate and configure predefined object classes, e.g. storage and conveyor systems, remanufacturing resources, and workers. The developed algorithm for the data driven generation of remanufacturing facility models creates entities of these object classes and forms an executable simulation model. The required data for the entity configuration is imported via the Open DataBase Connectivity (ODBC) interface from a database where the ILP model results as well as the given model structure of a remanufacturing facility are stored. Figure 2 shows the steps, required data and used software for adaptation and evaluation of a mobile phone remanufacturing facility. The developed methods, models and data structures support a fast and continuous adaptation of remanufacturing facilities under quickly changing product, process, and market constraints. However, a conducted sensitivity analysis clarified the enormous sensitivity of the factory in respect to the processing time for dis- and reassembly and the quality of the incoming mobile phones. This demonstrates the challenges in the planning of a re-
manufacturing factory for mobile phones, in particular against the background that there is no firm data about the amount and quality of mobile phones offered at the market.
Figure 2: Steps for remanufacturing facility design
7 CONCLUSION The presented approach for capacity and remanufacturing program planning by means of combinatorial optimization and discrete-event simulation supports the planner in the periodic adaptation of an existing remanufacturing system. The process capacities and the remanufacturing program are determined by the optimization model. Based on these results, an executable simulation model is generated automatically for the remanufacturing system considering process capacities, and resources for transport and storage. The simulation model allows the planner to determine the required transport and storage capacities, and the performance of the remanufacturing system. 8 ACKNOWLEDGMENTS This paper presents results of the CRC 281 financed by the Deutsche Forschungsgemeinschaft (DFG). 9
REFERENCES Westkamper, E., Alting, L., Arndt, G., 2000, Life cycle management and assessment, Approaches and visions towards sustainable manufacturing, Annals of the CIRP, Vol. 4912: 501-52. Marcussen, C.H., 2003, Mobile Phones, WAP and the Internet - The European Market and Usage Rates in a Global Perspective 2000-2003, http:l/www.crt.d Wu Wstafflch mlwap.htm Seliger, G., Bagdere, B., Ciupek, M., Franke, C., 2003, Remanufacturing of Cellular Phones, ClRP Seminar on Life Cycle Engineering, Copenhagen, Denmark. Seliger, G., Bagdere, B., Keil, T., Rebafka, U., 2002, Innovative Processes and Tools for Disassembly, Annals of the ClRP Vol. 5111: 37-40. Kim, H.-J., Lee, D.-H., Xrouchakis, P., Zust, R., 2003, Disassembly Scheduling with Multiple Product Types, Annals of ClRP Vol. 5211: 403-406. Gungor, A,; Gupta, S. M., 2001, Disassembly Sequence Plan Generation Using a Branch and Bound Algorithm, International Journal of Production Research, Vol. 3913: 481-509.
Abstract Successful remanufacturing of electric and electronic products must meet the challenges of continuously falling prices for new products, short life cycles, disassembly of unfriendly designs and prohibiting costs in high-wage countries. Mobile phones are identified as suitable products for profitable remanufacturing. A generic remanufacturing plan for mobile phones is developed. For the planning of remanufacturing capacities and production programs a linear optimization model is introduced. In order to analyze the performance of the remanufacturing facilities under consideration of uncertainties regarding quantity and conditions of mobile phones, reliability of capacities, processing times, and demand, discrete-event simulation is applied. The simulation model is generated by an algorithm using results from the linear optimization approach. The introduced method allows the continuous adaptation of remanufacturing facilities under quickly changing product, process, and market constraints. Keywords: Mobile phone remanufacturing, linear optimization, discrete-event simulation
1 INTRODUCTION Today, the remanufacturing of expensive, long living investment goods, e.g. machine tools, jet fans, military equipment or automobile engines, is extended to a large number of consumer goods with short life cycles and relatively low values. Reuse is an alternative to material recycling to comply with recovery rates and quantities as well as special treatment requirements as prescribed by European legislation with the directive on Waste of Electrical and Electronic Equipment (WEEE) [ I ] . Market studies regarding offer and demand for mobile phones with GSM standard [2] show the worldwide potential for mobile phone remanufacturing. The studies revealed that with a total quantity of over 200 Mio. unutilized mobile phones, Europe can serve as a supply market whereas demand markets can be found in Asia and Latin America, e.g. China and Brasil where market penetration is as low as 20% and - in the case of Brasil where the old TDMA mobile communication standard is replaced by the GSM standard. By means of low cost remanufactured phones, one cannot only serve communication demands of lower income classes in those regions, but it is possible to recycle phones complying with WEEE requirements and thus provide services for OEMs within the scope of the directive. In order to evolve mobile phone remanufacturing into a profitable business segment, it is necessary to provide remanufacturers with efficient planning methods and tools, capable to deal with the special procurement, remanufacturing and distribution processes. The tools and methods should allow to determine the cost minimal adaptation of remanufacturing facilities under consideration of the fast changing product, process and market situation. The most frequently changing input parameters are the type and quantity of mobile phones offered at the market. In Western Europe, with the average replacement cycle of phones being less than 18 months and more than 100 new phone models every year it is feasible to assume that the remanufacturing program
requires adaptation several times during a year. In this paper, an approach is presented to support the remanufacturing program planning under the above stated framework. The remanufacturing program and required capacities are determined by means of combinatorial optimization. Based on the results, the planner is enabled to adapt and evaluate the existing remanufacturing facility using discrete-event simulation.
2
CONSTRAINTS FOR PLANNING OF MOBILE PHONE REMANUFACTURING In the following, the process chain of mobile phone remanufacturing is analyzed to identify aspects that need to be considered in the planning of a remanufacturing facility. The procurement of phones can be realized in cooperation with OEMs, e.g. by acquisition of overproduction, or in cooperation with net providers, supermarkets or other private and public organizations who have frequent and close contact to phone users, in so-called take backs. Experience has shown, that consumers are willing to either turn in their used phones as a charitable donation or trade them in for benefits such as free phone minutes [3]. After the take back, phones need to be separated, e.g. from chargers or earphones, and identified. Experience of remanufacturers shows that about 70 percent of phones recovered in Europe and the USA are considered beyond economic reuse, i.e. that either remanufacturing costs are to high or demand is too low for these phones, and they are consequently sent to material recycling. The remaining phones need to be tested to determine optical or functional faults that can be ascribed to the main elements housing, printed circuit board (PCB), display, microphone and speaker. The combination of faults results in different process times for disassembly and reassembly [3,4]. Replacement components are supplied either by external procurement or internal retrieval of components from used phones.
Experience of mobile phone remanufacturing in the USA has shown, that customers are willing to remunerate value adding upgrades of phones, e.g. software update or surface treatment by polishing. Offering different quality classes for the same phone model is an approach to meet the market demand. Customers show more flexibility in accepting alternative phone models as substitutes, as long as they offer comparable features, such as software updates. A more elastic demand for mobile phones simplifies the handling of the high variability on the phone procurement side. Future demand could also come from OEMs or independent service entities procuring retrieved phone components to cope with post production supply, i.e. the supply of spare parts to customers and service networks beyond the time of the production of the product. Recovering components could help to reduce warehousing of large quantities of spare parts over long periods of time, respectively to reduce the extend of the continuing production of spare parts.
3 GENERIC REMANUFACTURING PROCESS CHAIN To enable meeting a cost efficient treatment decision for each phone, a generic remanufacturing process was modeled (figure 1). Options for phone utilization are reuse, components retrieval and material recycling. In case of reuse, three different quality classes are differentiated, according to the extent of remanufacturing. Upon arrival phones are separated from accessories and identified. Accessories, e.g. chargers or earphones, are identified and tested to assign them to reuse or recycling. Following identification, phones can be sent directly to recycling or can be tested. Faultless mobile phones are assigned to either reuse (ReMobile Class 1) or software update. Updated phones can be assigned to either reuse (ReMobile Class 2) or polishing (ReMobile Class 3). Defective phones are assigned to alternatively manual or automated disassembly, cleaning and reassembly. Hereafter, phones can undergo additional value adding processes, i.e. software update or polishing, or be sent directly to reuse. When deciding which phones are to be assigned to which process, certain constraints, e.g. the availability of, and demand for phones and components, the condition of available phones or the cost for and number of remanufacturing resources need to be considered. The problem of assigning each phone to a cost optimal treatment belongs to the class of combinatorial optimization. Combinatorial optimization deals with models and methods to find the best solution for problems with discrete choices, and is well established in disassembly planning [5]. In the described problem the discrete choices are related to the discrete amount of required capacities for remanufacturing processes and the discrete number of mobile phones which are assigned to every remanufacturing process.
4
MODEL FOR CAPACITY AND PROGRAM PLANNING Based on the generic remanufacturing process, a mathematical model was developed to determine the required process capacities for identification, testing, manual or automated disassembly, reassembly, software update, and polishing for a given number of offered and demanded mobile phones. Available product, process and market data are considered regarding product structure and condition of used phones, operating times for remanufacturing processes, capacities of resources, offer for used phones and demand and revenues for sold phones and components as well as costs for assigned process capacities.
Figure 1 represents all assignment options for products, and all types of remanufacturing resources considered in this model. For example, the decision variable HT, describes the quantity of the mobile phone type m with the condition z that is assigned to the process testing after being identified, whereas HY, represents the quantity of the mobile phone type m with the condition z that is assigned to recycling. All assigned mobile phone quantities are defined as non-negative integers.
Figure 1: Optional phone treatment. The following sets are used in the model: . . . , i}; index m E M Set of mobile phones: M; M = {I,
Set of components: C;
C = {I, ... ,j}; index c
E
C
Set of conditions: 2;
2 = {I, ... ,k}; index z
E
2.
Set of resources: R;
R = {I, ... ,I}; index r E R.
Set of processes: P;
P = {I, ... ,n}; index p E P
Analysed phones can have different conditions regarding the functionality of the five basic mobile phone components, i.e. housing, PCB, display, speaker, and microphone. In this model, only two conditions for each component - functional and non-functional - are considered resulting in 32 (=Z5) possible phone conditions. Data about the failure probability of mobile phone components is available from market surveys.
The objective in this approach is to maximize the profit margin considering revenues for material recycling RYm, components reuse RCU, and phone reuse, i.e. ReMobile Classes 1-111 RUI, RUII,, RUIII,, as well as costs CR, for installed resources RQ,.
B,, with B,=l indicating that automation is possible. Constraints 10 and 11 guarantee that no phones are assigned to automated disassembly if B,=O. xHDA,=
~HCA,=
0
z
z
(10)
VrnlB,,,= 0
o (11)
VrnlB,,,= 0
Constraint 12 assures the required reassembly capacity, considering the time required for reassembly RMT,,.
xxHR,
XRMT,,
g RQ, xRC,
m z
Vr=3
MAX
Constraints 13-17 guarantee resource capacities for identification (13), testing (14), cleaning (15), software update (16), and polishing (17). The process time PT, depends on the phone type m, not on the condition z.
The solution is being derived under consideration of constraints for material flow continuity, available resource capacity, and the demand and offer for phones and components. According to figure 1, the constraints 2-7 guarantee material flow continuity for the remanufacturing program.
K,
HT,
=
+ HY,
Vm,Vz HT,
=
HTY,,
HTU,
+ HCM,+HCA,,
+ HTS,
+ HDM,,
HDM,,
+ HDA,
+
+ FDA,
(3)
Vm,Vz
HR,
=
(4)
Vm,Vz
HR,
=
HRS,
+ HRU,
Vm,Vz HTS,
+ HRS,,
=
HSU,,
+ HPU,,
Vm,Vz HTS,+HTU,=
0
(7)
Vm,Vz t 2
Resources required to perform remanufacturing processes are assigned under consideration of the previously stated requirements of the remanufacturing program. Decision variables for resource capacities need to be defined as non-negative integers as only whole resources can be assigned. Constraint 8 guarantees that the capacity RC, of all assigned automated disassembly stations RQ, is sufficient for the disassembly of all phones assigned to these stations. The disassembly time DAT,, required for the automated disassembly of the mobile phone type m with a certain condition z is derived by test disassemblies.
~ ~ ( H D A +HCA,)XDAT, , ~ m z
~ R QXRC, , (8)
Vr=l
~ ~ ( H c M , +, HCA,,)XBCO,,,=
,n\
(31
Vr=2 Whether or not a disassembly process of a phone can be automated or not is described by the binary variable
CY,+CU, (18)
m z
vc
CU,
< DCO,
vc Constraints 20-22 assure that the quantity of phones assigned to ReMobile Classes 1-111 are smaller than the demand for these classes DUI, DUII, and DUIII,.
x
(HTU,, +HRU,
Z
Analogical, constraint 9 guarantees the required resource capacity for manual disassembly, with DMT,, being the disassembly time required for the manual disassembly of a phone with a certain condition. r n z
The market driven demands for phones and components are being considered in constraints 18-22. Constraint 18 determines the type and quantity of components that can be obtained by manual and automated disassembly of phones assigned to component recovery, and assigns components to material recycling CY, or to the components for reuse class Recover CU,. BCO,,, is the binary variable describing which functional component c can be obtained from phone type m with a certain condition z. Constraints 19 guarantees that the quantity of sold components CU, is not higher than the corresponding demand DCO,.
Vrn XHSU,
< DUII,
Z
Vrn
xHPU, Z
Vm
< DUIII,
) g DUI,
5 IMPLEMENTATION The developed capacity and program planning model is described as a combinatorial optimization problem. To solve this type of problem two classes of methods can be distinguished: exact methods, that guarantee an optimal solution and heuristic methods, without any a priori guarantee in terms of solution quality. Exact methods apply mainly tree search technique with complete enumeration and bounded enumeration. For bounded enumeration the branch 8, bound algorithm has been proved to find the optimal solution, yet with non polynomial running time behavior [6]. In recent years efficient meta heuristic search methods, e.g. Genetic Algorithms, Evolutionary Strategies, Simulated Annealing, Threshold Accepting and Tabu Search for formulation and solution of complex, reality-based problems have been developed. These heuristics are mainly applied for problems, where enumeration methods would require extremely long computation time, to find the optimal solution. The selection of an adequate method deals with the trade off between solution quality and computation time. Also, the selection of a method depends on the time available for the implementation of the model, and the necessity of adapting the model due to frequently changing decision variables or constraints in the decision problem. In this approach, modifications of the described problem like remanufacturing technologies or possible material flow alternatives are very probable. If the problem complexity, described by number of decision variables and constraints allows the application of enumeration methods it is advantageous to use standard solvers, e.g. CPLEX, GAMS or LINGO. These solvers are using branch 8, bound algorithms to find the optimal solution, according to the applied data. Solvers provide a modeling language for a fast implementation of the developed mathematical model. The developed Integer Linear Programming (ILP) model was implemented using the solver LINGO. 6 FACILITY PLANNING AND EVALUATION To support the planner in the periodic adaptation of an existing remanufacturing system he needs to be enabled to apply the results from the capacity and program planning model efficiently. Simulation models allow the planner to model and test systems under consideration of relevant factory elements, e.g. storage, transport and processing resources. In order to increase the efficiency, simulation models need to be generated automatically under consideration of the results derived by the ILP model. For this purpose the object oriented simulation tool eM-Plant was selected. The software allows to generate and configure predefined object classes, e.g. storage and conveyor systems, remanufacturing resources, and workers. The developed algorithm for the data driven generation of remanufacturing facility models creates entities of these object classes and forms an executable simulation model. The required data for the entity configuration is imported via the Open DataBase Connectivity (ODBC) interface from a database where the ILP model results as well as the given model structure of a remanufacturing facility are stored. Figure 2 shows the steps, required data and used software for adaptation and evaluation of a mobile phone remanufacturing facility. The developed methods, models and data structures support a fast and continuous adaptation of remanufacturing facilities under quickly changing product, process, and market constraints. However, a conducted sensitivity analysis clarified the enormous sensitivity of the factory in respect to the processing time for dis- and reassembly and the quality of the incoming mobile phones. This demonstrates the challenges in the planning of a re-
manufacturing factory for mobile phones, in particular against the background that there is no firm data about the amount and quality of mobile phones offered at the market.
Figure 2: Steps for remanufacturing facility design
7 CONCLUSION The presented approach for capacity and remanufacturing program planning by means of combinatorial optimization and discrete-event simulation supports the planner in the periodic adaptation of an existing remanufacturing system. The process capacities and the remanufacturing program are determined by the optimization model. Based on these results, an executable simulation model is generated automatically for the remanufacturing system considering process capacities, and resources for transport and storage. The simulation model allows the planner to determine the required transport and storage capacities, and the performance of the remanufacturing system. 8 ACKNOWLEDGMENTS This paper presents results of the CRC 281 financed by the Deutsche Forschungsgemeinschaft (DFG). 9
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