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Final Presentation

“LOGISTICS MODELS” Andrés Weintraub P. Departament Industrial Engineering University of Chile PASI Santiago Agosto 2013. Final Presentation. Xerox Fleet Design. Student: Daniel Leng Professors: Andrés Weintraub Cristian Cortes Michel Gendreau Pablo Rey.

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Final Presentation

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  1. “LOGISTICS MODELS”Andrés Weintraub P.Departament Industrial EngineeringUniversity of ChilePASISantiagoAgosto 2013

  2. Final Presentation Xerox Fleet Design Student: Daniel Leng Professors: Andrés Weintraub Cristian Cortes Michel Gendreau Pablo Rey

  3. Agenda • Problem Description • The Company • Precedents • The problem • Objectives • Primary Objective • Specific Objectives • Available Information • Information Analysis • Amount of Calls • Time of Call • Commune (County) • Service Time (by product line) • Target Arrival Time • Obtaining Instances • Routing Weeks • Results Analyses • Economic Analyses

  4. Problem Description • The Problem • How to determine the suitable number of technicians for each area, in order to fulfill the chosen performance indicators? • The Company • Xerox offers home or office technical support to its clients for its different lines of products: Printers, copiers, plotters, etc. • It is necessary to meet a target time of arrival from the client’s calling time, depending on the client’s priority. • There are 16 areas of attention, divided by type of equipment or geographical area. • There is a force of 102 technical personnel force assigned to the 16 areas. Problem Description Objectives Available Information • Precedents • There is a routing model for the dispatch of technicians. It works as an "24-hour-in-advance service". • The number of technicians assigned to each area has been calculated using only the judgment of the decision makers. Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  5. Objectives • Primary Objective • “To obtain the minimal possible number of technical personnel, capable of fulfilling the most accurate service level”. • Specific Objectives • “To estimate the demand for service and the parameters that conform it”. • “To construct a master model that integrates the weekdays interactions using the routing model”. • “To use the week model to simulate different scenarios”. • “To apply statistical studies on the results and use and economical approach to determine the optimal number of technical personnel”. Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  6. Available Information • Two areas were used for the pilot model, namely the 101 and 110 areas • For each of these areas we must analyze the following aspects: • Amount of calls • Time of call (for each call) • Commune (County) (for each call) • Service time (for each call) • Target arrival time (for each call) • There is one complete year of information (May, 2002- April, 2003) • Each call is defined according to : • Address • Commune (County) • Attending technician • Date and time of call • Target arrival time • Area • Model • Client • Service Time • Arrival Time Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  7. Information Analysis • Amount of Calls • By Area • By Month (all areas) Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  8. Information Analysis • Amount of Calls • By weekday • We used the Chi Squared Test at 95 % of confidence to check if there is a relation between: • Month - Area – Weekday – Amount of calls Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses • The following results were obtained for each area

  9. Information Analysis • Area 101 Problem Description Objectives Available Information Information Analysis • Area 110 Obtaining Instances Routing Weeks Results Analyses • Both areas Economic Analyses

  10. Information Analysis • We cannot assume the same relation by month in both areas • As a consequence of having found significant differences among areas, the monthly amount of calls were grouped in a different way for each area Problem Description Objectives Available Information January March June November Information Analysis August February Obtaining Instances October April September Routing Weeks May July Results Analyses December Economic Analyses Area 101 Area 110 Both areas

  11. Information Analysis • In the same way, groups were made for the relation: • Weekday – Amount of calls • Analogous results were obtained for both areas, individually and as a whole, so that the use of different criteria was not necessary. • Both Monday and Friday show distinct results from the rest of the week, and between them. • The rest of the week shows homogeneous results. Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  12. Information Analysis • Adjusting distributions to amount of calls • Several discrete distributions of probabilities were adjusted • Poisson’s distribution ended up fitting all combinations of Groups and Weekdays Problem Description Objectives Available Information Information Analysis • Lambda estimation [calls/day]: • Area 101 • Area 110 Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  13. Information Analysis • Time of call • Histograms were constructed to check relations of the type: • Amount of calls - Hour of the day - Monthly Groups • There were no significant differences among Areas or among Monthly Groups. Therefore analogous histograms will be used for both areas. Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  14. Information Analysis • Commune (County) • Histograms were constructed to check relations of the type: • Amount of calls - Commune (County) • Given that each Area has different communes (counties) assigned, it is necessary to use different histograms for each Area Problem Description Objectives Available Information • Santiago Communes (Counties) map and Xerox service areas Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  15. Information Analysis • Area 101 Problem Description Objectives Available Information Information Analysis • Area 110 Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  16. Information Analysis • Service Time • The different products are grouped by lines of products Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks • There is no known probabilities distribution function that can be adjusted to the service time at any confidence level. • A lot of observations are concentrated around a few points. • Cluster analyses were made to study this behavior • The result of the cluster study was used to generate a discrete probabilities distribution. Results Analyses Economic Analyses

  17. Information Analysis • Target Service Time (TST) • The TST is measured as the elapsed time between the calling time and the maximum allowed arrival time • This parameter depends on the client’s priority • Because of the absence of a priorities’ list, we use empiric probabilities to assign a TST to each call Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  18. Obtaining Instances • An instance is defined as the simulation of an entire week of calls • The algorithm to create an instance works as follows: • Define Group and Area • Use Poisson distribution to generate amount of calls for each day • For each call determine: • Commune (County) • Time of call • TST • Service Time Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  19. Routing Weeks • The construction of the week model is based on a set of policies of interaction • The clients that couldn’t be attended to on the previous day have priority one on the following day routing • If there are not enough technicians to look after all the left-outs at the beginning of the day, the one with the longest delay has priority • The rest of none-attended-clients will be included on the routing model with a TST equals cero. Problem Description Objectives Available Information Information Analysis • The routing model is applied to each instance with different numbers of available technicians. • A set of performance indicators will be obtained for every pair: • Instance(i) - Number of technicians (k) • Utilization • Average delay per client • Average travel time • Extra time Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  20. Routing Weeks Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  21. Routing Weeks • Definition of interval of the number of technicians • Estimation of the calculation time • Seven groups of months (three for area 110 and four for area 101) • 220 minutes per instance • One instance for every technicians quantity • It takes 0,6 days for area 101 and 0,45 for area 110 • Maximum of 640 days unfeasible of calculation time in the laboratory (80 days on nine computers) Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks • Area 101: • 11, 10, 9, 8 Technicians • Area 110: • 10, 9, 8 ,7 Technicians Results Analyses Economic Analyses

  22. Result analyses • The average delay indicator will determine the service level • Log-normal distribution showed to be the best-adjusted probabilities distribution • If Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  23. Results analyses • X is defined as the Maximum Average Delay feasible for a given confidence level • The confidence level selected is 98% (there are not significant differences between 95% and the selected level) • Then and X is defined as the Service Level Problem Description Objectives Available Information Information Analysis • Service Level (X) at 98% of confidence [min] • Area 101 • Area 110 Obtaining Instances Routing Weeks Results Analyses Economic Analyses • The other three indicators will be estimated using the sample mean

  24. Results analyses • Area 101 Problem Description Objectives Available Information Information Analysis Obtaining Instances • Area 110 Routing Weeks Results Analyses Economic Analyses

  25. Economic analyses • Fixed costs • Technicians salary ($600.000 a month, $3.333 per hour) • Variable costs • Real costs • Overtime cost (4.000 per hour) • Opportunity costs • Travel time (3.333 per hour) • Unused time (3.333 per hour) • Economic model • Variables Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  26. Economic analyses • Economic model • Parameters • Relations • Cost Function Problem Description Objectives Available Information Information Analysis Obtaining Instances Routing Weeks Results Analyses Economic Analyses

  27. Economic analyses • Area 101 Problem Description Objectives Available Information Information Analysis Obtaining Instances • Area 110 Routing Weeks Results Analyses Economic Analyses

  28. Economic analyses • Area 101 Problem Description Objectives Available Information Information Analysis Obtaining Instances • Area 110 Routing Weeks Results Analyses Economic Analyses

  29. Economic analyses • Feasible and efficient policies Problem Description • Area 101 Objectives Available Information Information Analysis Obtaining Instances Routing Weeks • Area 110 Results Analyses Economic Analyses

  30. Conclusions

  31. Final Presentation Xerox Fleet Design Student: Daniel Leng Professors: Andrés Weintraub Cristian Cortes Michel Gendreau Pablo Rey March 26, 2009

  32. Backup • Cluster analyses • CH-COP. PERSONAL Results Problem Description Objectives Available Information Information Analysis Obtaining Instances Obtaining Indicators The Model

  33. Backup • An instance is defined as follows: Problem Description Objectives Available Information Information Analysis Obtaining Instances Obtaining Indicators The Model

  34. Backup • The model was implemented on Java language and uses the following Pseudo code Problem Description Objectives Available Information Information Analysis Obtaining Instances Obtaining Indicators The Model

  35. Backup • Cost composition area 101 Problem Description Objectives Available Information Information Analysis Obtaining Instances Obtaining Indicators The Model

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