This app illustrates how the seminal workforce scheduling model invented by Prof. Dantzig[1,2] can be used to generate optimal/near-optimal weekly agent tour schedules for a call center operating 24x7 given a weekly call volume, service time for the calls, service level and tour definitions for the center. Knowledge of Dantzig's model/theory is not required to use this app. There is no need for expensive hardware or software to carry out the computationally intensive task involved in solving Dantzig's model except your Android device. At the click of a button, this app generates the model for user specified inputs, submits it over the INTERNET, solves it using state of the art solvers on powerful public cloud servers, retrieves the result back to the device. and generates a tabular view of the schedule. A time line or Gantt chart provides a bird's eye view of the weekly schedule along with scheduled vs. required number of agents for the week illustrating the schedule efficiency. The user can generate a schedule that minimizes one of 1) Total cost, 2) weekly head count, 3) idle hours or 4) relief hours. Using binary on-off decision variables internally, the app can generate near-optimal schedules with an upper bound on the total number of weekly tours and each tour having upper and lower bounds on number of agents. The user can send the results of an active run, namely, schedule(csv), model(lp), Gantt chart(jpeg), and Tour Definition(pdf) files to any valid email.
Network access is imperative for this app to connect to cloud database, make remote procedure calls and invoke an appropriate solver on the cloud server. This app can also generate a schedule in the device using the following open source solvers, namely, COIN-OR Branch and Cut (CBC) and GNU Linear Programming Kit (GLPK) (although these are slower than NEOS cloud solvers). The computing power of the processors in the device or the cloud servers determines the time taken to generate a schedule for large models. The user can specify a timeout condition and tolerance (MIP gap%) to limit execution time and desired level of schedule efficiency. The computation in the cloud server/local device will terminate if either one of these conditions is met and the near-optimal schedule at that point, if any, will be returned possibly with lower efficiency. It is left to the user to strike a balance between efficiency and computing time.
This app uses a sample scenario of a given weekly call volume and tour data that can be viewed and altered to a limited degree. The device's SQLite database stores results of all runs for review and analysis. This release offers connectivity to an open source MySQL database instance to generate schedules for any call volume and tour data adhering to SQL table definitions given in the user manual. Kokeb makes available a complimentary connection to a MySQL instance loaded with default data for testing purposes. The default built-in DB connection string parameters can be modified to point to user's own MySQL instance in the cloud. Future versions will offer connectivity to DBs such as ORACLE, MS SQL etc.
Best viewed in tablets >=7 inches.
1. Telephone Call Centers: Tutorial, Review and Research Prospects, Noah Gans, Ger Koole, Avishai Mandelbaum, Faculty of Ind Engg, Technion—Israel Inst of Tech Haifa 32000, Israel, Dec 23, 2003. http://ie.technion.ac.il/serveng/References/Gans-Koole-Mandelbaum-CCReview.pdf
2. Call Center Mathematics, Ger Koole, A scientific method for understanding and improving call centers, March 2006.
3. NEOS (network Enabled Optimization System) Server for Optimization, http://www.neos-server.org/neos/
4. Cbc (Coin-OR Branch and Cut) mixed integer programming solver, John J. Forrest, Version 2.8.9, Jan 2014. https://projects.coin-or.org/Cbc
5. GLPK(GNU Linear Programming Kit) Version 4.52, Jul 2013, http://www.gnu.org/software/glpk
Dantzig Model size in this app (depends on parameters chosen)
1) Small model : 504 int vars and 672 constraints
2) Large model : 2016 int vars, 2016 binary int vars and 4706 constraints
SQLite DB capability added to store results locally for review/analysis
Send weekly schedule.csv, Dantzig's model test.lp, High res Gantt chart (jpeg), Tour Definition(pdf) files to any valid email
Connectivity to MySQL database added to retrieve call volume and tour data