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Welcome to Kokeb

Our expertise is in developing low cost engineering and scientific applications using the wealth of publicly available models, algorithms, open source software libraries for Microsoft and Android platforms. We do all the research needed in consultation with our customers to incorporate both in-house and state of the art algorithms and models available in the open literature. An example of our recent work and research in applying Dantzig’s seminal workforce scheduling model to call centers is shown below.


Our Latest Publication

BookCover
A practical book for call center analysts to implement Dantzig’s seminal workforce scheduling model to generate, evaluate, and optimize service level performance of weekly agent schedules using Excel 2007, C#.NET components and publicly available solvers, algorithms, and hardware.

Book features:

– Introduction to Dantzig’s seminal workforce scheduling model: Minimize CTX subject to AX >= B, X >= 0. Formulation of tour (A), requirement (B), and objective (C) matrices for weekly tour scheduling of agents.
– Model solution using public solvers (GLPK, lp_solve, COIN-OR Cbc) on local hardware and in the cloud (using NEOS Feasibility Pump and SCIP) on public hardware.

– Generating a schedule with an upper bound on total number of weekly tours, each tour having lower and upper bounds on number of agents using auxiliary binary (on-off) decision variables. C# code snippets to create console and Excel 2007/VSTO applications in Microsoft Visual Studio 2005/2010

Monte Carlo stochastic simulation to estimate schedule service level and ASA. Effects of controllable parameters on schedule quality.

– Near optimal scheduling to meet a target service level for a given call load. Adjust SIPP (Erlang-C) requirement for period dependence to dampen “roller coaster” ride in service level performance.

– A novel frequency domain reformulation of Dantzig’s time domain model to reduce size by 75% by retaining only low frequency Fourier components of the requirement (B) and tour (A) vectors.


Our Low Cost Scheduling Approach

We accomplish the complex process of Dantzig’s model based workforce scheduling using inexpensive hardware and state of the art open-source (free) software.

    • HardwareRaspberry Pi 3Raspberry Pi, a $25 dollar credit card size single board computer with low power consumption. This piece of hardware is not kid stuff anymore. With the introduction of Pi 3, this device has serious computing power to handle major tasks. Our scheduler set up consisting of
      1. Raspberry Pi 3
      2. 32 GB Class 10 micro SD card hard drive loaded with Linux and other software listed below
      3. ethernet/WiFi connection to a router

      runs apache web server and an instance of a MySql database that serves both our site and our Android apps. The binary executables generated are directly compatible with ARM processors running Android in phones and tablets. This device is also used as a development machine in tandem for developing call center workforce scheduling software based on Dantzig’s model employing C#, C, C++ and Python. Examples of our Android apps developed on Pi 3 are shown on the right.

    • Software: The following open source software packages are used in our development: Ubuntu 15.10, GLPK, COIN-OR CBC, Mono, MonoDevelop, Python, IDLE, XMLRPC, PHP, GnuPlot, FFTW3, APACHE2, MySQL, MATPLOT Lib, RabbitMQ, Node.js

 Our Latest Research

Modifying traditional SIPP  (ErlangC) requirement in Dantzig’s model using stochastic simulation to minimize “roller coaster” ride of schedule service levels in a call center

Frequency domain and convolution formulations of Dantzig’s time domain model