customer service level is of prime importance in today competitive world and has various dimensions with delivery quality being one of the most important ones. delivery quality has several parameters such as deliver time window options, time window size, etc. in this paper we focus on one of these parameters, namely time window setting. it has a direct impact upon customer satisfaction and busi...

Column generation is an indispensable tool in computational optimization to solve a mathematical program by iteratively adding the variables of the model. Even though the method is simple in theory there are many algorithmic choices and we discuss the most common ones. Particular emphasis in put on the dual interpretation, relating column generation to Langrangian relaxation and cutting plane a...

In recent years, enriching traditional revenue management models by considering the customer choice behavior has been a main challenge for researchers. The terminology for the airline application is used as representative of the problem. A popular and an efficient model considering these behaviors is choice-based deterministic linear programming (CDLP). This model assumes that each customer bel...

This document describes an implementation of a Column Generation algorithm using GAMS. The well-known cutting stock problem is used as an example.

We introduce a new concept in column generation for handling complex large scale optimization problems, called two-stage column generation, where columns for the compact and extensive formulation are simultaneously generated. The new framework is specifically conceived for tackling complex problems that cannot be efficiently solved by standard column generation and exploits the relationship bet...

MDVSP k k p p k k p K k p k p k ip K k p k p k p k k k ip k k p k j ij i i ij i i p K k x K k n x N i x a x c K k n N i p a p c K k K N j i t d s t A j i A K N j i j i d N i s N i t N K k k k min depot at vehicles of number available : otherwise 0 ; task covers path if 1 path of cost : depot to and from paths of set : , for , if) , (arcs; of set : , for , node to node from go to time : for task...

The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper ACCPM is used for the first time in the vehicle routing problem with time windows (VRPTW) to accelerate lagrangian relaxation procedure for the problem. At first the basic cutting plane algorithm and its relationship with column generation method is clari...