Optimal Solution of Vehicle Routing Problems with Fractional Objective Function

This work proposes a first extensive analysis of the Vehicle Routing Problem with Fractional Objective Function (vrpfof). We investigate how the principal techniques used either in the context of fractional programming or in the context of vehicle routing problems interact. We present new dual and primal bounding procedures which have been incorporated in an exact method. The method proposed allows to extend specific variants of \vrp\ to their counterpart with a fractional objective function. Extensive numerical experiments prove the validity of our approach.

[1]  Roberto Roberti,et al.  An exact solution framework for a broad class of vehicle routing problems , 2010, Comput. Manag. Sci..

[2]  J. B. G. Frenk,et al.  Optimizing a General Optimal Replacement Model by Fractional Programming Techniques , 1997, J. Glob. Optim..

[3]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[4]  Moshe Dror,et al.  Inventory/routing: Reduction from an annual to a short-period problem , 1987 .

[5]  R. Ródenas,et al.  Extensions of Dinkelbach's algorithm for solving non-linear fractional programming problems , 1999 .

[6]  C Tofallis,et al.  Fractional Programming: Theory, Methods and Applications , 1997, J. Oper. Res. Soc..

[7]  S. Schaible.  Fractional Programming. II, On Dinkelbach's Algorithm , 1976 .

[8]  Gilbert Laporte,et al.  Thirty Years of Inventory Routing , 2014, Transp. Sci..

[9]  Roberto Roberti,et al.  New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem , 2011, Oper. Res..

[10]  MAX-MIN CASE,et al.  RECENT DEVELOPMENTS IN FRACTIONAL PROGRAMMING : SINGLE RATIO AND , 2004 .

[11]  Paolo Toth,et al.  Vehicle Routing , 2014, Vehicle Routing.

[12]  L.A.M. Knoben,et al.  Optimizing the moment of customer delivery in ORTEC Inventory Routing , 2016 .

[13]  S. Zionts,et al.  Programming with linear fractional functionals , 1968 .

[14]  Guy Desaulniers,et al.  Minimizing the logistic ratio in the inventory routing problem , 2016, EURO J. Transp. Logist..

[15]  Philippe Augerat,et al.  Approche polyèdrale du problème de tournées de véhicules. (Polyhedral approach of the vehicle routing problem) , 1995 .

[16]  Roberto Roberti,et al.  Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints , 2012, Eur. J. Oper. Res..

[17]  Christian Artigues,et al.  Optimization of occupancy rate in dial-a-ride problems via linear fractional column generation , 2011, Comput. Oper. Res..

[18]  Nicos Christofides,et al.  An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts , 2008, Math. Program..

[19]  Ricardo Fukasawa,et al.  Lifting, tilting and fractional programming revisited , 2010, Oper. Res. Lett..

[20]  Marcus Poggi de Aragão,et al.  Improved branch-cut-and-price for capacitated vehicle routing , 2016, Mathematical Programming Computation.

[21]  M. Lübbecke.  Column Generation , 2010 .

[22]  Guy Desaulniers,et al.  New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows , 2016, INFORMS J. Comput..

[23]  Daniele Vigo,et al.  Vehicle Routing Problems with Profits , 2014, Vehicle Routing.

[24]  I. Stancu-Minasian.  Nonlinear Fractional Programming , 1997 .

[25]  Siegfried Schaible,et al.  Fractional Programming , 2009, Encyclopedia of Optimization.

[26]  Susan C. Morton.  Pioneering solutions in supply chain management – a comprehensive insight into current management approaches, edited by W. Kersten, T. Blecker, and C. Luthje , 2011 .

[27]  Thierry Benoist,et al.  Randomized Local Search for Real-Life Inventory Routing , 2011, Transp. Sci..

[28]  Tomasz Radzik,et al.  Fractional Combinatorial Optimization , 2009, Encyclopedia of Optimization.

[29]  Martin W. P. Savelsbergh,et al.  Inventory Routing in Practice , 2002, The Vehicle Routing Problem.

[30]  J. B. G. Frenk,et al.  Modeling of inventory control with regenerative processes , 2001 .