Lot-sizing and inventory routing for a production-distribution supply chain

Dedication This dissertation is dedicated to my father. v Acknowledgements I like to thank several people for supporting my study at the University of Texas at Austin. First and foremost I like to thank Dr. Jonathan F. Bard, who serves as my advisor. With his expertise in the field, he has given invaluable advice for my research. for their invaluable comments and suggestion. Last, but not least, I would like to thank my wife Aei for her support and love during the past few years. I am also grateful to my parents for their love and support. The integration of production and distribution decisions presents a challenging problem for manufacturers trying to optimize their supply chain. At the planning level, the immediate goal is to coordinate production, inventory, and delivery to meet customer demand so that the corresponding costs are minimized. Achieving this goal provides the foundations for streamlining the logistics network and for integrating other operational and financial components of the system. In this paper, a model is presented that includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of vehicles for making the deliveries. Demand can be satisfied from either inventory held at the customer sites or from daily product distribution. A procedure centering on a reactive tabu search is developed for solving the full problem. After a solution is found, path relinking is applied to improve the results. A novel feature of the methodology is the use of an allocation model in the form of a mixed integer program to find good feasible solutions that serve as starting points for the tabu search. Lower bounds on the optimum are obtained by solving a modified version of the allocation model. Computational testing on a set of 90 benchmark instances with up to 200 customers and 20 time periods demonstrates the effectiveness of the approach. In all cases, improvements ranging from 10 – 20% were realized when compared to those obtained from an existing greedy randomized adaptive search procedure (GRASP). This often came at a three-to five-fold increase in runtime, however. vii A hybrid scheme that combines the features of reactive tabu search algorithm and branch-and-price algorithm is also developed. The combined approach takes advantage of the efficiency of the tabu search heuristic and the precision of the branch-and-price algorithm. Branching strategy that is suitable for the problem …

[1]  Luca Bertazzi,et al.  Deterministic Order-Up-To Level Policies in an Inventory Routing Problem , 2002, Transp. Sci..

[2]  Awi Federgruen,et al.  One warehouse multiple retailer systems with vehicle routing costs , 1990 .

[3]  A. Ruszczynski,et al.  On the integrated production, inventory, and distribution routing problem , 2006 .

[4]  Ki Ling Cheung,et al.  Balanced and synchronized ordering in supply chains , 2006 .

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

[6]  Hasan Pirkul,et al.  Planning and coordination of production and distribution facilities for multiple commodities , 2001, Eur. J. Oper. Res..

[7]  Moshe Dror,et al.  A Decomposition Approach to the Inventory Routing Problem with Satellite Facilities , 1998, Transp. Sci..

[8]  Toshihide Ibaraki,et al.  Metaheuristics : progress as real problem solvers , 2005 .

[9]  Marshall L. Fisher,et al.  A Periodic Inventory Routing Problem at a Supermarket Chain , 2004, Oper. Res..

[10]  A. Federgruen,et al.  A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0n log n or 0n Time , 1991 .

[11]  C. Prins,et al.  A MEMETIC ALGORITHM WITH POPULATION MANAGEMENT FOR A PRODUCTION-DISTRIBUTION PROBLEM , 2006 .

[12]  M. Mourgaya,et al.  The periodic Vehicle routing problem: classification and heuristic , 2006, RAIRO Oper. Res..

[13]  G. Nemhauser,et al.  Integer Programming , 2020 .

[14]  M. Mourgaya,et al.  Column generation based heuristic for tactical planning in multi-period vehicle routing , 2007, Eur. J. Oper. Res..

[15]  David L. Woodruff,et al.  Solving the medium newspaper production/distribution problem , 1999, Eur. J. Oper. Res..

[16]  Francesca Fumero,et al.  Synchronized Development of Production, Inventory, and Distribution Schedules , 1999, Transp. Sci..

[17]  Jonathan F. Bard,et al.  A Review of: “Lean Logistics: The Nuts and Bolts of Delivering Materials and Goods” , 2005 .

[18]  Joaquin Sicilia,et al.  A new characterization for the dynamic lot size problem with bounded inventory , 2003, Comput. Oper. Res..

[19]  Siwate Rojanasoonthon,et al.  A branch‐and‐price algorithm for parallel machine scheduling with time windows and job priorities , 2006 .

[20]  James R. Evans An efficient implementation of the Wagner-Whitin algorithm for dynamic lot-sizing , 1985 .

[21]  Awi Federgruen,et al.  Two-Echelon Distribution Systems with Vehicle Routing Costs and Central Inventories , 1993, Oper. Res..

[22]  Linet Özdamar,et al.  A hierarchical planning approach for a production-distribution system , 1999 .

[23]  François Vanderbeck,et al.  On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm , 2000, Oper. Res..

[24]  Stephen F. Love Bounded Production and Inventory Models with Piecewise Concave Costs , 1973 .

[25]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem , 1991 .

[26]  Joaquin Sicilia,et al.  A polynomial algorithm for the production/ordering planning problem with limited storage , 2007, Comput. Oper. Res..

[27]  Fred Glover,et al.  An Integrated Production, Distribution, and Inventory Planning System , 1979 .

[28]  Martin W. P. Savelsbergh,et al.  A Branch-and-Price Algorithm for the Generalized Assignment Problem , 1997, Oper. Res..

[29]  Celso C. Ribeiro,et al.  GRASP with Path-Relinking: Recent Advances and Applications , 2005 .

[30]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

[31]  Moshe Dror,et al.  A computational comparison of algorithms for the inventory routing problem , 1985 .

[32]  Chung-Yee Lee,et al.  A comparison of outbound dispatch policies for integrated inventory and transportation decisions , 2006, Eur. J. Oper. Res..

[33]  Gilbert Laporte,et al.  New Insertion and Postoptimization Procedures for the Traveling Salesman Problem , 1992, Oper. Res..

[34]  M. Tzur,et al.  The multilocation transshipment problem , 2006 .

[35]  Maged Dessouky,et al.  A genetic algorithm approach to the integrated inventory-distribution problem , 2006 .

[36]  Jacques Desrosiers,et al.  Selected Topics in Column Generation , 2002, Oper. Res..

[37]  Awi Federgruen,et al.  A Combined Vehicle Routing and Inventory Allocation Problem , 1984, Oper. Res..

[38]  Awi Federgruen,et al.  Time‐partitioning heuristics: Application to one warehouse, multiitem, multiretailer lot‐sizing problems , 1999 .

[39]  Tore Grünert,et al.  Sequential search and its application to vehicle-routing problems , 2006, Comput. Oper. Res..

[40]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[41]  Dong-wan Tcha,et al.  A column generation approach to the heterogeneous fleet vehicle routing problem , 2007, Comput. Oper. Res..

[42]  Renato F. Werneck,et al.  Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem , 2004, Math. Program..

[43]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[44]  Yves Pochet Valid inequalities and separation for capacitated economic lot sizing , 1988 .

[45]  William B. Carlton,et al.  Solving the traveling-salesman problem with time windows using tabu search , 1996 .

[46]  Jonathan F. Bard,et al.  A GRASP for the Vehicle Routing Problem with Time Windows , 1995, INFORMS J. Comput..

[47]  Kin Keung Lai,et al.  A partition approach to the inventory/routing problem , 2007, Eur. J. Oper. Res..

[48]  Martin Desrochers,et al.  A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows , 1990, Oper. Res..

[49]  Gilbert Laporte,et al.  The vehicle routing problem: An overview of exact and approximate algorithms , 1992 .

[50]  G. Laporte,et al.  Exact Algorithms for the Vehicle Routing Problem , 1987 .

[51]  Richard T. Wong,et al.  An Integrated Inventory Allocation and Vehicle Routing Problem , 1989, Transp. Sci..

[52]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[53]  Lap Mui Ann Chan,et al.  Probabilistic Analyses and Practical Algorithms for Inventory-Routing Models , 1998, Oper. Res..

[54]  Christian Prins,et al.  A reactive GRASP and path relinking for a combined production-distribution problem , 2007, Comput. Oper. Res..

[55]  Laurence A. Wolsey,et al.  Multi-item lot-sizing problems using strong cutting planes , 1991 .

[56]  Laurence A. Wolsey,et al.  Lot-Sizing with Constant Batches: Formulation and Valid Inequalities , 1993, Math. Oper. Res..

[57]  Rasaratnam Logendran,et al.  Periodic product distribution from multi-depots under limited supplies , 2006 .

[58]  Bruce L. Golden,et al.  Analysis of a large scale vehicle routing problem with an inventory component , 1984 .

[59]  Celso C. Ribeiro,et al.  Reactive GRASP: An Application to a Matrix Decomposition Problem in TDMA Traffic Assignment , 2000, INFORMS J. Comput..

[60]  Gérard P. Cachon,et al.  Managing Supply Chain Demand Variability with Scheduled Ordering Policies , 1999 .

[61]  Suresh P. Sethi,et al.  A dynamic lot sizing problem with multiple customers: customer-specific shipping and backlogging costs , 2007 .

[62]  Robin Roundy,et al.  Heuristics for a One-Warehouse Multiretailer Distribution Problem with Performance Bounds , 1997, Oper. Res..

[63]  Giuseppe Paletta,et al.  A Heuristic for the Periodic Vehicle Routing Problem , 1992, Transp. Sci..

[64]  J. F. Pierce,et al.  ON THE TRUCK DISPATCHING PROBLEM , 1971 .

[65]  R. Roundy 98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems , 1985 .

[66]  C. O'Brien,et al.  Integrated enterprise and supply chain management , 2006 .

[67]  Neale R. Smith,et al.  Supply chain dynamics: analysis of inventory vs. order oscillations trade-off , 2006 .

[68]  Marshall L. Fisher,et al.  Coordination of production and distribution planning , 1994 .