Integrated production inventory routing planning with time windows for perishable food

This paper investigates an integrated production inventory routing problem with time windows where a central depot is responsible for supplying single type of perishable food to multiple retailers within the planned time horizon. A mixed integer linear programming (MILP) model aiming at maximizing the total profit is formulated with explicitly tracing the food quality. To strengthen the formulation, a series of valid inequalities are introduced. Randomly generated instances with up to 40 retailers and 3 time periods are used to verify the effectiveness and the complexity of the proposed model, which is solved by the linear programming solver CPLEX. The computational results show that the proposed model is able to provide integrated plan for the decision makers, and instances with 20 retailers and 3 time periods are optimally solved with 102.97s on average. The results also indicate that the introduced valid inequalities are useful in helping CPLEX generate better upper bounds (maximization problem) for 20 out of 23 instances that are not optimally solved within the time limit.

[1]  Russell L. Ackoff,et al.  Optimization + objectivity = optout , 1977 .

[2]  Steven Nahmias,et al.  Perishable Inventory Theory: A Review , 1982, Oper. Res..

[3]  Stefan Voß,et al.  Integrating deterioration and lifetime constraints in production and supply chain planning: A survey , 2014, Eur. J. Oper. Res..

[4]  Gilbert Laporte,et al.  Optimal joint replenishment, delivery and inventory management policies for perishable products , 2014, Comput. Oper. Res..

[5]  Jonathan F. Bard,et al.  The integrated production–inventory–distribution–routing problem , 2009, J. Sched..

[6]  Jun Zhang,et al.  Quality control in food supply chain management: An analytical model and case study of the adulterated milk incident in China , 2014 .

[7]  Wei Zhou,et al.  RFID and item-level information visibility , 2009, Eur. J. Oper. Res..

[8]  P. Amorim,et al.  Managing perishability in production-distribution planning: a discussion and review , 2013 .

[9]  Ruud H. Teunter,et al.  Review of inventory systems with deterioration since 2001 , 2012, Eur. J. Oper. Res..

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

[11]  Iftekhar A. Karimi,et al.  Integrated Supply Chain Planning for Multinational Pharmaceutical Enterprises , 2011 .

[12]  Abbas Seifi,et al.  Considering lost sale in inventory routing problems for perishable goods , 2015, Comput. Ind. Eng..

[13]  Renzo Akkerman,et al.  Quality, safety and sustainability in food distribution: a review of quantitative operations management approaches and challenges , 2010, OR Spectr..

[14]  Luca Bertazzi,et al.  A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem , 2007, Transp. Sci..

[15]  Josefa Mula,et al.  A review of tactical optimization models for integrated production and transport routing planning decisions , 2015, Comput. Ind. Eng..

[16]  Hans-Otto Günther,et al.  Multi-objective integrated production and distribution planning of perishable products , 2012 .

[17]  Mingzhou Jin,et al.  Cross-Facility Production and Transportation Planning Problem with Perishable Inventory , 2006, ICCSA.

[18]  Yuehwern Yih,et al.  A column generation-based heuristic algorithm for an inventory routing problem with perishable goods , 2012, Optim. Lett..

[19]  T. Liao,et al.  A new age-based replenishment policy for supply chain inventory optimization of highly perishable products , 2013 .

[20]  Leandro C. Coelho,et al.  Improved solutions for inventory-routing problems through valid inequalities and input ordering , 2014 .

[21]  R. Akkerman,et al.  An optimization approach for managing fresh food quality throughout the supply chain , 2011 .

[22]  Feng Chu,et al.  A Production Inventory Routing Planning for Perishable Food with Quality Consideration , 2016 .

[23]  H. Wee,et al.  Integrated inventory model for deteriorating items under a multi-echelon supply chain environment , 2003 .

[24]  D. L. Woodruff,et al.  Production Planning and Deterioration Constraints: A Survey , 2007 .

[25]  Kannan Govindan,et al.  Two-echelon multiple-vehicle location-routing problem with time windows for optimization of sustainable supply chain network of perishable food , 2014 .

[26]  Mei-Shiang Chang,et al.  Production scheduling and vehicle routing with time windows for perishable food products , 2009, Comput. Oper. Res..

[27]  Wei Huang,et al.  A Heuristic Approach to the Multi-Period Single-Sourcing Problem with Production and Inventory Capacities and Perishability Constraints , 2007, INFORMS J. Comput..

[28]  Jean-François Cordeau,et al.  The production routing problem: A review of formulations and solution algorithms , 2015, Comput. Oper. Res..

[29]  J. Bloemhof-Ruwaard,et al.  Modeling an Inventory Routing Problem for perishable products with environmental considerations and demand uncertainty , 2015 .

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

[31]  Eylem Tekin,et al.  Age-based vs. stock level control policies for a perishable inventory system , 2001, Eur. J. Oper. Res..

[32]  Jesus René Villalobos,et al.  Application of planning models in the agri-food supply chain: A review , 2009, Eur. J. Oper. Res..

[33]  ChenHuey-Kuo,et al.  Production scheduling and vehicle routing with time windows for perishable food products , 2009 .