https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2013-49.pdf

The production routing problem

The inventory routing problem (IRP) and the production routing problem (PRP) are two difficult problems arising in the planning of integrated supply chains. These problems are solved in an attempt to jointly optimize production, inventory, distribution, and routing decisions. Although several studies have proposed exact algorithms to solve the single-vehicle problems, the multivehicle aspect is often neglected because of its complexity. We introduce multivehicle PRP and IRP formulations, with and without a vehicle index, to solve the problems under both the maximum level (ML) and order-up-to level (OU) inventory replenishment policies. The vehicle index formulations are further improved using symmetry breaking constraints; the nonvehicle index formulations are strengthened by several cuts. A heuristic based on an adaptive large neighborhood search technique is also developed to determine initial solutions, and branch-and-cut algorithms are proposed to solve the different formulations. The results show tha...

Formulations and Branch-and-Cut Algorithms for Multivehicle Production and Inventory Routing Problems

Formulations and Branch-and-Cut Algorithms for Multi-Vehicle Production and Inventory Routing Problems

Operational problems arising in the planning of integrated supply chains have been increasingly studied in the past decade. Among these, the production routing problem (PRP) is a difficult problem that aims to jointly optimize production, inventory, distribution, and routing decisions in order to satisfy the dynamic demand of customers and minimize the overall system cost. This paper introduces an optimization-based adaptive large neighborhood search heuristic for the PRP. In this heuristic, binary variables representing setup and routing decisions are handled by an enumeration scheme and upper-level search operators, respectively, and continuous variables associated with production, inventory, and shipment quantities are set by solving a network flow subproblem. Extensive computational experiments have been performed on benchmark instances from the literature. The results show that our algorithm generally outperforms existing heuristics for the PRP and can produce high-quality solutions in short computin...

Optimization-Based Adaptive Large Neighborhood Search for the Production Routing Problem

https://hal-emse.ccsd.cnrs.fr/emse-01792227/document

Single-item dynamic lot-sizing problems: An updated survey

The production-routing problem can be seen as a combination of two well known combinatorial optimization problems: the lotsizing and the vehicle routing problems. The variant considered in this paper consists in designing a production schedule for an uncapacitated plant, replenishment schedules for multiple customers, and a set of routes for a single uncapacitated vehicle starting and ending at the plant. The aim of the problem is to fulfill the demand of the customers over a finite horizon such that the total cost of distribution, setups, and inventories is minimized. This paper introduces a basic mixed integer linear programming formulation and several strong reformulations of the problem. Two families of valid inequalities, 2-matching and generalized comb inequalities, are introduced to strengthen these formulations, and they are used within a branch-and-cut algorithm. Computational results on a large set of randomly generated instances are presented. Instances with up to 40 customers and 15 time periods or with 80 customers and 8 periods have been solved to optimality within a two-hour limit. The tests clearly indicate the effectiveness of the new formulations and of the valid inequalities. In addition, an uncoordinated approach is considered to demonstrate the benefits of the simultaneous optimization of production and distribution planning. The total cost increases on average by 47% when employing such an uncoordinated approach. Finally, a heuristic algorithm, based on defining an a priori tour for the vehicle routing part, is investigated. The heuristic algorithm shows an excellent performance. The average CPU time is less than 1% of the CPU time for the optimal solution, whereas the average cost increase is only 0.33%.

Mirko Ruokokoski

Papers

Efficient Formulations and a Branch-and-Cut Algorithm for a Production-Routing Problem