A Benders Decomposition Approach for the Multivehicle Production Routing Problem with Order-up-to-Level Policy

2020 ◽  
Author(s):  
Zhenzhen Zhang ◽  
Zhixing Luo ◽  
Roberto Baldacci ◽  
Andrew Lim
Keyword(s):  
Benders Decomposition ◽  
Valid Inequalities ◽  
Planning Horizon ◽  
Set Partitioning ◽  
Master Problem ◽  
Inventory Level ◽  
Inventory Routing ◽  
Routing Problem ◽  
Decomposition Approach ◽  
Production Routing

The production routing problem (PRP) arises in the applications of integrated supply chain which jointly optimize the production, inventory, distribution, and routing decisions. The literature on this problem is quite rare due to its complexity. In this paper, we consider the multivehicle PRP (MVPRP) with order-up-to-level inventory replenishment policy, where every time a customer is visited, the quantity delivered is such that the maximum inventory level is reached. We propose an exact Benders’ decomposition approach to solve the MVPRP, which decomposes the problem as a master problem and a slave problem. The master problem decides whether to produce the product, the quantity to be produced, and the customers to be replenished for every period of the planning horizon. The resulting slave problem decomposes into a capacitated vehicle routing problem for each period of the planning horizon where each problem is solved using an exact algorithm based on the set partitioning model, and the identified feasibility and optimality cuts are added to the master problem to guide the solution process. Valid inequalities and initial optimality cuts are used to strengthen the linear programming relaxation of the master formulation. The exact method is tested on MVPRP instances and on instances of the multivehicle vendor-managed inventory routing problem, a special case of the MVPRP, and the good performance of the proposed approach is demonstrated.

scholarly journals Analysis of the effects of Lead-Time variation and Lateral Transshipment insertion in a Supply Chain Network

2021 ◽  
Author(s):  
Mohamed Salim Amri Sakhri ◽  
Mounira Tlili ◽  
Ouajdi Korbaa
Keyword(s):  
Supply Chain ◽  
Inventory Management ◽  
Planning Horizon ◽  
Inventory Level ◽  
Inventory Routing ◽  
Routing Problem ◽  
Network Cost ◽  
Lateral Transshipment ◽  
The Impact ◽  
Number Of Customers

Abstract In a supply chain, inventory is the single largest source of costs for a company. This is due to the various physical and informational activities that accompany inventory management, primarily the holding and transportation of inventory. Companies are looking to streamline these activities and minimize the associated costs. One of the most coveted models to jointly solve these two problems is the Inventory Routing Problem (IRP), which will be the focus of this study. This paper addresses the case of a deterministic replenishment demand in a distribution network consisting of a supplier and a number of customers to be served by a single vehicle over a finite planning horizon. We will first study the impact of increasing supplier lead times on network costs. Then, we will study the effects of the Lateral Transshipment (LT) technique on the overall network cost. A mathematical model is developed and solved by an exact method. The results obtained will show that LT is an effective tool capable of improving the total network cost and balancing the customers’ inventory level.

scholarly journals A Decomposition Approach for Stochastic Shortest-Path Network Interdiction with Goal Threshold

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 237 ◽  
Author(s):  
Xiangyu Wei ◽  
Kai Xu ◽  
Peng Jiao ◽  
Quanjun Yin ◽  
Yabing Zha
Keyword(s):  
Shortest Path ◽  
Real World ◽  
Benders Decomposition ◽  
Research Problem ◽  
Resource Consumption ◽  
Network Interdiction ◽  
Master Problem ◽  
Decomposition Approach ◽  
Stochastic Shortest Path ◽  
T Path

Shortest-path network interdiction, where a defender strategically allocates interdiction resource on the arcs or nodes in a network and an attacker traverses the capacitated network along a shortest s-t path from a source to a terminus, is an important research problem with potential real-world impact. In this paper, based on game-theoretic methodologies, we consider a novel stochastic extension of the shortest-path network interdiction problem with goal threshold, abbreviated as SSPIT. The attacker attempts to minimize the length of the shortest path, while the defender attempts to force it to exceed a specific threshold with the least resource consumption. In our model, threshold constraint is introduced as a trade-off between utility maximization and resource consumption, and stochastic cases with some known probability p of successful interdiction are considered. Existing algorithms do not perform well when dealing with threshold and stochastic constraints. To address the NP-hard problem, SSPIT-D, a decomposition approach based on Benders decomposition, was adopted. To optimize the master problem and subproblem iteration, an efficient dual subgraph interdiction algorithm SSPIT-S and a local research based better-response algorithm SSPIT-DL were designed, adding to the SSPIT-D. Numerical experiments on networks of different sizes and attributes were used to illustrate and validate the decomposition approach. The results showed that the dual subgraph and better-response procedure can significantly improve the efficiency and scalability of the decomposition algorithm. In addition, the improved enhancement algorithms are less sensitive and robust to parameters. Furthermore, the application in a real-world road network demonstrates the scalability of our decomposition approach.

scholarly journals Production, Replenishment and Inventory Policies for Perishable Products in a Two-Echelon Distribution Network

2020 ◽  
Vol 12 (11) ◽  
pp. 4735
Author(s):  
Mingyuan Wei ◽  
Hao Guan ◽  
Yunhan Liu ◽  
Benhe Gao ◽  
Canrong Zhang
Keyword(s):  
Inventory Management ◽  
Valid Inequalities ◽  
Distribution Network ◽  
Planning Horizon ◽  
Branch And Cut ◽  
Computational Time ◽  
Perishable Products ◽  
Inventory Cost ◽  
Routing Problem ◽  
Selection Of

The research on production, delivery and inventory strategies for perishable products in a two-echelon distribution network integrates the production routing problem (PRP) and two-echelon vehicle routing problem (2E-VRP), which mainly considers the inventory and delivery sustainability of perishable products. The problem investigated in this study is an extension of the basic problems, and it simultaneously optimizes production, replenishment, inventory, and routing decisions for perishable products that will deteriorate over the planning horizon. Additionally, the lead time has been considered in the replenishment echelon, and the unit inventory cost varying with the inventory time is considered in the inventory management. Based on a newly designed model, different inventory strategies are discussed in this study: old first (OF) and fresh first (FF) strategies both for the first echelon and second echelon, for which four propositions to model them are proposed. Then, four valid inequalities, including logical inequalities, a ( ℓ , S , W W ) inequality, and a replenishment-related inequality, are proposed to construct a branch-and-cut algorithm. The computational experiments are conducted to test the efficiency of valid inequalities, branch-and-cut, and policies. Experimental results show that the valid inequalities can effectively increase the relaxed lower bound by 4.80% on average and the branch-and-cut algorithm can significantly reduce the computational time by 58.18% on average when compared to CPLEX in small and medium-sized cases. For the selection of strategy combinations, OF–FF is suggested to be used in priority.

Stochastic inventory-routing problem with lateral transshipment for perishable product

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Parviz Fattahi ◽  
Mehdi Tanhatalab
Keyword(s):  
Supply Chain ◽  
Valid Inequalities ◽  
Upper And Lower Bounds ◽  
Inventory Routing ◽  
Routing Problem ◽  
Content Type ◽  
Inventory Routing Problem ◽  
Perishable Product ◽  
New Variant ◽  
Lateral Transshipment

Purpose This study aims to design a supply chain network in an uncertain environment while exists two options for distribution of the perishable product and production lot-sizing is concerned. Design/methodology/approach Owing to the complexity of the mathematical model, a solution approach based on a Lagrangian relaxation (LR) heuristic is developed which provides good-quality upper and lower bounds. Findings The model output is discussed through various examples. The introduction of some enhancements and using some heuristics results in better outputs in the solution procedure. Practical implications This paper covers the modeling of some real-world problems in which demand is uncertain and managers face making some concurrent decisions related to supply chain management, transportation and logistics and inventory control issues. Furthermore, considering the perishability of product in modeling makes the problem more practically significant as these days there are many supply chains handling dairy and other fresh products. Originality/value Considering uncertainty, production, transshipment and perishable product in the inventory-routing problem makes a new variant that has not yet been studied. The proposed novel solution is based on the LR approach that is enhanced by some heuristics and some valid inequalities that make it different from the current version of the LR used by other studies.

scholarly journals Cover Inequalities for a Vehicle Routing Problem with Time Windows and Shifts

2019 ◽  
Vol 53 (5) ◽  
pp. 1354-1371 ◽  
Author(s):  
Said Dabia ◽  
Stefan Ropke ◽  
Tom van Woensel
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Valid Inequalities ◽  
Time Windows ◽  
Branch And Cut ◽  
Master Problem ◽  
Loading Capacity ◽  
Routing Problem ◽  
Cover Inequalities ◽  
And Shifts

This paper introduces the vehicle routing problem with time windows and shifts (VRPTWS). At the depot, several shifts with nonoverlapping operating periods are available to load the planned trucks. Each shift has a limited loading capacity. We solve the VRPTWS exactly by a branch-and-cut-and-price algorithm. The master problem is a set partitioning with an additional constraint for every shift. Each constraint requires the total quantity loaded in a shift to be less than its loading capacity. For every shift, a pricing subproblem is solved by a label-setting algorithm. Shift capacity constraints define knapsack inequalities; hence we use valid inequalities inspired from knapsack inequalities to strengthen the linear programming relaxation of the master problem when solved by column generation. In particular, we use a family of tailored robust cover inequalities and a family of new nonrobust cover inequalities. Numerical results show that nonrobust cover inequalities significantly improve the algorithm.

Combinatorial Heuristics for Inventory Routing Problems

2021 ◽  
Author(s):  
Ziye Tang ◽  
Yang Jiao ◽  
R. Ravi
Keyword(s):  
Steiner Tree ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Inventory Routing ◽  
Optimal Solutions ◽  
Routing Problem ◽  
Holding Costs ◽  
Prize Collecting ◽  
Finite Time Horizon

We consider the deterministic inventory routing problem over a discrete finite time horizon. Given clients on a metric, each with daily demands that must be delivered from a depot and holding costs over the planning horizon, an optimal solution selects a set of daily tours through a subset of clients to deliver all demands before they are due and minimizes the total holding and tour routing costs over the horizon. In the capacitated case, a limited number of vehicles are available, where each vehicle makes at most one trip per day. Each trip from the depot is allowed to carry a limited amount of supply to deliver. We develop fast heuristics for both cases by solving a family of prize-collecting Steiner tree instances. Computational experiments show our heuristics can find near-optimal solutions for both cases and substantially reduce the runtime compared with a pure mixed integer programming formulation approach.

A Decomposition Approach to the Inventory Routing Problem with Satellite Facilities

1998 ◽  
Vol 32 (2) ◽  
pp. 189-203 ◽  
Author(s):  
Jonathan F. Bard ◽  
Liu Huang ◽  
Patrick Jaillet ◽  
Moshe Dror
Keyword(s):  
Inventory Routing ◽  
Routing Problem ◽  
Decomposition Approach ◽  
Inventory Routing Problem

An Exact Algorithm for Heterogeneous Drone-Truck Routing Problem

2021 ◽  
Author(s):  
Munjeong Kang ◽  
Chungmok Lee
Keyword(s):  
Benders Decomposition ◽  
Waiting Times ◽  
Exact Algorithm ◽  
Mixed Integer ◽  
Routing Problem ◽  
Decomposition Approach ◽  
Proposed Model ◽  
Battery Capacity ◽  
Truck Routing ◽  
Different Characteristics

Recently, there are attempts to utilize drones in the logistic application. We consider the case in which there are multiple drones with different characteristics, such as speed and battery capacity. The truck and drone collaborate the delivery to serve all customers, while the drones are carried by and dispatched from the truck. The multiple drones can be deployed simultaneously; however, the truck must wait until all drones return. Therefore, the goal is to minimize the total sum of truck travel and waiting times for drones to return after deliveries. We call the proposed model a heterogeneous drone-truck routing problem (HDTRP), and a mixed-integer programming formulation for the problem is presented. We develop an exact algorithm based on the logic-based Benders decomposition approach, which outperforms the state-of-the-art solvers.

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