Variable Transportation Costs Research Articles

Research on a Joint Distribution Vehicle Routing Problem Considering Simultaneous Pick-Up and Delivery under the Background of Carbon Trading

In order to explore the positive impact of the joint distribution model on the reduction in logistics costs in small-scale logistics enterprises, considering the demand on enterprises for simultaneous pick-up and delivery, as well as the cost of carbon emissions, this study considers the vehicle routing problem of simultaneous pick-up and delivery under a joint distribution model. First of all, an independent distribution model and a joint distribution model including fixed transportation, variable transportation, time penalty, and carbon emissions costs are established; second, by adding the self-adaption cross-mutation probability and the destruction and repair mechanism in the large-scale neighborhood search algorithm, the genetic algorithm is improved to adapt to the solution of the model in this paper, and the effectiveness of the improved algorithm is verified and analyzed. It is found that the improved genetic algorithm is more advantageous than the original algorithm for solving the problems of both models designed in this paper. Finally, the improved genetic algorithm is used to solve the two models, and the results are compared and analyzed. It is found that the joint distribution model can reduce the total cost by 6.61% and the carbon emissions cost by 5.73%. Additionally, the impact of the carbon trading mechanism on the simultaneous pick-up and delivery vehicle routing problem under the joint distribution model is further explored. The results of this study prove that enterprises can effectively reduce costs, improve profits, reduce carbon emissions, and promote the sustainable development of logistics enterprises under the condition of joint distribution.

Payment policy for a three-echelon supply chain management under advertisement-driven demand

Payment and selling are two important policies for a supply chain management. All participating supply chain players can earn profit based on the successful implementation of these two policies. The payment policy provides buyers some extra time to pay for the product. This research introduces a single-supplier, a single-manufacturer, and multi-retailer-based three-echelon supply chain management under advertising and payment policies. Product delivery among supply chain players is made with the help of a transportation policy. The transportation policy is environment-friendly and helps retailers with their cost management. It is demonstrated that advertising positively influences sales through an advertisement-driven market demand for the product. The model aims to reduce supply chain cost and maximizes profit by considering a single-setup multiple-delivery policy, variable transportation cost, variable carbon emissions costs, and trade-credit policy. The objective function is optimized for cases: Case 1 and Case 2, based on the payment period. A classical optimization method is employed to obtain the solution of the model. A numerical example, sensitivity analysis, and graphical representations are given to illustrate the model. Results show that Case 2, where cycle time is greater than the payment period, is 45.36% more profitable than Case 1.

Improved Lagrangian-relaxation based approaches for multi-period multi-stage fixed charge transportation problem

This paper considers the Fixed-Charge Transportation Problem (FCTP), which spans multiple time periods and includes multiple stages, termed as Multi-Period, Multi-Stage Fixed-Charge Transportation Problem (MPMS-FCTP) in a supply chain. A generalised mathematical model which minimises the fixed and variable transportation, storage and backlog costs is proposed for the problem under study. Subsequently, two improved Lagrangian-Relaxation (LR)-based approaches are developed to efficiently solve the MPMS-FCTP. In addition, heuristics based on the improved LR approaches are proposed to obtain good upper bounds. The experimental results show that the proposed LR approaches perform better than the traditional LR approach with the sub-gradient optimisation. The lower bounds obtained using the proposed approaches are always non-decreasing in successive iterations of LR, providing tighter lower bounds. In addition, the proposed LR-based heuristics yield better solutions than the existing heuristics in the literature. Finally, the convergence to optimality of the proposed approaches is also discussed.

Multiple allocation hub location with service level constraints for two shipment classes

In this paper, we study a hub network design problem arising in the context of a third-party logistics (3PL) service provider, which acts as an intermediary between shippers and carriers. A 3PL service provider usually caters to different classes of shipments that require different levels of service, e.g. two-day delivery, next-day delivery etc. We, therefore, study the problem under stochastic demand from two classes of shipments, with one class receiving priority over the other in service at the hubs to maintain the different service levels required by them. To this end, we present two models for designing a capacitated hub network with a service level constraint, defined using the distribution of time spent at hubs, for each shipment class. The models seek to design the hub network at the minimum total cost, which includes the total fixed cost of equipping open hubs with sufficient processing capacity and the variable transportation costs. The network of hubs, given their locations, is thus modeled as spatially distributed priority queues. The resulting model is challenging to solve, for which we propose a cutting plane-based exact solution method.

Modified metaheuristic algorithms to design a closed-loop supply chain network considering quantity discount and fixed-charge transportation

Discount is an efficient way to reduce the closed-loop supply chain costs, and applying it would make the model closer to real ones. In this paper, the quantity discount is firstly applied along with fixed and variable transportation costs. The application of well-known, efficient algorithms, alongside developing modified versions to address the developed model is another contribution of this study. To calibrate the proposed algorithms’ parameters and operators, the Taguchi method is used. In this regard, several test problems in different sizes are generated considering the concerns of real-world cases, and the algorithms’ efficiencies are investigated by the relative percentage deviation method. The results show the superior performance of the hybrid algorithm of modified differential evolution and restart mechanism (MDE_Restart) and the algorithm of modified differential evolution (MDE) compared to the other employed algorithms.

Modelling and optimising the capacity and production network planning in plastics processing factories

ABSTRACT This paper deals with the capacity planning and production network planning in plastics processing factories. We lay emphasis on the opportunity and – potentially – necessity to move machines, tools and material. Furthermore, we consider the option to outsource production to external suppliers. Demand is deterministic and has to be satisfied in the same period. We present a linear mixed integer programming model representing the problem to find a minimum-cost production plan where total cost accounts for variable production cost, setup cost, transportation cost, relocation cost and cost caused by machine purchases. The decisions to be made are the allocation of machines to plants. This includes to decide for investments or relocating machines between plants. In addition, the allocation of products to machines and the determination of the corresponding optimal quantities of production, purchase and transportation within the network of suppliers, plants and customers are decided. We provide a computational study validating the model and conduct a sensitivity analysis of the run time using an off-the-shelf solver. Finally, we present a real-world case of an international automobile supplier. Tackling the instance with an off-the-shelf solver the problem cannot be solved in reasonable time. Thus we apply a simple decomposition scheme to provide decision support for the real-world case.

Proposing a model for a resilient supply chain: A meta-heuristic algorithm

The resilient supply chain considers many capabilities for companies to overcome financial crises and to supply and distribute products. In this study, we address the allocation of inventory distribution for a distribution network, including a factory, a number of potential locations for distribution centers and a number of retailers. Customers demand is assumed to be certain and deterministic for all periods but time varying in the limited planning horizon. The proposed model in this research is a linear complex integer programming model with two-objective functions. The first objective function minimizes the total costs of the entire distribution system in the planning horizon, and the second objective function seeks to minimize the difference between the maximum and minimum distances traveled by vehicles over the planning horizon. Therefore, the model tries to satisfy the demand and at the same time reduce costs using the best route transportation option configuration and transportation option. The routing problem is developed, and as the problem is a NP-hard problem, a meta-heuristic method is used to solve it. In this model, the demand volume for each customer in a period of the network, vehicle capacity, factory capacity, constant transportation cost, variable transportation cost, etc., are considered as factors affecting the model. The results show that the model proposed in the network can be used as a lever to improve the performance of the financial economic supply network through saving in routes.

Multi-echelon green supply chain model with random defectives, remanufacturing and rework under setup cost reduction and variable transportation cost

Multi-echelon green supply chain model with random defectives, remanufacturing and rework under setup cost reduction and variable transportation cost

ANALISIS PEMILIHAN MODA TRANSPORTASI ONLINE DAN TRANSPORTASI KONVENSIONAL DI KOTA DENPASAR (Contoh Kasus: Go-Car dan Sarbagita)

Transportation is very necessary to meet the main needs of society in general in Denpasar, such as the need for education, health, economy, and social. Currently, there are various choices of vehicles or modes of transportation that you want to use to reach your destination, be it online transportation (Go-Car) or conventional transportation (Sarbagita). The choice of transportation modes in Denpasar City aims to find out the factors that influence the community in choosing the online mode of transportation (Go - Car) and conventional transportation (Sarbagita). The questionnaire in this study was in the form of google form and then distributed via online media to respondents and processed using a multiple linear regression analysis approach with the help of the SPSS V25 program. The results of the study of 100 respondents were 94 respondents who chose the online mode of transportation (Go-Car) and 6 respondents who chose the conventional mode of transportation (Sarbagita). From the results of the data analysis shows that the variable transportation cost variation (x1) affects the community in choosing the transportation mode in Denpasar City by 21% with the choice of conventional transportation mode (Sarbagita), variations in waiting time (x2) affect the community in choosing the mode of transportation in Denpasar City. 58.5% with the choice of online transportation mode (Go-Car), variations in the level of comfort (x3) affecting the community in Denpasar City by 17.3% with the choice of online transportation mode (Go-Car).

A hybrid metaheuristic algorithm for location inventory routing problem with time windows and fuel consumption

We introduce a multi-period location-inventory-routing problem with time windows and fuel consumption, which simultaneously optimizes the location, routing, and inventory decisions for both the distribution center and customers in a multi-echelon supply chain. To better reflect reality, the fuel consumption is also incorporated into the variable transportation cost. The problem is formulated as a mixed integer nonlinear programming model. We then propose a two-stage hybrid metaheuristic algorithm to address this problem. In the first stage, a customized genetic algorithm is proposed. In the second stage, a gradient descent algorithm is used to improve the inventory decision to further reduce the total cost. Results of numerical experimentations on generated instances confirm the effectiveness of the algorithm. Results show that inventory management activities contribute considerably to total cost saving. Given the cost trade-off between transportation and inventory, the retailers’ inventory level shows more shortages after post-optimization, while the inventory level in the distribution centers can be either reduced or increased, depending on the spatial distribution of retailers in the vicinity of the distribution center. Sensitivity analysis on the model parameters is also conducted to provide managerial insights.

An Efficient Hybrid Genetic Approach for Solving the Two-Stage Supply Chain Network Design Problem with Fixed Costs

This paper deals with a complex optimization problem, more specifically the two-stage transportation problem with fixed costs. In our investigated transportation problem, we are modeling a distribution network in a two-stage supply chain. The considered two-stage supply chain includes manufacturers, distribution centers, and customers, and its principal feature is that in addition to the variable transportation costs, we have fixed costs for the opening of the distribution centers, as well as associated with the routes. In this paper, we describe a different approach for solving the problem, which is an effective hybrid genetic algorithm. Our proposed hybrid genetic algorithm is constructed to fit the challenges of the investigated supply chain network design problem, and it is achieved by incorporating a linear programming optimization problem within the framework of a genetic algorithm. Our achieved computational results are compared with the existing solution approaches on a set of 150 benchmark instances from the literature and on a set of 50 new randomly generated instances of larger sizes. The outputs proved that we have developed a very competitive approach as compared to the methods that one can find in the literature.

Influence of controllable lead time, premium price, and unequal shipments under environmental effects in a supply chain management

Recently, carbon emission becomes a major issue during transportation of products from one player to another player. Due to the increasing number of single-setup-multi-delivery (SSMD) policies by several industries, fixed and variable transportation cost and carbon emission cost are considered. The aim of the model is to reduce the total cost of supply chain for controlling the lead time and to diminish setup cost by a discrete investment. A premium cost is introduced and Stackelberg game policy is employed to obtain the analytical solution. Some numerical examples are given to validate the model. Sensitivity analysis and managerial insights are given to show the applicability of the model. Finally, the outcomes show that the model minimizes the optimum cost at the optimal values of the decision variables. It is found that the total cost is minimized when the multi-buyer is leader and vendor is follower.

Stochastic vehicle routing problem with heterogeneous vehicles and multiple prioritized time windows: Mathematical modeling and solution approach

This study addresses the vehicle routing problem with multiple hard prioritized time windows (VRPMPTW) with heterogeneous fleet of vehicles based on restrictions of a real-life distribution system. Three multi-objective models are proposed to address the VRPMPTW from different perspectives. The first one formulates the VRPMPTW, where travel times and transportation costs are deterministic. In the second model, a linear bi-objective model with stochastic fixed and variable transportation costs is developed to minimize total transportation costs and maximize satisfaction of customers, simultaneously. Third, a novel multi-objective stochastic VRPMPTW model, where travel times and costs are normal random variables. Due to the NP-hard essence of the problem, a binary artificial bee colony (ABC) algorithm is developed to solve the problem. The ABC algorithm is tuned via the Taguchi method. To validate the proposed algorithm, the results obtained by the ABC algorithm are compared with the optimal solutions of several small-size test problems. For the case study tackled in this paper, the ABC algorithm is utilized to solve the problem. The results of the binary ABC algorithm are approved by management experts.

On the Two-Stage Transportation Problem With Fixed Charge for Opening the Distribution Centers

In this paper, we are addressing the two-stage transportation problem with fixed charge for opening the distribution centers, which is an extension of the classical transportation problem. The problem models a distribution network in a two-stage supply chain which involves: manufacturers, distribution centers and customers, and its main characteristic is that a fixed charge for opening the distribution centers is associated, in addition to the variable transportation cost which is proportional to the amount of goods shipped. We describe a novel solution approach for the minimization of total distribution costs: a fast and efficient constructive heuristic algorithm that reduces the solution search space to a subspace with a reasonable size, without losing optimal or sub-optimal solutions by considering a perturbation mechanism that allows us to reconsider discarded feasible solutions that might lead to such solutions. Computational results are reported and discussed for the existing benchmark instances and on a set of instances that contains eight new randomly generated larger instances. The obtained results show that our solution approach is highly competitive as compared to the existing methods from the literature.

A holistic framework for lot sizing problem in fast-moving perishable products

One of the major challenges being faced by manufacturing companies today is the issue of addressing various aspects of perishable products in a supply chain environment. To address this issue, the integrated lot size problem for a perishable product has been investigated in the present work. The problem is modeled as a single vendor multiple buyer system. A variant of the truckload discount scheme is applied and the proposed model is formulated as a mixed integer program (MIP). The traditional warehouses are replaced by ‘cross-docks’ and situations in which, cross-docking would be more beneficial are highlighted. The problem of fleet selection is also addressed and various strategies to minimize the vendor cost are also highlighted for centralized and decentralized supply chains. Sensitivity analysis is then carried out on various input parameters such as setup cost at plant, variable transportation cost, fixed transportation cost, setup cost per order, holding cost and, lost cost, which underscores the significant impact of economies of scale in transportation on the total supply chain cost. Analysis of lead time-cost trade-off reveals that alternate modes of transportation could be explored, which significantly reduces the lead time of transportation, thereby minimizing the total supply chain cost.

Prioritized K-mean clustering hybrid GA for discounted fixed charge transportation problems

Abstract The problem of allocating different types of vehicles for transporting a set of products in an existing transportation network, to minimize the total transportation costs, is considered. The distribution network involves a heterogeneous fleet of vehicles each with the given capacity and with a variable transportation cost and a fixed cost with a discounting mechanism. Due to nonlinearity of the discounting mechanism, a nonlinear mathematical programming model is developed. A prioritized K-mean clustering encoding is introduced to designate the distribution depots distances, their demands, and the vehicles’ capacity. Using this priority clustering, a heuristic routine is developed by which heavy capacity vehicles are assigned to the longer distance depots. Then the proposed heuristic is incorporated into a new GA to construct a hybrid GA. Through an extensive computational experiment, first the algorithm parameters are tuned using “factorial experimental designs”, and then the efficiency of the proposed algorithm is compared with the powerful package of the CPLEX solver (OPL 12.3.0.1 Model) and two existing algorithms. The results are revealed that the proposed algorithm can provide superior solutions with the minimal computational effort.

Fuel Consumption Optimization Model for the Multi-Period Inventory Routing Problem

In the traditional multi-period inventory routing problem (MIRP), traveling distance is considered as the only measurement of vehicles’ variable transportation cost; however, it is in fact the fuel consumption cost, not the distance, which is the greater concern. This paper evaluates vehicles’ variable transportation cost by fuel consumption, which is influenced by distance, load, and fuel price. It presents an integer program to formally characterize the fuel consumption considered MIRP (FCMIRP), which can help enterprises obtain a more accurate tradeoff between transportation and inventory costs. It also benefits the environment, because reducing fuel consumption will curb carbon dioxide (CO2) emissions. Valid inequalities are added to strengthen the model and use a branch-and-cut algorithm. Computational tests indicate that the FCMIRP can decrease fuel consumption and total cost over the traditional model. Factors that influence the results of FCMIRP are also discussed.

Joint effects of variable carbon emission cost and multi-delay-in-payments under single-setup-multiple-delivery policy in a global sustainable supply chain

Abstract In today's global market, supply chain players have to cooperate mutually for extra benefits, long lasting paybacks, and to control carbon emission for a clean environment. This study develops the three-echelon sustainable supply chain model in the context of multi-level trade credit and single-setup-multiple-delivery policy for mutual coordination in financial support and reducing carbon emissions. These joint effects will benefit the firms for interim financing as well as minimize carbon emission for a clean environment. This model quantifies the effects of the environmental regulations and trade credit period under the single-setup-multiple-delivery policy. The supplier produces semi-finished items and transports it to the manufacturer, the manufacturer transform these semi-finished items into final products. These finished products finally transported to multi-retailer. The shipments are permitted to proceed from the particular lot during production instead after completing the entire lot This strategy save the environment by minimizing carbon emission. Additionally, a multi-level trade credit policy is considered in this model for short-term investment. An algebraic approach is used to derive a closed form optimal result for the designed model. This non-derivative method provides the effective solution algorithm. The main contribution of this study is to minimize the sustainable supply chain cost of the system by jointly considering the multi-level delay-in-payment, variable carbon emission cost, and variable transportation cost under the single-setup-multi-delivery policy. The study presents an optimal solution for the individual scenario and also derived a comparison between them with a numerical example. The findings directed that implementation of multi-level trade credit under single setup-multiple-delivery improves the economic and environmental performance of three-echelon supply chain. Sensitivity analysis of the developed study is also illustrated to prove the real practice.

An integrated inventory model with variable transportation cost, two-stage inspection, and defective items

The paper deals with an integrated inventory model with make-to-order policy from buyer to vendor. A variable transportation cost is used as a power function of the delivery quantity for either tapering or considering proportional rate data to maintain single-setup multi-delivery (SSMD) policy with reduced transportation cost. A two-stage inspection process is introduced by the vendor to ensure the perfect quality of product even though the first inspection process indicates a constant defective rate of imperfect production is present during the long-run production system and all defective items are reworked with some fixed cost. The aim is to minimize the total cost of the integrated inventory model by using classical optimization technique. Two numerical examples, sensitivity analysis, and graphical representations are given to illustrate the model.

Effect of variable transportation and carbon emission in a three-echelon supply chain model

Several industries controls carbon emission during transporting products due to increased transportation for obtaining the best transportation way with reduced cost. This study considers a three-echelon supply chain model where the supplier makes semi-finished products and transports to manufacturer for finished products. The manufacturer transports products by single-setup-multi-delivery policy to multi-retailer. The aim of the model is to reduce the supply chain cost by considering variable transportation and carbon emission costs are considered due to several shipments. An algebraic approach is employed to obtain the closed-form solution. Numerical example, sensitivity analysis, and graphical representations are given to illustrate the model.