Maximum Delivery Time Research Articles

Developing a Robust Multi-Skill, Multi-Mode Resource-Constrained Project Scheduling Model with Partial Preemption, Resource Leveling, and Time Windows

Real-world projects encounter numerous issues, challenges, and assumptions that lead to changes in scheduling. This exposure has prompted researchers to develop new scheduling models, such as those addressing constrained resources, multi-skill resources, and activity pre-emption. Constrained resources arise from competition among projects for limited access to renewable resources. This research presents a scheduling model with constrained multi-skill and multi-mode resources, where activity durations vary under different scenarios and allow for partial pre-emption due to resource shortages. The main innovation is the pre-emption of activities when resources are unavailable, with defined minimum and maximum delivery time windows. For this purpose, a multi-objective mathematical programming model is developed that considers Bertsimas and Sim’s robust model in uncertain conditions. The model aims to minimize resource consumption, idleness, and project duration. The proposed model was solved using a multi-objective genetic algorithm and finally, its validation was completed and confirmed. Analysis shows that limited renewable resources can lead to increased activity pre-emption and extended project timelines. Additionally, higher demand raises resource consumption, reducing availability and prolonging project duration. Increasing the upper time window extends project time while decreasing the lower bound pressures resources, leading to higher consumption and resource scarcity.

Исследование особенностей использования рекламного инструмента «Продвижение в поиске» на площадке Wildberries

This article explores the current dynamics among entrepreneurs on the rapidly growing Wildberries market-place. The main emphasis is placed on the strategies that sellers choose to maximize sales and ensure that their goods are viewed by a wide audience of users. It is emphasized that self-purchase tactics used to be widespread. However, the Wildberries platform-imposed sanctions against it, which forced entrepreneurs to focus on internal advertising. One of the key areas of focus has been the study of various advertising tools, es-pecially centered on search engine promotion. One of the key areas of activity was the study of various adver-tising tools, especially those focused on promotion in search engines. The aim of the present study is to identify the factors that maximize the frequency of product card views by users. The results of launching advertising campaigns, collection and analysis of data on the delivery time of goods from different positions, comparative analysis of cost per thousand views (CPM) in different regions, collection of statistics on views, clicks, click-through rate (CTR), cost per click (CPC) were analyzed. Conclusion dwells upon the fact that the indexing of ads when working with it depends on a number of factors: the availability of the product, compliance with the maximum delivery time, attribution to the priority category and optimized consideration of key search phrases.

Vaccine distribution network opportunities on a national scale

Building an effective distribution network is a significant advantage for any company. This is especially true for easily damaged or perishable items, where the length and speed of the transport, as well as the loading time, play a major role in maintaining quality. In this article, we examined the transport/distribution options for the creation of a vaccine distribution network in Hungary, which can meet strict rules. We took into account the driver’s working hours, the maximum delivery time of the vaccine, the storage options of the county seats, and as a result we got the most efficient distribution plan of Hungary. To solve the problem, we use conventional-, greedy-, and heuristic algorithms, which were compiled by Excel and its SOLVER extension.

Development of queue management model for effective service delivery in automobile repair shops

In this study, a queue management model/software was developed for automobile repair shops. This software minimizes both waiting time of customers, and idle time of workers. The software groups all jobs done in an automobile repair shop into three sections: mechanical, electrical and air conditioning (A/C) sections. The developed software prioritizes all jobs performed in a typical automobile repair shop in terms of urgency, using the ‘shortest processing time’ scheduling approach. The jobs are then ranked and assigned to workers based on number of available workstations. Also, expected time of delivery of the job is estimated by the software. The software was tested using data obtained over a two weeks period and percentage reduction in waiting time was found to range between: 0.889-0.122, 0.895-0.25 and 1-0.167 for the mechanical, electrical and A/C sections respectively. In the mechanical section, servicing/replacement of piston and rings and changing/servicing of gear box were discovered to be the jobs with maximum delivery time (15 hrs) while changing of engine belt was seen as the job with the least delivery time (0.3 hrs). For the electrical section, changing of alternator, with delivery time of 3 hrs 30 mins and changing of headlamp and fuse breakage with delivery time of 0.15 hrs are the jobs with maximum and minimum delivery times respectively. For the A/C section, changing of freezer with delivery time of 10 hrs and refilling of gas with delivery time of 0.10 hrs are the maximum and minimum respectively. Implementation of this research will reduce time wastage experienced by customers, idle time at service facilities, frustration caused by unnecessary queue, and encourage allocation of resources accordingly.

Solution approaches for the integrated production and outbound distribution scheduling problem with multiple plants and perishable items

In this manuscript, we consider the integrated production and outbound distribution system in which there are several geographically dispersed facilities. These facilities are responsible for producing and delivering time-sensitive customer demands. We propose a mixed integer programming (MIP) formulation, MIP with an initial solution using Clarke and Wright (MIPCW) and a metaheuristic algorithm (Variable Neighborhood Search-VNS) for the problem whose objective is to minimize the maximum delivery time whereby satisfying all customer demands. We conduct a two-stage experimental study to determine the effectiveness of the proposed metaheuristic algorithm. We compare the VNS algorithm with the best-known solutions for the single plant version of the problem, in the first stage. These results indicate that the VNS algorithm yields promising results. The second stage includes the results for the MIP formulation and the VNS algorithm on a set of newly generated test instances. The average percentage gap between the VNS algorithm and the MIPCW formulation is about 5% which means that the VNS algorithm gives better results in average about 70 s computation time. These results show how effective the suggested VNS algorithm is at solving the test instances.

Improving the efficiency of patient diagnostic specimen collection with the aid of a multi-modal routing algorithm

The Sustainable Specimen Collection Problem (SSCP), in which diagnostic specimens are collected from GP surgeries (doctor’s office/clinics) and subsequently transported to a hospital laboratory for analysis using more sustainable transport modes, is introduced in this paper. Using a weighted objective function, we solve a new multi-objective problem using cycle consolidation to limit driving time and the numbers of vans used whilst improving overall service quality, reducing costs and emissions. This particular heterogeneous vehicle routing problem is explored and applied to two real-world case studies in the UK, where 97 and 22 sites (respectively) are currently served, using a column generation based heuristic algorithm with some additional improvement heuristics. The results demonstrated a potential improvement in the system’s maximum delivery time between 41% and 74% compared to business-as-usual activity using solely road vehicles. Road vehicle (van) fleets could be reduced by up to 40%, and the total driving time across the fleet by between 41% and 65%. Operational costs were estimated to increase by up to 38%, though additional workloads for gig-economy cycle couriers and improvement in specimen quality and service reliability may make this trade-off worthwhile. Tailpipe CO2 emissions were also reduced by up to 43%. The proposed algorithm was effective, reducing computational time by up to 99% whilst achieving an average of 5% deviation from optimality.

Multi-modal and multi-product hierarchical hub location problem with fuzzy demands

The hub location is a major problem in the systems with high dependence on the transportation of goods, information, and passengers between the constituent parts. The present study is aimed to introduce a multi-commodity multi-model hierarchical hub location problem with uncertain demand. Thus, it is estimated by intuitionistic fuzzy variables. The objective function in the present problem is to minimize the total transportation costs in the network to determine the optimal hub location, allocate non-hub nodes to the hubs and the ground hubs to the air hubs, and identify the type of vehicles required in each route. The model has a hierarchical structure consisting of a three-echelon network (i.e., central hubs, non-central hubs, and demand nodes) connected in the star-tour-star form. A four-index mathematical model was presented and solved by GAMS optimization software. The results indicated that the objective function (cost) has a descending trend with increasing the number of hubs which can be assigned to the decline in the transportation costs. The costs increased by a decrease in the maximum delivery time which could be due to the selection method of the transportation mode. In the multi-product case, the costs declined by increasing the number of hubs as these hubs decremented the network complexity. Regarding the NP-Hard nature of the hub problems, a genetic meta-heuristic algorithm was proposed in the MATLAB software to solve the large-scale problem. According to the results, this algorithm offered close-optimal solutions. Noteworthy, this study employed known AP datasets.

Development of a Dynamically Adaptable Routing System for Data Analytics Insights in Logistic Services

This work proposes an effective solution to the Vehicle Routing Problem, taking into account all phases of the delivery process. When compared to real-world data, the findings are encouraging and demonstrate the value of Machine Learning algorithms incorporated into the process. Several algorithms were combined along with a modified Hopfield network to deliver the optimal solution to a multiobjective issue on a platform capable of monitoring the various phases of the process. Additionally, a system providing viable insights and analytics in regard to the orders was developed. The results reveal a maximum distance saving of 25% and a maximum overall delivery time saving of 14%.

Analysis of multi-objective vehicle routing problem with flexible time windows: The implication for open innovation dynamics

Renewable energy has been a worldwide interest due to a growing energy demand as well as a mounting concern over the hostile impacts from traditional fuels. One of a direction for future renewable energy is the use of biofuel. In this research, we initially apply the K-means algorithm to evaluate the possible locations of collection sites at the upstream of the biofuel supply chain. Next, we propose the multi-objective vehicle routing problem model, in which flexible time windows are synchronized in the model. Additionally, our integrated model evaluates the perspective of socioeconomic by considering total cost – the surrogate criterion for economic aspect as well as the lateness for delivery and the maximum delivery time – the surrogate criteria for social aspect, into account. Finally, we apply a model to a regional case study based on the wood-biomass data of the biofuel supply chain in Thailand, in which the geographic information system is applied.

Online scheduling on parallel-batch machines with periodic availability constraints and job delivery

We address an online scheduling problem on identical parallel-batch machines with periodic availability constraints and job delivery. A parallel-batch machine can process several jobs simultaneously in a batch without any preemption. The processing time of a batch is equal to the maximum processing time of the jobs in this batch, and the job processing times we consider are identical on all machines. Available and unavailable time intervals occur alternately on machines. The unavailable time intervals have the same start and end time on different machines. Jobs are released over time, which means that no information of the job is known in advance before its release date. After completion, job is delivered to customer. Three objective functions, namely, maximum flow time, maximum delivery time and total flow time are considered separately. For these objectives, we derive lower bounds on competitive ratios, provide online algorithms and analyze their competitive ratios.

Branch Less, Cut More and Schedule Jobs with Release and Delivery Times on Uniform Machines

We consider the problem of scheduling n jobs with identical processing times and given release as well as delivery times on m uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (“branch less and cut more”). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is O(γm2nlogn), where γ can be either n or the maximum job delivery time qmax. This complexity can even be reduced further by using a smaller number κ<n in the estimation describing the number of jobs of particular types. However, this number κ becomes only known when the algorithm has terminated.

Impact of External Conditions on Selecting Special Transport Vehicle for Perishable Cargo Transportation

The list of special transport vehicles used for transporting the perishable goods by rail in Russia is presented in the study. The maximum allowable cargo delivery time was estimated depending on the type of used vehicle. The impact of external factors on the heat transfer coefficient of a vehicle body and the temperature head during transportation of perishable goods by rail are presented. It is determined that the heat transfer coefficient increases by 3 ÷ 10% at a train speed of 100 km/h, which reduces the maximum permissible delivery time of refrigerated cargo to the consumer. The effect of insolation on the car surface increases the heat flux inside the car body when transporting refrigerated goods and reduces the heat flux when transporting heated goods in vehicles, which also affects the deadlines for cargo delivery. The method of selecting a special vehicle considering the known maximum allowable time of perishable goods transportation is exposed in the study. The conclusions indicate what changes should be implemented in the existing methodology for calculating the deadline for perishable goods transportation, which will reduce the risk of their delivery in inadequate condition.

A multi-objective approach in expanding the pre-positioning warehouse networks in humanitarian logistics

In this study, we focus on the structure of the pre-positioning warehouse networks which have a great effect on the response to a disaster. We determine the pre-positioning warehouse network configuration of CARE International with a multi-objective approach using the recent decade data. In addition to the minimisation of the average response time of an item, we also consider the maximum response time and maximum water delivery time as additional objectives. After analysis of the non-dominated solutions, we conclude that CARE International should open a warehouse in Kenya and pre-position 39%-44% of all relief items other than tents to this location while starting to operate the Denmark warehouse instead of the Dubai warehouse. [Received: 20 March 2018; Revised: 12 September 2019; Accepted: 26 February 2020]

Modelling of just-in-time distrubution network under raw material quality and time constraints

Just-in-time (JIT) delivery is one of the key delivery strategies that enable the right quality product to reach the point of demand at the right time without creating unnecessary costs in the supply chain network. The concepts of quality and time are two main factors to be considered in this issue. Particularly because the variability in quality directly affects cost and time, it is very important for JIT delivery. In this study, the effect of raw material quality within the supply chain network which tries to ensure JIT delivery is examined. For this, a multi-stage, multi-period mixed-integer mathematical model is proposed in the study. The model aims to minimize the total supply chain cost by trying to balance the purchasing and quality costs for manufacturers. In addition to standard constraints, the stock balance and time constraints have been developed for JIT delivery. As a result of the model resolved with the GAMS Distribution 21.6 program, 34.5% of the raw material supplied from suppliers is provided from 1st quality raw materials, while 65.5% is provided from 2nd quality raw materials. Despite its low purchasing costs, 3rd quality raw material has not been preferred by the producers in any period because it causes a delay in JIT delivery. Besides, it is seen that deliveries are made very close to the maximum delivery time of distribution centers, depending on the variability in raw material quality. It is understood that raw material quality is an important concept in a JIT supply chain network due to its significant impact on time.

Routing order pickers in warehouses considering congestion and aisle width

Due to the importance of routing order pickers, there has been extensive research in the area of routing in warehouses. Still, there are some prominent factors that should receive more attention, as they may provide unsatisfactory services and incur considerable operational costs if ignored. In real-world applications, warehouse configuration, width of aisles, and controlling the vehicle congestion in the aisles greatly influence the efficiency of the routing process. Therefore, this paper proposes a mixed-integer programming model. The model aims to minimize maximum delivery time by finding the shortest pickup and delivery routes of all goods for all vehicles. Since the problem is NP-hard, a Simulated Annealing metaheuristic approach is designed to solve the model in large-size problems. This research contributes to picker routing literature by considering dynamic congestion, narrow and wide aisles, and pickup times and proposing a metaheuristic algorithm. The validation and efficiency of our proposed model are proved by solving some various generated benchmark problems. In summary, the developed route planning mathematical model works effectively for any two-dimensional rectangular layout, and the collision prevention constraints are incorporated in the mathematical model.

Integrated Scheduling Problem on a Single Bounded Batch Machine with an Unavailability Constraint

We consider a scheduling problem where a set of jobs are first processed on a machine with an unavailability interval and, then, delivered to the customer directly. We focus on an integrated schedule of production and distribution such that the sum of the maximum delivery time and total delivery cost is optimized. We study two classes of processing machines in the production part. In the first class, the serial-batch machine, the processing time of a batch is the sum of the processing times of its jobs. In the second class, the parallel-batch machine, the processing time of a batch is the maximum processing time of the jobs contained in the batch. The machine has a fixed capacity, and the jobs are processed in batches under the condition that the total size of the jobs in a batch cannot exceed the machine capacity. Two patterns of job’s processing, i.e., resumable and non-resumable, are considered if it is interrupted by the unavailability interval on the machine. In the distribution part, there are sufficient vehicles with a fixed capacity to deliver the completed jobs. The total size of the completed jobs in one delivery cannot exceed the vehicle capacity. We show that these four problems are NP-hard in the strong sense in which the jobs have the same processing times and arbitrary sizes, and we propose an approximation algorithm for solving these four problems. Moreover, we show that the performance ratio of the algorithm is 2 for the serial-batch machine setting, and the error bound is 71/99 for the parallel-batch machine setting. We also evaluate the performance of the approximation algorithm by the computational results.

Heuristic algorithms for the bi-objective hierarchical multimodal hub location problem in cargo delivery systems

In this paper, we introduce an extended version of hub location problem, called bi-objective hierarchical multimodal hub location problem to simultaneously minimize the overall system-wide costs and the maximum delivery time. This problem is distinct from the classic hub location problem in designing a hierarchical multimodal hub-and-spoke network involving multiple transportation modes, multi-class hubs and corresponding layers. Combining cost and time dimensions, we first propose a bi-objective mixed-integer linear programming to model this problem formally with diverse flow balance constraints. We then show that the proposed model can be efficiently solved by a reformulation approach based on the ε-constraint method for only small instances. Hence, we develop two heuristics, a variable neighborhood search algorithm and an improved non-dominated sorting genetic algorithm-II to obtain high-quality Pareto solutions for realistic-sized instances. We further illustrate the application of the proposed model to provide decision support for cargo delivery systems. Finally, we conduct extensive numerical experiments based on Turkish network to demonstrate the superiority of the proposed solution methods compared to the standard non-dominated sorting genetic algorithm-II. The statistical results confirm the efficacy of the developed heuristic algorithms by adopting the Wilcoxon test.

Proposed Modified Clarke-Wright Saving Algorithm for Capacitated Vehicle Routing Problem

A multi-objective distribution routing algorithm by using modified Clarke and Wright Saving algorithm is presented. The problem to solve is to deliver loads to a number of outlets based load requirement. The objective function to minimize is the distance saving and traveling time of the resulted route started from depot to the outlets and return to the original depot. Problem to solve is generating a distribution route in a week considering traffic condition for each day. The original Clarke and Wright saving algorithm is modified such that the resulted routes (from a depot to some outlets) accommodates some constraints such as the maximum allowable traveling time, maximum number of delivery shifts, and maximum number of vehicles. The algorithm is applied to a distributor company with nine outlets, two vehicles, and two delivery shifts. In addition, the traffic condition on the outlet-to-outlet and the depot-to-outlet routes is considered. The simulation of the proposed algorithm shows that the algorithm can generate routes that comply with shift’s maximum delivery time and the vehicles’ capacities.

A coordinated algorithm for integrated production scheduling and vehicle routing problem

In this paper, the integrated production scheduling and vehicle routing problem is considered for a Make-to-Order manufacturer, who has a single machine for production and limited vehicles with capacity constraints for transportation. The objective is to determine production scheduling and vehicle routing, which are two interacted decisions, to minimise the maximum order delivery time. A property on optimal production sequence is proposed first, based on which backward and forward batching methods are developed and are embedded into a proposed genetic algorithm. The proposed genetic algorithm is capable of providing high-quality solutions by determining the two decisions simultaneously. For comparison purpose, a two-stage algorithm is developed, which decomposes the overall problem into two successively solved sub-problems. The experiments show that the proposed genetic algorithm can provide higher quality solutions than the proposed two-stage algorithm and two published algorithms studying related problems.

A mathematical approach to model humanitarian aid distribution in disaster area

This paper deals with the response phase of humanitarian relief. We model the first operations of distribution of humanitarian aid in a disaster area that correspond to a rich vehicle routing problem (VRP) where we aim at minimising maximum delivery time. Regarding the model attributes' complexity, we develop a column generation approach to solve the optimisation model. This approach relies on a specific pricing problem that generates routes with negative reduced costs to add to the master problem. These routes define the sequence of demand points to visit and the quantities to be carried to each one.