Delivery Scheduling Problem Research Articles

Research on Fresh Produce Delivery Scheduling Problems under the Perspective of Community E-commerce

This paper addresses the challenges associated with the high costs and logistical difficulties in the distribution of fresh agricultural products from the perspective of community e-commerce. The paper takes the perspective of merchant scheduling and integrates a classical vehicle scheduling model. The study meticulously examines the various costs associated with the distribution process, encompassing fixed costs, transportation costs, refrigeration costs, storage costs and time subsidies. A vehicle routing optimisation model was developed with the dual objectives of cost control and product quality assurance. The use of a genetic algorithm for analysis and solution indicates that this approach can achieve superior cost efficiency and more optimal delivery routes. The results not only confirm the validity of the model and the effectiveness of the solution algorithm, but also provide theoretical underpinnings and viable optimisation strategies for analogous route optimisation challenges. This research has significant reference value and practical relevance for improving delivery efficiency and cost management in community e-commerce.

A novel fuzzy finite-horizon economic lot and delivery scheduling model with sequence-dependent setups

This paper addresses the economic lot and delivery scheduling problem (ELDSP) within three-echelon supply chains, focusing on the complexities of demand uncertainty, limited shelf-life of products, and sequence-dependency of setups. We develop a novel mixed-integer non-linear programming (MINLP) model for a supply chain comprising one supplier, multiple manufacturers with flexible flow shop (FFS) production systems, and multiple retailers, all operating over a finite planning horizon. The common cycle (CC) strategy is adopted as the synchronization policy. Our model employs fuzzy set theory, particularly the “Me measure,” to effectively handle the retailers’ demand uncertainty. Our findings indicate that total supply chain costs escalate with an increase in demand, final components’ holding costs, and sequence-dependent setup costs, but decrease with increasing production rates. Furthermore, while total costs are significantly sensitive to changes in demand, they are relatively insensitive to fluctuations in sequence-dependent setup times. The models developed offer valuable managerial insights for optimizing costs in synchronized multi-stage supply chains, aiding managers in making informed decisions about production lot sizes and delivery schedules under both deterministic and fuzzy demand scenarios. Additionally, the proposed models bridge key research gaps and provide robust decision-making tools for cost optimization, enhancing supply chain synchronization in practical settings.

A decision making framework for joint replenishment and delivery scheduling problems under mixed uncertainty

Concerning the essence of risk, a joint replenishment and delivery scheduling problem with fuzzy cost-related parameters and random number of imperfect quality items is developed to make it suitable for the inherent uncertainties of procurement-shipment process. The mathematical modelling-based decision system is formulated as a chance-constrained programming with the idea of embedding decision makers’ risk tolerance. Following this notion, the model is translated into an equivalent non-linear counterpart and a neighbourhood heuristic search is designed based on the properties of the cost function. We introduce an integrated cross-entropy algorithm, incorporating the heuristic in the cross-entropy framework, to solve it. The numerical results demonstrate that ICE is quite effective in comparison to state-of-the-art algorithms. Our framework is helpful for decision makers to determine economically acceptable performance objectives in the presence of uncertain issues, and thus to build resilience in supply chain.

Exploring fairness in food delivery routing and scheduling problems

Demand for delivery of take-away meals to customers has been growing worldwide, with deliveries often performed by non-specialised gig economy couriers working for online platform operators such as Deliveroo or Just Eat. This has led to the introduction of the ‘meal delivery problem’, characterised by a series of individual pickup and delivery tasks to be assigned to available couriers. While there is a vast set of algorithms proposed in the literature that aim to minimise total workload, very little attention has been given to equitably distributing work between couriers. We propose a new multi-objective problem that is aiming at distributing orders equitably between couriers as well as minimising total workload, where all information is known upfront. We propose an integer linear programming (ILP) model with a weighted objective function that is used to derive the Pareto front in small-scale problems by exploiting the ϵ−constraint approach. This formulation has been proven to solve in a reasonable time for problems with up to 60 orders, however, the optimal Pareto front can only be computed within a reasonable time for problems up to 30 orders. For problems with more orders, we propose a Variable Neighbourhood Search (VNS) algorithm, for which the fitness evaluation evolves in order to explore a wider set of the solution space. The VNS is compared against the ILP and also tested on more realistic size instances with up to 3123 orders, improving the performance over the business as usual and shows that equitable distribution of work can be achieved alongside reducing the total travelled distance.

Two is better than one? Order aggregation in a meal delivery scheduling problem

We address a single-machine scheduling problem motivated by a last-mile-delivery setting for a food company. Customers place orders, each characterized by a delivery point (customer location) and an ideal delivery time. An order is considered on time if it is delivered to the customer within a time window given by the ideal delivery time ±δ2, where δ is the same for all orders. A single courier (machine) is in charge of delivery to all customers. Orders are either delivered individually, or two orders can be aggregated in a single courier trip. All trips start and end at the restaurant, so no routing decisions are needed. The problem is to schedule courier trips so that the number of late orders is minimum. We show that the problem with order aggregation is NP-hard and propose a combinatorial branch and bound algorithm for its solution. The algorithm performance is assessed through a computational study on instances derived by a real-life application and on randomly generated instances. The behavior of the combinatorial algorithm is compared with that of the best ILP formulation known for the problem. Through another set of computational experiments, we also show that an appropriate choice of design parameters allows to apply the algorithm to a dynamic context, with orders arriving over time.

An efficient discrete artificial bee colony algorithm with dynamic calculation method for solving the AGV scheduling problem of delivery and pickup

To meet the production demand of workshop, this paper proposes an efficient discrete artificial bee colony (DABC) algorithm to solve a new automatic guided vehicle (AGV) scheduling problem with delivery and pickup in a matrix manufacturing workshop. The goal is to produce a AGV transportation solution that minimizes the total cost, including travel cost, time cost, and AGV cost. Therefore, a mixed integer linear programming model is established. To improve the transportation efficiency, a dynamic calculation method is developed. In the DABC algorithm, a heuristic algorithm and a median based probability selection method are used. For improving the quality of the solutions, four effective neighborhood operators are introduced. In the local search, a rule is given to save the operation time and a problem-based search operator is proposed to improve the quality of the best individual. Finally, a series of comparison experiments were implemented with the iterative greedy algorithm, artificial bee colony algorithm, hybrid fruit fly optimization algorithm, discrete artificial bee colony algorithm, improved harmony search, and hybrid genetic-sweep algorithm. The results show that the proposed DABC algorithm has high performance on solving the delivery and pickup problem.

Coordinated production and delivery scheduling for service-oriented manufacturing systems with deterioration effect

Service-oriented manufacturing (SOM) is a new industrial model that combines manufacturing with service. To enhance the competitiveness of manufacturers in SOM systems, we investigate a coordinated production and delivery scheduling problem considering a third-party logistics (3PL) provider. The considered problem can be divided into two phases, including production phase and delivery phase. In the production phase, jobs are processed by multiple manufacturers located in different geographical zones. Jobs are with deteriorating processing time and set-up time. Several structural properties of the problem in the production phase are proposed, based on which a heuristic algorithm is designed to make decisions on job batching and batch sequencing. After being processed, the finished jobs are immediately delivered to a customer by manufacturers’ own vehicles or the 3PL provider. A dynamic programming algorithm is developed to solve the problem in the delivery phase. The integrated scheduling problem is proved to be NP-hard. Hence, we develop a general variable neighbourhood search (GVNS) to solve the problem in a reasonable time. The basic variable neighbourhood descent (BVND) is used as a local search method in the GVNS. Finally, the computational experiments are conducted and the results verify the effectiveness and stability of the proposed approach.

Population-Based Meta-Heuristic Algorithms for Integrated Batch Manufacturing and Delivery Scheduling Problem

This paper addresses an integrated scheduling problem of batch manufacturing and delivery processes with a single batch machine and direct-shipping trucks. In the manufacturing process, some jobs in the same family are simultaneously processed as a production batch in a single machine. The batch production time depends only on the family type assigned to the production batch and it is dynamically adjusted by batch deterioration and rate-modifying activities. Each job after the batch manufacturing is reassigned to delivery batches. In the delivery process, each delivery batch is directly shipped to the corresponding customer. The delivery time of delivery batches is determined by the distance between the manufacturing site and customer location. The total volume of jobs in each production or delivery batch must not exceed the machine or truck capacity. The objective function is to minimize the total tardiness of jobs delivered to customers with different due dates. To solve the problem, a mixed-integer linear programming model to find the optimal solution for small problem instances is formulated and meta-heuristic algorithms to find effective solutions for large problem instances are presented. Sensitivity analyses are conducted to find the effect of problem parameters on the manufacturing and delivery time.

Applied real-valued genetic algorithm for an extended model of economic lot, purchase and delivery scheduling problem

Abstract Supply chain management intends to integrate supply chains' activities such as material flow, information flow and financial issues. Material flow management is the most significant issue since the inventory level in the whole supply chain could be optimized by an integrated plan. In other words, when one member of the supply chain plans to reduce its inventory level solely, despite reducing inventory in this node the inventory will be stocked in other partners' warehouses. Therefore, in this paper a new mathematical model has been developed to facilitate the process of finding the optimum solution in economic production, purchase and delivery lots and their schedules in a three-echelon supply chain environment; including raw material in suppliers, manufacturer and assembly facility as a customer. The manufacturer with a flow shop system provides its requirements from supplier, assemble multiple products, and delivers products to the customer (automotive OEM alike) on an optimum multiple delivery points. The delivery cycles would be identified through the production common cycle regarding the supply chain flexibility. Finally, a modified real-valued Genetic Algorithm (MRGA), and an Optimal Enumeration Method (OEM) are developed, and some numerical experiments have been done and compared as well.

Parallel batch processing machines scheduling in cloud manufacturing for minimizing total service completion time

This paper considers the integrated scheduling problem of production and delivery on parallel batch processing machines with non-identical capacities in different locations in cloud manufacturing. It is assumed that the jobs have arbitrary release times, different job sizes, unequal processing times, and unique information of customers submitting jobs. The service completion time of a job is the sum of the production completion time and the delivery duration. The objective of the studied problem is to minimize the total service completion time. A mixed-integer programming (MIP) model is presented to solve this problem. Since the problem is NP-hard, an efficient heuristic algorithm and an improved particle swarm optimization algorithm are proposed. The two proposed algorithms are compared with several state-of-the-art algorithms and the commercial optimization solver (Gurobi) through extensive experiments, verifying the effectiveness of the proposed algorithms.

An approximate dynamic programming approach for production‐delivery scheduling under non‐stationary demand

AbstractWe consider an integrated production and delivery scheduling problem with non‐stationary demand in a two‐stage supply chain, where orders arrive dynamically and the demand is time‐varying. Orders should be first processed on identical machines and then delivered to a single next‐stage destination by the transporters with fixed departure times. The objective is to minimize the order waiting time via production‐delivery scheduling. We formulate the problem into a Markov decision process model and develop an approximate dynamic programming (ADP) method. To shrink action (decision) space, we propose the shorter processing time first and first completion first delivery (SPTm/FCFD) principle to determine order processing sequences and order delivery, and then we establish two constraints to eliminate a fraction of inferior actions. Based on the SPTm/FCFD principle, we propose the SPT/FCFD rule, and show its optimality for two scenarios. In addition, we deploy five basis functions to approximate the value function. The superior performance of ADP policy is validated via numerical experiments, compared with four benchmark policies. We also empirically study the impact of demand features on the waiting time, and results show that these features significantly affect the performances of all polices. In practice, it is suggested to postpone the peak demand, when total demand exceeds the available production capacity.

Approximate and robust bounded job start scheduling for Royal Mail delivery offices

Motivated by mail delivery scheduling problems arising in Royal Mail, we study a generalization of the fundamental makespan scheduling P||C_{max } problem which we call the bounded job start scheduling problem. Given a set of jobs, each specified by an integer processing time p_j, that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound gle m on the number of jobs that may simultaneously begin per unit of time. With perfect input knowledge, we show that Longest Processing Time First (LPT) algorithm is tightly 2-approximate. After proving that the problem is strongly {mathcal {N}}{mathcal {P}}-hard even when g=1, we elaborate on improving the 2-approximation ratio for this case. We distinguish the classes of long and short instances satisfying p_jge m and p_j<m, respectively, for each job j. We show that LPT is 5/3-approximate for the former and optimal for the latter. Then, we explore the idea of scheduling long jobs in parallel with short jobs to obtain tightly satisfied packing and bounded job start constraints. For a broad family of instances excluding degenerate instances with many very long jobs, we derive a 1.985-approximation ratio. For general instances, we require machine augmentation to obtain better than 2-approximate schedules. In the presence of uncertain job processing times, we exploit machine augmentation and lexicographic optimization, which is useful for P||C_{max } under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in a low number of used machines. Given a collection of schedules of makespan le D, this approach allows distinguishing which are the more robust. We substantiate both the heuristics and our recovery approach numerically using Royal Mail data. We show that for the Royal Mail application, machine augmentation, i.e., short-term van rental, is especially relevant.

A joint production and delivery schedule for a single-vendor single-buyer system over finite horizon

In this paper, we address a joint production and delivery scheduling problem in which a single-vendor supplies goods to a single-buyer over a finite horizon. The vendor's production rate and the buyer's demand rate can vary from period to period and are known in advance. The objective is to determine a production/shipment schedule that minimises the total cost of production setup, shipment, and holding of inventory at both the vendor and the buyer. We approach this problem using a dynamic programming framework, each stage of which constitutes solutions to different types of single-period problems depending on the production phase encountered. We develop effective methods for the solutions of these single-period problems, which are then embedded within the dynamic programming framework. We show that the optimal solution in each period follows a pattern of geometric-then-equal shipment sizes except for the last shipment, which may be larger in size. Furthermore, we show that an optimal solution for the infinite horizon problem can be obtained by using a special case of our finite horizon approach. In addition, we propose two fast heuristic methods for the finite horizon problem, which, as we show, can obtain almost optimal solutions.

A joint production and delivery schedule for a single-vendor single-buyer system over finite horizon

In this paper, we address a joint production and delivery scheduling problem in which a single-vendor supplies goods to a single-buyer over a finite horizon. The vendor's production rate and the buyer's demand rate can vary from period to period and are known in advance. The objective is to determine a production/shipment schedule that minimises the total cost of production setup, shipment, and holding of inventory at both the vendor and the buyer. We approach this problem using a dynamic programming framework, each stage of which constitutes solutions to different types of single-period problems depending on the production phase encountered. We develop effective methods for the solutions of these single-period problems, which are then embedded within the dynamic programming framework. We show that the optimal solution in each period follows a pattern of geometric-then-equal shipment sizes except for the last shipment, which may be larger in size. Furthermore, we show that an optimal solution for the infinite horizon problem can be obtained by using a special case of our finite horizon approach. In addition, we propose two fast heuristic methods for the finite horizon problem, which, as we show, can obtain almost optimal solutions.

An effective heuristic with evolutionary algorithm for the coordinated capacitated dynamic lot-size and delivery problem

This study considers an extensive coordinated capacitated dynamic lot-size problem that contains a delivery scheduling problem. The coordinated capacitated dynamic lot-size and delivery problem (CCLSDP) assumes that a family of products is subject to capacity constraints, and the demand without backorders is dynamic or time-varying but deterministic. The objective is to determine a replenishment and delivery schedule that minimizes the total system costs, including the family and minor setup costs, delivery costs, and inventory holding costs. We develop a six-phase heuristic (SPH) to solve the CCLSDP. The SPH contains six phases that can efficiently reschedule replenishment and delivery planning. Each phase of the SPH evaluates the cost and feasibility of the shifting operations, and determines whether to reschedule the system planning through a series of sequential shifting operations. To further enhance the overall performance, we embed SPH as a lifting procedure into evolutionary algorithms contributing to explore the search space and escapes the local optimum. Experimental results of randomly generated instances that were over a wide range of parameters indicate that the proposed heuristics could efficiently and effectively solve the complicated CCLSDP.

A new mathematical model for production and delivery scheduling problem with common cycle in a supply chain with open-shop system

A new mathematical model for production and delivery scheduling problem with common cycle in a supply chain with open-shop system

A new mathematical model for production and delivery scheduling problem with common cycle in a supply chain with open-shop system

In order to coordinate the supply chain, reordering strategy of needed goods must be synchronised and sequence of production and replenishment cycle time must be optimised in terms of cost. Therefore, this paper studies the economic lot and delivery scheduling problem for multi-stage supply chain. The common cycle time and integer multiplier policies were adopted to accomplish the desired synchronisation. In this regard, a new mathematical model has been presented where a manufacturer with open-shop system purchases raw materials from suppliers and sends them to packaging companies after converting them into the final product and then they are sold. Since this is a non-deterministic polynomial-time hard (NP-hard) problem, simulated annealing algorithms have been developed for it. For this algorithm, two different scenarios have been proposed for solving the study problem and at the end the numerical results have been applied on problems with different dimensions by the algorithm.

Destination Prediction-Based Scheduling Algorithms for Message Delivery in IoVs

Destination related applications are playing an important role in Internet of Vehicles(IoVs), which can provide people with convenience or business profit, such as traffic jam warning or parking guide. However, in reality, people hesitate to share their destination information to other people due to operation inconvenience, which requires service providers to predict vehicles' destinations in advance in order to deliver them destination related messages. Some papers have considered the delivery scheduling problem of destination related information. But, they neglect the destination prediction problem with the assumption that vehicle's destinations are known in advance. In this paper, we target the delivery scheduling problem of destination related information in the case of destinations unknown to others in IoVs. First, a realtime destination prediction framework with machine learning models is proposed, with which a vehicle's destination can be predicted while traveling. Then, we propose a delivery profit maximization algorithm for service providers to select a proper location to deliver destination related information to each vehicle. Simulations with real vehicle trajectories show that our scheduling algorithm performs well and can successfully select a proper location to disseminate destination related information.

Integrated Scheduling of Production and Two-Stage Delivery of Make-to-Order Products: Offline and Online Algorithms

We study integrated production- and delivery-scheduling problems that arise in practical make-to-order settings in several industries. In these problems, make-to-order products are first processed in a plant and then delivered to customer sites through two stages of shipping: first, from the plant to a pool point (e.g., a port, a distribution, or a consolidation center) and, second, from the pool point to customer sites. The objective is to obtain a joint schedule of job processing at the plant and two-stage shipping of completed jobs to customer sites to optimize a performance measure that takes into account both delivery timeliness and total transportation costs. We consider two problems in which delivery timeliness is measured by total or maximum lead time of the jobs and study both offline and online versions of these problems. For the offline problems involving a single production line at the plant, we provide optimal dynamic programming algorithms. For the more general offline problems involving multiple production lines at the plant, we propose fast heuristics and analyze their worst-case and asymptotic performances. For the online problems, we propose online algorithms and analyze their competitive ratios. By comparing our offline heuristics with lower bounds using randomly generated test instances, it is shown that these heuristics are capable of generating near-optimal solutions quickly. Using real data from Baosteel’s Meishan plant, we also show that our corresponding offline heuristic generates significantly better solutions than Baosteel’s rule-based approach. In addition, our computational results on the performance of the online algorithms relative to the offline heuristics generate important methodological insights that can be used by practitioners in choosing a specific solution approach.

Optimization of ready mixed concrete delivery for commercial batching plants of Ahmedabad, India

This paper is an attempt to develop a delivery schedule model with real time data for a commercial ready mixed concrete (RMC) plant in Ahmedabad city of Gujarat, India. Without a proper delivery schedule, either a truck-mixer would need to wait for the concrete to be placed at site or the construction site would need to wait for the truck-mixer to arrive on time. Developing an optimized dispatching and delivery sequence scheduling would improve the dispatching order of delivery of the RMC through truck-mixers from commercial batching plants to the respective construction sites. In the present research, this problem has been addressed through optimization techniques developed through mixed integer programming. Mixed integer programming considers both discrete and continuous variables which affect the delivery of RMC to the respective construction sites. The delivery scheduling problem was defined by identifying the objective function and the associated constraints. The mixed integer programming code was written with the help of MATLAB software. It has been observed after 101 iterations in MATLAB software that the dispatching sequence 1,2,2,1,1,3,2,3,2,3,3,3 has the least total waiting time of 155.4 min. After validating the same model with real time data, it has been observed that for the above dispatching sequence, the total waiting time is 153 min with one obstruction resulting in a delay of 48 min for the casting of concrete at site. Furthermore, based on the computations, it is recommended that the plant authorities need to increase the number of RMC truck-mixers from five to seven.