Single Depot Research Articles

Optimal allocation of spares to maximize the window fill rate in a two-echelon exchangeable-item repair system

We solve the spares allocation problem in a two-echelon, exchangeable-item repair system in which the lower echelon comprises multiple locations and the higher echelon is a single depot. We assume that customers tolerate a certain wait and therefore the optimization criterion is the window fill rate, i.e., the expected portion of customers who are served within the tolerable wait. We develop two algorithms to solve this problem. The first algorithm (FTEA) is formula-based and is suboptimal. The second algorithm (HTEA) combines simulations into the first algorithm and obtains a higher degree of accuracy at the cost of extra running time. We characterize the near-optimal solution by its degree of pooling and concentration. Pooling happens when spares are allocated to the depot and are therefore shared by all the lower-echelon locations. Concentration takes place when spares are allocated to only a few lower-echelon locations whereas the other lower-echelon locations receive no spares. We use numerical examples to compare the algorithms and to illustrate how the budget, shipment time, local repair and customer patience affect the optimal solution and degree of pooling in varying ways. Using the numerical results, we propose a third algorithm (ETEA) that obtains HTEA’s output in 30% of the time.

Tabu search algorithm for the distance-constrained vehicle routing problem with split deliveries by order.

The vehicle routing problem (VRP) has a wide range of applications in the field of logistics distribution. In order to reduce the cost of logistics distribution, the distance-constrained and capacitated VRP with split deliveries by order (DCVRPSDO) was studied. We show that the customer demand, which can’t be split in the classical VRP model, can only be discrete split deliveries by order. A model of double objective programming is constructed by taking the minimum number of vehicles used and minimum vehicle traveling cost as the first and the second objective, respectively. This approach contains a series of constraints, such as single depot, single vehicle type, distance-constrained and load capacity limit, split delivery by order, etc. DCVRPSDO is a new type of VRP. A new tabu search algorithm is designed to solve the problem and the examples testing show the efficiency of the proposed algorithm. This paper focuses on constructing a double objective mathematical programming model for DCVRPSDO and designing an adaptive tabu search algorithm (ATSA) with good performance to solving the problem. The performance of the ATSA is improved by adding some strategies into the search process, including: (a) a strategy of discrete split deliveries by order is used to split the customer demand; (b) a multi-neighborhood structure is designed to enhance the ability of global optimization; (c) two levels of evaluation objectives are set to select the current solution and the best solution; (d) a discriminating strategy of that the best solution must be feasible and the current solution can accept some infeasible solution, helps to balance the performance of the solution and the diversity of the neighborhood solution; (e) an adaptive penalty mechanism will help the candidate solution be closer to the neighborhood of feasible solution; (f) a strategy of tabu releasing is used to transfer the current solution into a new neighborhood of the better solution.

An Application of Analytic Hierarchy Process in Vehicle Routing Problem

Vehicle Routing Problem (VRP) facilitates on finding a set of trips, one for each vehicle and to deliver known quantities of goods from a single depot to a set of geographically dispersed customers. This paper proposes an effective hybrid approach that combines customer prioritization with the Clarke and Wright's savings algorithm to solve the capacitated vehicle routing problem. In this model, in addition to traditional objective of resolving vehicle routing problem, the customer satisfaction have been taken into account. Initially, all the customers have been clustered with the help of Clarke and Wright's saving algorithm and later the customers have been prioritized on assigning optimal route using Analytic Hierarchy Process (AHP) as a Multi Criteria Decision Making (MCDM) tool. The highlight of this research is to diminish the total transportation cost without violating the vehicle capacity and ultimately improve the customer satisfaction.

Ant Colony Optimization Based Memetic Algorithm to Solve Bi-Objective Multiple Traveling Salesmen Problem for Multi-Robot Systems

This paper considers the problem of having a team of mobile robots to visit a set of target locations. This problem is known as multi-robot patrolling problems. In this paper, the problem is formulated as a multiple traveling salesman problem (MTSP) with single depot or multiple depot, which is an non-deterministic polynomial-hard problem. Unlike most previous research works, in real-world applications, the requirement of optimizing the maximum traveled distance and the total traveled distance simultaneously widely exists. In this paper, a bi-objective ant colony optimization (ACO) based memetic algorithm is proposed to solve the problem. In the algorithm, a simple multi-ACO is integrated with a sequential variable neighborhood descent. A powerful local optimization method for bi-objective MTSP is proposed to improve the candidate solutions. In addition, we adopt the technique for order preference by similarity to an ideal solution method to select a reasonable solution from the optimal Pareto. Through computational experiments, we demonstrated the benefits of our algorithm as compared with four other existing algorithms. Computational results show that proposed algorithm is promising and effective for the bi-objective MTSP s.

Two models of the capacitated vehicle routing problem

The aim of the Capacitated Vehicle Routing Problem (CVRP) is to find a set of minimum total cost routes for a fleet of capacitated vehicles based at a single depot, to serve a set of customers. There exist various integer linear programming models of the CVRP. One of the main dierences lies in the way to eliminate sub-tours, i.e. cycles that do not go through the depot. In this paper, we describe a well-known ow formulation of CVRP, where sub-tour elimination constraints have a cardinality exponentially growing with the number of customers. Then we present a mixed linear programming formulation with polynomial cardinality of sub-tour elimination constraints. Both of the models were implemented and compared on several benchmarks.

Complexity of routing problems with release dates and deadlines

The desire of companies to offer same-day delivery leads to interesting new routing optimization problems. We study the complexity of single depot dispatching problems in which a delivery to a customer must occur within a pre-specified time after the customer places the order. Thus, each order has a release date (when the order can be dispatched from the depot) and a service guarantee that implies a deadline (when the order needs to be delivered). A vehicle delivering an order cannot depart the depot before the order is released, and must arrive at the customer at or before the order’s deadline. We show that single and multiple vehicle variants where customers are located on a half-line can be solved to optimality in polynomial time. This setting, as well as our results, generalize those found in Archetti, Feillet, and Speranza (2015).

A choice function hyper-heuristic framework for the allocation of maintenance tasks in Danish railways

A new signalling system in Denmark aims at ensuring fast and reliable train operations. However, it imposes very strict time limits on recovery plans in the event of failure. As a result, it is necessary to develop a new approach to the entire maintenance scheduling process. In the largest region of Denmark, the Jutland peninsula, there is a decentralised structure for maintenance planning where the crew start their duties from their home locations rather than starting from a single depot. In this paper, we allocate a set of maintenance tasks in Jutland to a set of maintenance crew members, defining the sub-region that each crew member is responsible for. Two key considerations must be made when allocating tasks to crew members. Firstly a fair balance of workload must exist between crew members. Secondly, the distance between two tasks in the same sub-region must be minimised in order to facilitate a quick response in the case of unexpected failure. We propose a perturbative selection hyper-heuristic framework to improve initial solutions by reassigning outliers (those tasks that are far away) to another crew member at each iteration, using one of five low-level heuristics. The results from two hyper-heuristics, using a number of different initial solution construction methods are presented over a set of 12 benchmark problem instances.

Emergency logistics for wildfire suppression based on forecasted disaster evolution

This paper aims to develop a two-layer emergency logistics system with a single depot and multiple demand sites for wildfire suppression and disaster relief. For the first layer, a fire propagation model is first built using both the flame-igniting attributes of wildfires and the factors affecting wildfire propagation and patterns. Second, based on the forecasted propagation behavior, the emergency levels of fire sites in terms of demand on suppression resources are evaluated and prioritized. For the second layer, considering the prioritized fire sites, the corresponding resource allocation problem and vehicle routing problem (VRP) are investigated and addressed. The former is approached using a model that can minimize the total forest loss (from multiple sites) and suppression costs incurred accordingly. This model is constructed and solved using principles of calculus. To address the latter, a multi-objective VRP model is developed to minimize both the travel time and cost of the resource delivery vehicles. A heuristic algorithm is designed to provide the associated solutions of the VRP model. As a result, this paper provides useful insights into effective wildfire suppression by rationalizing resources regarding different fire propagation rates. The supporting models can also be generalized and tailored to tackle logistics resource optimization issues in dynamic operational environments, particularly those sharing the same feature of single supply and multiple demands in logistics planning and operations (e.g., allocation of ambulances and police forces).

Approximability of the Vehicle Routing Problem in finite-dimensional Euclidean spaces

The Capacitated Vehicle Routing Problem (CVRP) is a classic combinatorial optimization problem with a wide range of applications in operations research. Since the CVRP is NP-hard even in a finite-dimensional Euclidean space, special attention is traditionally paid to the issues of its approximability. A major part of the known results concerning approximation algorithms and polynomial-time approximation schemes (PTAS) for this problem are obtained for its particular statement in the Euclidean plane. In this paper, we show that the approach to the development of a PTAS for the planar problem with a single depot proposed by Haimovich and Rinnooy Kan in 1985 can be successfully extended to the more general case, for instance, in spaces of arbitrary fixed dimension and for an arbitrary number of depots.

Optimization of sawmill residues collection for bioenergy production

The collection of sawmill residues is an important logistic activity for the pulp and paper industry, which uses the biomass as a source of energy. We study a vehicle routing problem for a network composed of a single depot and several sawmills. The sawmills serve as potential suppliers of biomass residues to the depot, which in turn processes and distributes the residues to the pulp and paper mills. This problem consists of identifying the best daily routing schedule for a fixed number of trucks. The objective is to maximize the ratio of energy returned on energy invested, while satisfying a minimum daily amount of dried biomass residues. There are several random components in the problem, including the availability and moisture content of the biomass residues. We use a combination of scenario analysis and heuristics to solve this stochastic vehicle routing problem. A performance comparison of the proposed method reveals an estimated daily energy savings of 6 GJ over the benchmark method.

An MILP approach for detailed scheduling of oil depots along a multi-product pipeline

Oil depots along products pipelines are important components of the pipeline transportation system and down-stream markets. The operating costs of oil depots account for a large proportion of the total system’s operating costs. Meanwhile, oil depots and pipelines form an entire system, and each operation in a single oil depot may have influence on others. It is a tough job to make a scheduling plan when considering the factors of delivering contaminated oil and batches migration. So far, studies simultaneously considering operating constraints and contaminated oil issues are rare. Aiming at making a scheduling plan with the lowest operating costs, the paper establishes a mixed-integer linear programming model, considering a sequence of operations, such as delivery, export, blending, fractionating and exchanging operations, and batch property differences of the same oil as well as influence of batch migration on contaminated volume. Moreover, the paper verifies the linear relationship between oil concentration and blending capability by mathematical deduction. Finally, the model is successfully applied to one of the product pipelines in China and proved to be practical.

Algorithm for directing cooperative vehicles of a vehicle routing problem for improving fault-tolerance

This paper presents a new algorithm for solving capacitated single depot vehicle routing problems without time windows in a fault-tolerant manner where the distances between points are symmetrical. The sudden breakdown of a vehicle on its pre-planned route is considered as a fault. In this case one of the other cooperating vehicles will take over the remaining tasks and perform them in the most effective way. We introduce the concept of “route change cost” as the difference between the length of the modified and the original routes of the helper vehicle, and our goal is to minimize this value. Starting from an arbitrary VRP solution, we determine the optimal direction, in terms of the route change cost, in which each route should be performed by a vehicle. A simulation with case studies was used to test the algorithm. We found that applying the proposed method, the execution of the original tasks requires routes with lengths 4.1–8.6% shorter on average than using the non-directed routes of the solution of the original vehicle routing problem in arbitrary directions.

Prolonged high-fat diet induces gradual and fat depot-specific DNA methylation changes in adult mice

High-fat diets (HFD) are thought to contribute to the development of metabolism-related diseases. The long-term impact of HFD may be mediated by epigenetic mechanisms, and indeed, HFD has been reported to induce DNA methylation changes in white adipose tissue (WAT) near metabolism related genes. However, previous studies were limited to a single WAT depot, a single time-point and primarily examined the pre-pubertal period. To define dynamic DNA methylation patterns specific for WAT depots, we investigated DNA methylation of Pparg2 and Leptin in gonadal adipose tissue (GAT) and subcutaneous adipose tissue (SAT), at baseline and after 6, 12 and 24 weeks of HFD exposure in adult mice. HFD induced hypermethylation of both the Leptin promoter (max. 19.6% at week 24, P = 2.6·10−3) and the Pparg2 promoter in GAT (max. 10.5% at week 12, P = 0.001). The differential methylation was independent of immune cell infiltration upon HFD exposure. In contrast, no differential methylation in the Pparg2 and Leptin promoter was observed in SAT. Leptin and Pparg2 DNA methylation were correlated with gene expression in GAT. Our study shows that prolonged exposure to HFD in adulthood is associated with a gradually increasing DNA methylation level at the Leptin and Pparg2 promoters in a depot-specific manner.

Non-prespecified Starting Depot Formulations for Minimum-Distance Trajectory Optimization in Patrolling Problem

In this paper, two new formulations are presented for trajectory optimization in the patrolling problem. It is assumed that the starting depot is not prespecified; an assumption that distinguishes the present work from the existing literature. A number of viewpoints are assigned to be visited in a certain sequence to minimize the total travel distance. The problem turns out to be a variant of the well-known Traveling Salesmen Problem (TSP), namely the Single depot multiple Traveling Salesmen Problem (mTSP). Comparisons between the commonly-used prespecified starting depot approach and the proposed formulations are performed and the efficacy of the results is presented through simulations. It is noted that by using the new approach, the total travel distance can be improved by an average of about 20 % compared to the case where the starting depot is prespecified, and by about 40 % in the worst-case scenario (in terms of the starting depot).

Fuzzy capacitated location-routing problem with simultaneous pickup and delivery demands

ABSTRACTIn this work, the fuzzy capacitated location-routing problem with simultaneous pickup and delivery demands (FCLRP-SPD) is considered. This problem is a more realistic case of the capacitated location-routing problem and belongs to the reverse logistics. In FCLRP-SPD, a set of customers with simultaneous pickup and delivery demands should be supplied by a fleet of vehicles that start and end their tours at a single depot. In addition, both pickup and delivery demands of customers are fuzzy variables. The objective function is minimizing the routing costs, fixed costs of establishing the depot(s), and employing the vehicles. To model the problem, a fuzzy chance-constrained programming model is designed based upon the fuzzy credibility theory. To solve the FCLRP-SPD, a greedy clustering method (GCM) is developed, which includes four iterative phases. To achieve the best value of two types of parameters of the model, named ‘vehicle indexes’ and ‘depots indexes’, and to analyze their influences on the final solution, numerical experiments are carried out. Moreover, the efficiency of the GCM is demonstrated using a standard benchmark set of test problems.

A new mathematical formulation for the static demand responsive transport problem

Demand responsive transport is a new transportation mode aiming to make the transportation system easier and more flexible. This mode allows passengers to be carried to their destinations through a set of transportation requests established by customers. These requests are to be answered by a single depot with different vehicle configurations. The idea is to group a number of passengers in the same vehicle respecting of the capacity of each vehicle in order to reduce the operational cost while maintaining a good quality of service. In this paper, we treated the static case of demand responsive transport problem. A new mathematical model for this problem is presented aiming to optimise the cost and the quality of service. This model integrates an original concept; penalty concept to enhance the quality of service. The model is validated on small and medium size instances.

Polynomial Time Algorithms to Minimize Total Travel Time in a Two-Depot Automated Storage/Retrieval System

We sequence storage and retrieval jobs to minimize total travel time of a storage/retrieval (S/R) machine in a two-depot automated storage/retrieval system. These systems include storage systems with aisle-captive S/R machines and storage blocks with bridge cranes. The S/R machine must move retrieval unit loads from their current locations in the system to one of the two depots. In addition, it must move storage unit loads from given depots to given locations in the system. We model the problem as an asymmetric traveling salesman problem, which is in general 𝒩𝒫-hard. We develop an algorithm to solve the problem in polynomial time, using the property that the system has two depots and the S/R machine always returns to one of the depots to pick up or deliver a load. Furthermore, we develop additional polynomial time algorithms for the following four special cases: (1) retrieval loads have to be delivered to given depots; (2) the system has one input depot and one output depot; (3) the system has a single depot; and (4) there are arbitrary S/R machine starting and ending locations. The computational results show the effectiveness of the proposed algorithms. Compared to first-come-first-served and nearest neighbor algorithms, commonly used in practice, the total travel time reduces on average by more than 30% and 15%, respectively.

The impact of postnatal leuprolide acetate treatment on reproductive characteristics in a rodent model of polycystic ovary syndrome

In this study, a GnRH agonist, leuprolide acetate (LA), was given as a single depot injection before 48 h of life to Wistar female rats allotted to prenatal (E16-18) and postnatal androgenization (day 5 of life) by the use of testosterone propionate, looking for reproductive endpoints. Remarkably, a single injection of LA increased the estrus cycles in the postnatal group (PostN) from 0% to 25% of the estrus cycles in the postnatal LA treated group (PostN L). LA also reduced the serum testosterone levels and cysts and atretic follicles in PostN L in contrast with rats (>100 days) from the PostN group (p = 0.04). Prenatally androgenized rats (PreN) exhibited significant modifications in the hypothalamic genes, such as Gnrh. To the best of our knowledge, this is the first study to show that blockage of the GnRH axis with leuprolide acetate depot prevented the development of typical features (anovulation, cysts, atretic follicles) in a postnatal testosterone propionate rat model of PCOS.

Path scheduling for multiple mobile actors in wireless sensor network

ABSTRACTIn wireless sensor network (WSN), energy is the main constraint. In this work we have addressed this issue for single as well as multiple mobile sensor actor network. In this work, we have proposed Rendezvous Point Selection Scheme (RPSS) in which Rendezvous Nodes are selected by set covering problem approach and from that, Rendezvous Points are selected in a way to reduce the tour length. The mobile actors tour is scheduled to pass through those Rendezvous Points as per Travelling Salesman Problem (TSP). We have also proposed novel rendezvous node rotation scheme for fair utilisation of all the nodes. We have compared RPSS with Stationery Actor scheme as well as RD-VT, RD-VT-SMT and WRP-SMT for performance metrics like energy consumption, network lifetime, route length and found the better outcome in all the cases for single actor. We have also applied RPSS for multiple mobile actor case like Multi-Actor Single Depot (MASD) termination and Multi-Actor Multiple Depot (MAMD) termination and observed by extensive simulation that MAMD saves the network energy in optimised way and enhance network lifetime compared to all other schemes.

Integer Programming Model for Two-Centered Double Traveling Salesman Problem

Traveling Salesman Problem (TSP) is among the most popular combinatorial problems and has been widely studied with many extensions in the literature. There have been integer programming formulations and solution approaches for TSP and its variations. One of the most popular topics is the multiple TSP (m-TSP). It has been started to work on the last decades. Generally, m-TSP has a single depot and more than one tour. However, some types have more than one depot. Besides, if seeking, many encounter with double traveling salesman problem (d-TSP). As inferred from the literature, d-TSP is a variation of m-TSP in which two salespersons operate in parallel. They start and end either in a single or two depots. Apart from the literature, a new TSP model has been constructed in this study. The model analyzes the behaviors of traveling salesmen both in the main and secondary tour. Tours have been aggregated via single node existing in the secondary tour. In the application part, Simulated Annealing (SA) was used to optimize the traveling paths of salesmen. The objective parameters of both tours have been explored within a numerical example. According to them, several cost values have been found. The optimum parameters and costs of both tours are to be determined and some practical issues relevant to the behaviors of traveling salesmen have been given. Results suggest that alternative travel plans of traveling salesmen could be possible. Also, findings give hints about both tours and their characteristics.