Job scheduling in virtual manufacturing cells with lot-streaming strategy: a new mathematical model formulation and a genetic algorithm approach

This paper discusses the job scheduling problem in virtual manufacturing cells (VMCs) with the objective of makespan minimization. In the VMC scheduling problem, each job undergoes different processing routes and there is a set of machines to process any operation. Jobs are produced in lot and lot-streaming is permitted. In addition, machines are distributed through the facility, which raises the travelling time issue. For this reason, the decisions are machine assignments, starting times and sub-lot sizes of the operations. We develop a new Mixed Integer Linear Programming (MILP) formulation that considers all aspects of the problem. Owing to the intractability matter, it is unlikely that the MILP could provide solutions for big-sized instances within a reasonable amount of time. We therefore present a Genetic Algorithm (GA) with a new chromosome structure for the VMC environment. Based on a wide range of examinations, comparative results show that GA is quite favourable and that it obtains the optimum solution for any of the instances in the case where sub-lot number equals 1.     

Job shop scheduling with unit time operations under resource constraints and release dates

We consider the problem of job shop scheduling with m machines and n jobs J_i, each consisting of l_i unit time operations. There are s distinct resources R_h and a quantity q_h available of each one. The execution of the j-th operation of J_i requires the presence of u_ijh units of R_h, 1 ≤i≤n, 1 ≤j≤l_i, and 1 ≤h≤s. In addition, each J_i has a release date r_i, that is J_i cannot start before time r_i. We describe algorithms for finding schedules having minimum length or sum of completion times of the jobs. Let l=max{l_i} and u=|{u_ijh}|. If m, u and l are fixed, then both algorithms terminate within polynomial time.     

Truck routing and scheduling

The problem is part of a complex software solution for truck itinerary construction for one of the largest public road transportation companies in the EU. In practice a minor improvement on the operational cost per tour can decide whether a freight services company is profitable or not. Thus the optimization of routes has key importance in the operation of such companies. Given an initial location and an asset state one must be able to calculate a cost optimal itinerary containing all Point of Interests. Such an itinerary is an executable plan which exactly specifies the location and activity of an asset during the whole timespan of the itinerary. If parking places and gas stations are included in the planning then it is NP hard to find an optimal solution. This means that for long range tours an approximately optimal solution for refueling has to be given within an acceptable running time. Also the corridoring of the trucks is an important problem so that we try to optimize the performance, hence tours cannot be recalculated at each data arrival. The vehicle assignment part of this work is already finished and applied with very good results. The remaining part is subject of an ongoing research which started at January 2014. The company started to apply and test our product in the beginning of 2015 under increased human supervision. As a consequence of the project a large cost saving is anticipated by the company.     

City-courier routing and scheduling problems

This research seeks to propose innovative routing and scheduling strategies to help city couriers reduce operating costs and enhance service level. The strategies are realized by constructing a new type of routing and scheduling problem. The problem directly takes into account the inherent physical and operating constraints associated with riding in city distribution networks, which makes the problem involve multiple objectives and visiting specified nodes and arcs. Through network transformations, this study first formulates the city-courier routing and scheduling problem as a multi-objective multiple traveling salesman problem with strict time windows (MOMTSPSTW) that is NP-hard and new to the literature, and then proposes a multi-objective Scatter Search framework that seeks to find the set of Pareto-optimal solutions to the problem. Various new and improved sub-procedures are embedded in the solution framework. This is followed by an empirical study that shows and analyzes the results of applying the proposed method to a real-life city-courier routing and scheduling problem.     

Home health care routing and scheduling problems: a literature review

4OR - Home health services arise from the need for hospitals to care for patients and/or dependent persons who, due to special conditions, require hospitalisation and/or care at home. The...     

Disruption management in vehicle routing and scheduling for road freight transport: a review

Disruption management is an approach to the rescheduling of operations following an unanticipated event occurring that has been applied in a wide range of applications, including airline scheduling and project management. This review focusses on the use of disruption management in vehicle routing and scheduling applied to road freight distribution. The paper discusses the key features of disruption management and examines the relevant objectives and types of disruption that may occur in this context. Different formulations and solution methods are described. A set of relevant papers are summarised and classified according to the type of disruption addressed, the relevant objectives and the solution approach.     

Cargo ships routing and scheduling: Survey of models and problems

When a ship costs thousands of dollars per day, significant savings can be achieved by proper fleet routing and scheduling. In contrast to vehicle scheduling, relatively little work has been done in ship routing and scheduling. This paper discusses briefly the differences between vehicle and ship routing and scheduling and the reasons for the low attention to ship scheduling in the past. The various modes of operation of cargo ships are described and a classification scheme for ship routing and scheduling models and problems is proposed. A review of ship routing, scheduling and related models is provided. The review is broken down into the following categories: transportation system models, liner operations, tramp shipping, industrial operations and other models. Finally, recent trends in ship scheduling, shortcomings in existing models and requirements from realistic models are discussed.     

Job scheduling, cooperation, and control

This paper studies one machine job scheduling situations where clients can have more than one job to be processed and where a job can be of interest for different players. Corresponding cooperative games are introduced and a result on balancedness is provided.     

Ship routing and scheduling with flexible cargo sizes

Here, we describe a real planning problem in the tramp shipping industry. A tramp shipping company may have a certain amount of contract cargoes that it is committed to carry, and tries to maximize the profit from optional cargoes. For real long-term contracts, the sizes of the cargoes are flexible. However, in previous research within tramp ship routing, the cargo quantities are regarded as fixed. We present an MP-model of the problem and a set partitioning approach to solve the multi-ship pickup and delivery problem with time windows and flexible cargo sizes. The columns are generated a priori and the most profitable ship schedule for each cargo set–ship combination is included in the set partitioning problem. We have tested the method on several real-life cases, and the results show the potential economical effects for the tramp shipping companies by utilizing flexible cargo sizes when generating the schedules.     

Ship routing and scheduling in the new millennium

We review research on ship routing and scheduling and related problems during the new millennium and provide four basic models in this domain. The volume of research in this area about doubles every decade as does the number of research outlets. We have found over a hundred new refereed papers on this topic during the last decade. Problems of wider scope have been addressed as well as more specialized ones. However, complex critical problems remain wide open and provide challenging opportunities for future research.     

Flow-shop scheduling with setup and assembly operations

A scheduling model for a production system including machining, setup and assembly operations is considered. Production of a number of single-item products is ordered. Each product is made by assembling a set of several different parts. First, the parts are manufactured in a flow-shop consisting of multiple machines. Then, they are assembled into products on a single assembly stage. Setup operation and setup time are needed when a machine starts processing the parts or it changes items. The operations are partitioned into several blocks. Each block consists of the machining operations, the setup operations, and the assembly operation(s) for one or several products. The parts of the same item in a block are processed successively. The objective function is the mean completion time for all products. We consider a problem to partition the operations into blocks and sequence the parts in each block so as to minimize the objective function. Solution procedures using pseudo-dynamic programming and a branch-and-bound method are proposed. Computational experiments are carried out to evaluate the performance of the solution procedures. It has been found that a good near-optimal schedule is obtained efficiently by the proposed solution procedures.     

Vehicle routing and scheduling with time-varying data: A case study

A heuristic algorithm is described for vehicle routing and scheduling problems to minimise the total travel time, where the time required for a vehicle to travel along any road in the network varies according to the time of travel. The variation is caused by congestion that is typically greatest during morning and evening rush hours. The algorithm is used to schedule a fleet of delivery vehicles operating in the South West of the United Kingdom for a sample of days. The results demonstrate how conventional methods that do not take time-varying speeds into account when planning, except for an overall contingency allowance, may still lead to some routes taking too long. The results are analysed to show that in the case study using the proposed approach can lead to savings in CO₂ emissions of about 7%.     

Computing inter-site distances for routing and scheduling problems

Routing and scheduling problems have received considerable attention in the literature in terms of model building and algorithm development. On these fronts, progress has been substantial. However, one often neglected (yet critical) aspect concerning the use of these models and algorithms is their data requirements. In particular, the distance matrix yielding the shortest distance between each pair of sites (nodes) represents a major portion of the data required by all such problems. Yet, such data are seldom available with the degree of accuracy desired and often are not available at all.This paper describes an efficient method for obtaining this distance matrix that is based on the underlying road structure for the geographic region in question. Thus, the distances obtained reflect ‘actual’ distances. Finally, the paper presents some brief computational experience and discusses an implementation concerning the routing of environmental inspectors in the state of Pennsylvania.     

A note on a mixed routing and scheduling problem on a grid graph

We consider a particular case of the Fleet Quickest Routing Problem (FQRP) on a grid graph of m × n nodes that are placed in m levels and n columns. Starting nodes are placed at the first (bottom) level, and nodes of arrival are placed at the mth level. A feasible solution of FQRP consists in n Manhattan paths, one for each vehicle, such that capacity constraints are respected. We establish m*, i.e. the number of levels that ensures the existence of a solution to FQRP in any possible permutation of n destinations. In particular, m* is the minimum number of levels sufficient to solve any instance of FQRP involving n vehicles, when they move in the ways that the literature has until now assumed. Existing algorithms give solutions that require, for some values of n, more levels than m*. For this reason, we provide algorithm CaR, which gives a solution in a graph m* × n, as a minor contribution.     

Integrated machine scheduling and vehicle routing with time windows

This paper integrates production and outbound distribution scheduling in order to minimize total tardiness. The overall problem consists of two subproblems. The first addresses scheduling a set of jobs on parallel machines with machine-dependent ready times. The second focusses on the delivery of completed jobs with a fleet of vehicles which may differ in their loading capacities and ready times. Job-dependent processing times, delivery time windows, service times, and destinations are taken into account. A genetic algorithm approach is introduced to solve the integrated problem as a whole. Two main questions are examined. Are the results of integrating machine scheduling and vehicle routing significantly better than those of classic decomposition approaches which break down the overall problem, solve the two subproblems successively, and merge the subsolutions to form a solution to the overall problem? And if so, is it possible to capitalize on these potentials despite the complexity of the integrated problem? Both questions are tackled by means of a numerical study. The genetic algorithm outperforms the classic decomposition approaches in case of small-size instances and is able to generate relatively good solutions for instances with up to 50 jobs, 5 machines, and 10 vehicles.     

A tabu search heuristic for ship routing and scheduling

The purpose of this paper is to solve a planning problem faced by many shipping companies dealing with the transport of bulk products. These shipping companies are committed to carrying some contract cargoes and will try to derive additional revenue from optional spot cargoes. An efficient tabu search algorithm has been developed to ensure quick decision support for the planners. The solutions generated by the tabu search heuristic are compared with those produced by a previously published multi-start local search heuristic. Computational results show that the tabu search heuristic yields optimal or near-optimal solutions to real-life instances within reasonable time. For large and tigthly constrained cases, the tabu search heuristic provides much better solutions than the multi-start local search heuristic. A version of the tabu search heuristic will be integrated as an improved solver in a prototype decision support system used by several shipping companies.     

Iterated local search for workforce scheduling and routing problems

The integration of scheduling workers to perform tasks with the traditional vehicle routing problem gives rise to the workforce scheduling and routing problems (WSRP). In the WSRP, a number of service technicians with different skills, and tasks at different locations with pre-defined time windows and skill requirements are given. It is required to find an assignment and ordering of technicians to tasks, where each task is performed within its time window by a technician with the required skill, for which the total cost of the routing is minimized. This paper describes an iterated local search (ILS) algorithm for the WSRP. The performance of the proposed algorithm is evaluated on benchmark instances against an off-the-shelf optimizer and an existing adaptive large neighbourhood search algorithm. The proposed ILS algorithm is also applied to solve the skill vehicle routing problem, which can be viewed as a special case of the WSRP. The computational results indicate that the proposed algorithm can produce high-quality solutions in short computation times.