A global MILP model for FMS scheduling

Flexible manufacturing systems (FMS) require intelligent scheduling strategies to achieve their principal benefit — combining high flexibility with high productivity. A mixed-integer linear programming model (MILP) is presented here for FMS scheduling. The model takes a global view of the problem and specifically takes into account constraints on storage and transportation. Both of these constrained resources are critical for practical FMS scheduling problems and are difficult to model. The MILP model is explained and justified and its complexity is discussed. Two heuristic procedures are developed, based on an analysis of the global MILP model. Computational results are presented comparing the performance of the different solution strategies. The development of iterative global heuristics based on mathematical programming formulations is advocated for a wide class of FMS scheduling problems.     

A sequential integer programming method for discontinuous labor tour scheduling

General set-covering formulations (GSCFs) of labor tour scheduling problems have recently received substantial attention in the research literature. The most successful heuristic approaches to these problems have used the linear programming (LP) solution to the GSCF as a starting point and subsequently applied heuristic augmentation and improvement procedures to obtain feasible integer solutions. Integer programming (IP) methods eliminate the need for augmentation and improvement procedures, but have generally been considered intractable for large GSCFs. In this paper we present a sequential mixed-integer programming (SMIP) heuristic for discontinuous (< 24 hours/day) tour-scheduling problems which takes advantage of the structure of the GSCF. The new heuristic substantially outperformed two prominent LP-based methods across 432 full-time workforce test problems, yielding optimal solutions for 429 of the problems. For a set of 36 test problems associated with a mixed-workforce scheduling environment that allowed both full-time and part-time employees with varying levels of cost and productivity, the SMIP heuristic yielded solution costs that were significantly better than previously published costs obtained with competitive methods.     

A market-based multi-agent system model for decentralized multi-project scheduling

We consider a multi-project scheduling problem, where each project is composed of a set of activities, with precedence relations, requiring specific amounts of local and shared (among projects) resources. The aim is to complete all the project activities, satisfying precedence and resource constraints, and minimizing each project schedule length. The decision making process is supposed to be decentralized, with as many local decision makers as the projects. A multi-agent system model, and an iterative combinatorial auction mechanism for the agent coordination are proposed. We provide a dynamic programming formulation for the combinatorial auction problem, and heuristic algorithms for both the combinatorial auction and the bidding process. An experimental analysis on the whole multi-agent system model is discussed.     

The Impact of Operational Research on Agriculture

The paper shows that agriculture is one of the United Kingdom's largest industries. It would therefore be expected that O.R. could have made a significant contribution to decision making. But achievements in practice have been disappointingly small. The industry comprises of a large number of small individual businesses which do not permit specialisation in management functions. Consequently, technical advice and much R and D is provided from public funds. O.R. applications for agriculture have mainly been developed by Universities, Colleges, State Advisory Services and QUANGOS.The paper discusses some techniques used in agriculture—linear programming, dynamic programming and simulation—and outlines some problems encountered with these. Other techniques have had limited uptake and application. Reasons for the disappointing impact of O.R. are discussed as a set of problems-those specific to farmers and their systems; those specific to computer use; problems in recruiting and training O.R. specialists and problems in communication.     

Charging scheduling problem of an M-to-N electric vehicle charger

This study investigates a real case of charging scheduling of an electric vehicle charger with multiple ports called M-to-N charger. The charger is designed for a multi-unit dwelling facility and can charge N electric vehicles simultaneously despite the supplied charging capacity being limited to only M electric vehicles. The electric vehicles arrive at the charger randomly and stay for their desired length of time, during which they must be charged as much as possible with minimum electric cost. The scheduling problem considers four objectives: maximizing the total charging amount, minimizing the total charging cost, minimizing the charging completion time, and maximizing the charging balance among the electric vehicles. A mixed-integer linear programming model and a relaxation-based heuristic algorithm are developed. Computational experiment results show that the proposed heuristic algorithm can generate schedules within 8 s for this case study by using an open-source linear programming solver. Compared with the mixed-integer programming algorithm, the proposed heuristic algorithm can provide solutions with less than 7% charging amount gap and 4% price gap. The proposed heuristic algorithm is successfully implemented in a real M-to-N charger.     

Dynamic programming based heuristics for the topological design of local access networks

This paper deals with the terminal layout problem, which is a problem arising in data communication network design. The problem consists of finding the best way to link terminals to a computer site and, in graph-theoretical terms, it resorts to determining a minimal spanning tree with an additional constraint (CMST). We present a class of heuristics that combine dynamic programming with clustering and decomposition techniques. More specifically, the original problem is transformed, either by clustering or decomposition, in order to obtain smaller size problems that can be handled by a dynamic programming approach. Such heuristics were specifically aimed at improving solutions produced by the Esau-Williams algorithm, which is one of the most effective heuristics presented in the literature for the CMST. Actually, computational experience confirms that such improvements can be achieved by the new heuristic.This research was partially supported by JNICT (Junta Nacional de Investigação Científica e Tecnológica) under Research Contract No. 87383/MIC.     

Multiple orders per job batch scheduling with incompatible jobs

The multiple orders per job (MOJ) scheduling problem is presented for the batch-processing environment such as that exemplified by diffusion ovens. A mixed-integer programming formulation is presented for the incompatible job family case wherein only jobs that belong to the same family may be grouped together in a production batch. This optimization formulation is tested through an extensive experimental design with the objective of minimizing total weighted tardiness (maximizing on-time delivery performance). Optimal solutions are achievable for this initial set of 6-to-12 order problems, but it is noted that the optimization model takes an unreasonable amount of computation time, which suggests the need for heuristic development to support the analysis of larger, more practical MOJ batch scheduling problems. A number of simple heuristic approaches are investigated in an attempt to find near-optimal solutions in a reasonable amount of computation time. It is seen that a combination of the heuristics produces near-optimal solutions for small order problems. Further testing proves that these heuristic combinations are the best for large order problems as well.     

A bicriteria m-machine flowshop scheduling with sequence-dependent setup times

In this study, a bicriteria m-machine flowshop scheduling with sequence-dependent setup times is considered. The objective function of the problem is minimization of the weighted sum of total completion time and makespan. Only small size problems with up to 6 machines and 18 jobs can be solved by the proposed integer programming model. Also the model is tested on an example. We also proposed three heuristic approaches for solving large jobs problems. To solve the large sizes problems up to 100 jobs and 10 machines, special heuristics methods is used. Results of computational tests show that the proposed model is effective in solving problems.     

Evaluation of mathematical models for flexible job-shop scheduling problems

With the rapid development in computer technologies, mathematical programming-based technique to solve scheduling problems is significantly receiving attention from researchers. Although, it is not efficient solution method due to the NP-hard structure of these problems, mathematical programming formulation is the first step to develop an effective heuristic. Numerous comparative studies for variety scheduling problems have appeared over the years. But in our search in literature there is not an entirely review for mathematical formulations of flexible job shop scheduling problems (FJSP). In this paper, four the most widely used formulations of the FJSP are compiled from literature and a time-indexed model for FJSP is proposed. These formulations are evaluated under three categories that are distinguished by the type of binary variable that they rely on for using of sequencing operations on machines. All five formulations compared and results are presented.     

Minimizing makespan in a two-machine flowshop scheduling with batching and release time

This paper studies two-machine flowshop scheduling with batching and release time, whose objective is to minimize the makespan. We formulate the scheduling problem as a mixed integer programming model and show that it is a strongly NP-hard problem. We derive a lower bound and develop dynamic programming-based heuristic algorithms to solve the scheduling problem. Computational experiments are carried out to evaluate the performance of the heuristic algorithms. The numerical results show that some of the heuristic algorithms can indeed find effective solutions for the scheduling problem.     

A bicriteria flowshop scheduling with a learning effect

In many situations, a worker’s ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the learning effect. In this paper the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes a weighted sum of total completion time and makespan. Total completion time and makespan are widely used performance measures in scheduling literature. To solve this scheduling problem, an integer programming model with n² + 6n variables and 7n constraints where n is the number of jobs is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, the problem with up to 30 jobs can be solved. A heuristic algorithm and a tabu search based heuristic algorithm are presented to solve large size problems. Experimental results show that the proposed heuristic methods can solve this problem with up to 300 jobs rapidly. According to the best of our knowledge, no work exists on the bicriteria flowshop with a learning effect.     

Combined vehicle routing and scheduling with temporal precedence and synchronization constraints

We present a mathematical programming model for the combined vehicle routing and scheduling problem with time windows and additional temporal constraints. The temporal constraints allow for imposing pairwise synchronization and pairwise temporal precedence between customer visits, independently of the vehicles. We describe some real world problems where in the literature the temporal constraints are usually remarkably simplified in the solution process, even though these constraints may significantly improve the solution quality and/or usefulness. We also propose an optimization based heuristic to solve real size instances. The results of numerical experiments substantiate the importance of the temporal constraints in the solution approach. We also make a computational study by comparing a direct use of a commercial solver against the proposed heuristic, where the latter approach can find high quality solutions within specific time limits.     

A hybrid heuristic and linear programming approach to multi-product machine scheduling

A new heuristic approach is presented for scheduling economic lots in a multi-product single-machine environment. Given a pre-defined master sequence of product setups, an integer linear programming formulation is developed which finds an optimal subsequence and optimal economic lots. The model takes explicit account of initial inventories, setup times and allows setups to be scheduled at arbitrary epochs in continuous time, rather than restricting setups to a discrete time grid. We approximate the objective function of the model and solve to obtain an optimal capacity feasible schedule for the approximate objective. The approach was tested on a set of randomly generated problems, generating solutions that are on average 2.5% above a lower bound on the optimal cost. We also extend the approach to allow shortages.     

An approximate solution approach for a scenario-based capital budgeting model

Real options techniques such as contingent claims analysis and dynamic programming can be used for project evaluation when the project develops stochastically over time and the decision to invest into this project can be postponed. Following that perspective, Meier et al. (Oper Res 49(2):196–2 06, 2001) presented a scenario based model that captures risk uncertainty and managerial flexibility, maximizing the time-varying of a portfolio of investment options. However, the corresponding linear integer program turns out to be quite intractable even for a small number of projects and time periods. In this paper, we propose a heuristic approach based on an alternative scenario based model involving a much less number of variables. The new approach allows the determination of reasonable quality approximate solutions with huge reductions on the computational times required for solving large size instances.     

Models and algorithms for a staff scheduling problem

We present mathematical models and solution algorithms for a family of staff scheduling problems arising in real life applications. In these problems, the daily assignments to be performed are given and the durations (in days) of the working and rest periods for each employee in the planning horizon are specified in advance, whereas the sequence in which these working and rest periods occur, as well as the daily assignment for each working period, have to be determined. The main objective is the minimization of the number of employees needed to perform all daily assignments in the horizon. We decompose the problem into two steps: the definition of the sequence of working and rest periods (called pattern) for each employee, and the definition of the daily assignment to be performed in each working period by each employee. The first step is formulated as a covering problem for which we present alternative ILP models and exact enumerative algorithms based on these models. Practical experience shows that the best approach is based on the model in which variables are associated with feasible patterns and generated either by dynamic programming or by solving another ILP. The second step is stated as a feasibility problem solved heuristically through a sequence of transportation problems. Although in general this procedure may not find a solution (even if one exists), we present sufficient conditions under which our approach is guaranteed to succeed. We also propose an iterative heuristic algorithm to handle the case in which no feasible solution is found in the second step. We present computational results on real life instances associated with an emergency call center. The proposed approach is able to determine the optimal solution of instances involving up to several hundred employees and a working period of up to 6 months. Mathematics Subject Classification (2000): 90B70, 90C10, 90C27, 90C39, 90C57, 90C59     

A decision theory based scheduling procedure for single-machine weighted earliness and tardiness problems

We consider the dynamic single-machine scheduling problem where the objective is to minimize the sum of weighted earliness and weighted tardiness costs. A single pass heuristic, based on decision theory, is developed for constructing schedules. The heuristic permits schedules with idle time between jobs and behaves like a dispatching procedure. The performance of the new heuristic is examined using 116 published problems for which the optimum solution is known. Its performance is also investigated using 540 randomly generated problems covering a variety of conditions by comparing it to two well known dispatching procedures, adapted for dynamic early/tardy problems. The results indicate that the heuristic performs very well.     

Evolutionary hybrid approaches for generation scheduling in power systems

Generation scheduling (GS) in power systems is a tough optimisation problem which continues to present a challenge for efficient solution techniques. The solution is to define on/off decisions and generation levels for each electricity generator of a power system for each scheduling interval. The solution procedure requires simultaneous consideration of binary decision and continuous variables. In recent years researchers have focused much attention on developing new hybrid approaches using evolutionary and traditional exact methods for this type of mixed-integer problems. This paper investigates how the optimum or near optimum solution for the GS problem may be quickly identified. A design is proposed which uses a variety of metaheuristic, heuristics and mathematical programming techniques within a hybrid framework. The results obtained for two case studies are promising and show that the hybrid approach offers an effective alternative for solving the GS problems within a realistic timeframe.     

A New Application of Incremental Analysis in Resource Allocations

This paper presents an optimization procedure which would offer a much simpler and faster procedure than dynamic programming in reaching optimal solutions for a special class of resource allocation problems. The solution method is based upon an incremental analysis and does not require further computation beyond the conversion of a payoff table to a table of marginal payoffs by simple subtractions. The optimality of the incremental solution will be demonstrated by a heuristic proof with several examples; and a numerical problem to illustrate the use of incremental analysis as well as to compare it with the solution procedure of dynamic programming will also be given.     

Matheuristic for the decentralized factories scheduling problem

In this study, a novel mixed integer linear programming (MILP) model is developed for the decentralized factories scheduling problem, where a set of transporters is used for shipping goods among parallel factories to minimize the production costs over all of the factories. Due to its typical features, such as multiple heterogeneous factories and transportation times, this problem is extremely difficult to solve, especially for large-scale problems. In order to address this difficulty, the main aim of this study is to develop a new solution algorithm based on the interoperation of metaheuristics and mathematical programming techniques to minimize the production costs for jobs. The algorithm comprises an electromagnetism-like algorithm and variable neighborhood search. In this hybridization based on MILP relaxation, the guiding principle involves the ordering of neighborhood structures. The results obtained by the proposed algorithm and MILP are analyzed and compared for various test problems.