Tour Scheduling and Task Assignment of a Heterogeneous Work Force: A Heuristic Approach

The dual problem of work tour scheduling and task assignment involving workers who differ in their times of availability and task qualifications is examined in this paper. The problem is presented in the context of a fast food restaurant, but applies equally well to a diverse set of service operations. Developing a week-long labor schedule is a nontrivial problem, in terms of complexity and importance, which a manager spends as much as a full workday solving. The primary scheduling objective (the manager's concern) is the minimization of overstaffing in the face of significant hourly and daily fluctuations in minimum staffing requirements. The secondary objective (the workers’ concern) is the minimization of the sum of the squared differences between the number of work hours scheduled and the number targeted for each employee. Contributing to scheduling complexity are constraints on the structure of work tours, including minimum and maximum shift lengths and a maximum number of workdays. A goal programming formulation of a representative problem is shown to be too large, for all practical purposes, to be solved optimally. Existing heuristic procedures related to this research possess inherent limitations which render them inadequate for our purposes. Subsequently, we propose and demonstrate a computerized heuristic procedure capable of producing a labor schedule requiring at most minor refinement by a manager.     

Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry

We study the Mean-SemiVariance Project (MSVP) portfolio selection problem, where the objective is to obtain the optimal risk-reward portfolio of non-divisible projects when the risk is measured by the semivariance of the portfolio׳s Net-Present Value (NPV) and the reward is measured by the portfolio׳s expected NPV. Similar to the well-known Mean-Variance portfolio selection problem, when integer variables are present (e.g., due to transaction costs, cardinality constraints, or asset illiquidity), the MSVP problem can be solved using Mixed-Integer Quadratic Programming (MIQP) techniques. However, conventional MIQP solvers may be unable to solve large-scale MSVP problem instances in a reasonable amount of time. In this paper, we propose two linear solution schemes to solve the MSVP problem; that is, the proposed schemes avoid the use of MIQP solvers and only require the use of Mixed-Integer Linear Programming (MILP) techniques. In particular, we show that the solution of a class of real-world MSVP problems, in which project returns are positively correlated, can be accurately approximated by solving a single MILP problem. In general, we show that the MSVP problem can be effectively solved by a sequence of MILP problems, which allow us to solve large-scale MSVP problem instances faster than using MIQP solvers. We illustrate our solution schemes by solving a real MSVP problem arising in a Latin American oil and gas company. Also, we solve instances of the MSVP problem that are constructed using data from the PSPLIB library of project scheduling problems.     

Hospital resident scheduling problem

This paper addresses the resident scheduling problem (RSP) at hospitals concerned with prescribing work-nights for residents while considering departmental staffing and skill requirements as well as residents' preferences. Three scenarios that represent most situations and account for various departmental requirements and needs are described. Although similar scheduling problems are considered in the literature, no analysis exists that adequately deals with the speciffic nature of this problem. The problem is modeled as a mixed-integer program and heuristic solution procedures are developed for the different identified scheduling scenarios. These procedures exploit the inherent network structure of the problem which is an important feature that enhances problem solvability. For the sake of comparison, the problem is also solved exactly via the CPLEX-MIP (version 6.0) package. The contribution of this work is important since many hospitals are still utilizing manual techniques in preparing their own schedules, expending considerable effort and time and yet contending with limited scheduling flexibility.     

An object-oriented methodology for solving the RCPSPs with heuristics and metaheuristics

Because various heuristics and metaheuristics have been proposed to solve the well known NP-hard, resourceconstrained project scheduling problem (RCPSP), it is currently difficult to compare the computational efficiency of these heuristics implemented on different computers where, in addition, the computer codes may have been written in different computer languages. This problem is solved when all relevant heuristics can be applied within the framework of a single computer program. By use of the object-oriented programming (OOP) methodology, we developed a general software framework for the heuristics and metaheuristics for solving the RCPSP. Currently this includes six heuristics and two metaheuristics. The framework of the software allows a more advanced user to append more effective heuristics and play around with several parameters of these metaheuristics with a bare minimum of coding effort.     

Scheduling algorithms for computer-aided line balancing in printed circuit board assembly

Generalized flexible flow line (GFFL) is a scheduling environment comprising several machine banks which the products visit in the same order but can skip some machine banks. The type of machines in a bank can differ but they are suitable for performing the same manufacturing tasks. To change one product to another demands a set-up operation of the machine. This paper describes several scheduling algorithms for the GFFL problem. The overall structure of these algorithms is similar, consisting of machine allocation and sequencing phases. The algorithms have been integrated into an interactive production scheduling system for electronics assembly. Sample cases are used to illustrate the operation of the system in practice.     

Robust Resource Allocation Decisions in Resource‐Constrained Projects*

The well‐known deterministic resource‐constrained project scheduling problem involves the determination of a predictive schedule (baseline schedule or pre‐schedule) of the project activities that satisfies the finish–start precedence relations and the renewable resource constraints under the objective of minimizing the project duration. This baseline schedule serves as a baseline for the execution of the project. During execution, however, the project can be subject to several types of disruptions that may disturb the baseline schedule. Management must then rely on a reactive scheduling procedure for revising or reoptimizing the baseline schedule. The objective of our research is to develop procedures for allocating resources to the activities of a given baseline schedule in order to maximize its stability in the presence of activity duration variability. We propose three integer programming–based heuristics and one constructive procedure for resource allocation. We derive lower bounds for schedule stability and report on computational results obtained on a set of benchmark problems.     

Single-machine batch delivery scheduling with an assignable common due window

This paper addresses a batch delivery single-machine scheduling problem in which jobs have an assignable common due window. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find the optimal size and location of the window, the optimal dispatch date for each job, as well as an optimal job sequence to minimize a cost function based on earliness, tardiness, holding time, window location, window size, and batch delivery. We show that the problem can be optimally solved in O(n⁸)$O(n^8)$ time by a dynamic programming algorithm under a reasonable assumption on the relationships among the cost parameters. A computational experiment is also conducted to evaluate the performance of the proposed algorithm. We also show that some special cases of the problem can be optimally solved by lower order algorithms.     

TECHNICAL NOTE: A SIMPLE MODEL FOR OPTIMIZING THE SINGLE MACHINE EARLY/TARDY PROBLEM WITH SEQUENCE-DEPENDENT SETUPS

A simple mixed integer programming model for the N job/single machine scheduling problem with possibly sequence-dependent setup times, differing earliness/tardiness cost penalties, and variable due dates is proposed and evaluated for computational efficiency. Results indicated that the computational effort required to reach optimality rose with the number of jobs to be scheduled and with decreased variance in due dates. Though computational effort was significant for the largest problems solved, the model remained viable for optimizing research scale problems.     

Constraint-based model for the cyclic multi-hoists scheduling problem

This article presents a method for the resolution of a material handling scheduling problem. The case studied is a real industrial problem. It consists of finding a cyclic schedule for hoist movements in a treatment surface shop. In this kind of facility, several hoists are used for all the handling operations and they have to share common zones. Then it is necessary to control that there is no collision. The mathematical formulation of the problem is based on a combination of disjunctive constraints. The constraints describe either movement schedule or collision avoidance. The resolution procedure presented identifies all the collision configurations and then uses a branch and bound-like algorithm to find the optimal solution of a given problem. The language chosen for our implementation is the constraint logic programming language: Prolog IV, which is able to solve constraints with rational variables. It actively uses the constraint propagation mechanism that can be found in several languages.     

Data Driven Modeling: An Application in Scheduling

This paper presents a data driven modeling (DDM) approach to certain types of optimization problems. DDM relinquishes control of the completed model to the user department rather than the operations research (OR) staff. The approach emphasizes development of models that are dependent on data maintained and understood by the users. The data base consists of coded user rules which describe when changes will occur in the problem structure and data which captures the generalization of the problem. Both the rules and data can be updated by user department personnel. These data drive a matrix generator controlled by the rules which uses the data base as input to generate the specific model formulation. This DDM system is designed by OR consultants or staff to allow independence of use along with low-cost and minimal-effort maintenance. The DDM approach is illustrated with an application to a real-world medical scheduling problem.     

Multimode time-cost-robustness trade-off project scheduling problem under uncertainty

The time/cost trade-off problem is a well-known project scheduling problem that has been extensively studied. In recent years, many researchers have begun to focus on project scheduling problems under uncertainty to cope with uncertain factors, such as resource idleness, high inventory, and missing deadlines. To reduce the disturbance from uncertain factors, the aim of robust scheduling is to generate schedules with time buffers or resource buffers, which are capped by project makespan and project cost. This paper addresses a time-cost-robustness trade-off project scheduling problem with multiple activity execution modes under uncertainty. A multiobjective optimization model with three objectives (makespan minimization, cost minimization, and robustness maximization) is constructed and three propositions are proposed. An epsilon-constraint method-based genetic algorithm along with three improvement measures is designed to solve this NP-hard problem and to develop Pareto schedule sets, and a large-scale computational experiment on a randomly generated dataset is performed to validate the effectiveness of the proposed algorithm and the improvement measures. The final sensitivity analysis of three key parameters shows their distinctive influences on the three objectives, according to which several suggestions are given to project managers on the effective measures to improve the three objectives.

     

Interactive Job Shop Scheduling: An Experiment

An experiment is discussed in which three computer-aided, interactive job shop scheduling approaches are compared using an interactive job shop scheduling simulator (JOB) developed for the project. All three approaches use a combination of computer and human capabilities to develop job shop schedules, but differ in terms of the timing and degree of human involvement required. The three scheduling approaches are (1) the successive approach, (2) the interactive approach, and (3) the semi-interactive approach. The successive approach is characterized by the computer scheduling all work orders without any human intervention. The interactive approach is distinguished by the human scheduling one work order at a time until all work orders are scheduled. The schedule is developed interactively by the person who must simultaneously consider work-order scheduling needs and machine group load capacities. The semi-interactive approach may be viewed as a combination of the successive and interactive approaches. Work orders are automatically scheduled one at a time using the successive approach criteria, but with prespecified machine-group load thresholds. As long as the load threshold is not exceeded, the successive approach is used to schedule work orders. When a threshold is exceeded, the algorithm (successive approach) pauses and human rescheduling (interactive approach) is required to rectify the overload situation. A second (reallocation) phase, identical for all three approaches, is used to overcome any scheduling problems generated in phase one. Experimental results based on nine different performance criteria (including scheduling time, makespan, machine group utilization, and work-in-process inventory) and 45 experimental runs indicate that there are differences between the results produced by the three scheduling approaches. The interactive approach yields the best overall scheduling results, but the other two approaches are clearly better than the interactive approach in some situations. The success of the interactive approach indicates that it is usually best for the human scheduler to become involved early in the computer-based job shop scheduling process.     

Joint Lot Sizing and Scheduling of Multiple Items with Sequence-Dependent Setup Costs

The objective of this research is to investigate the effects of setup-cost estimating methods on the lot sizing and scheduling of multiple products in multiple periods. These initial setup cost estimators (ISCEs) are used to estimate sequence-independent initial setup costs from sequence-dependent setup costs. A search of the literature reveals that, although sequence-dependent setup costs are frequently found in practice and ISCEs are frequently used, there is a dearth of research concerning the effect of using ISCEs. After a review of the literature, a mixed integer formulation of the joint problem of lot sizing and scheduling is presented, followed by a discussion of the difficulty in solving the formulation. Next, the six ISCEs evaluated are presented. These ISCEs range from simple (select the minimum setup cost) to complex (use the branch-and-bound solution to a traveling salesman-type problem). Each ISCE is evaluated using a full factorial design with five independent variables: demand distribution (three levels), demand trend (three levels), setup to inventory level (six levels), setup distribution (three levels), and setup variability (two levels). Two hypotheses are researched. Do the more computationally complex ISCEs produce lower overall costs than do the simpler ISCEs? Does the reduction in total cost justify the additional computation cost? The results of this study demonstrate that it may be incorrect to use “conventional wisdom'’when selecting an ISCE.     

Flow shop scheduling by transportation model

This paper describes the classical problem of scheduling n jobs on m machines in a flow shop. A schedule evaluation algorithm is presented, which for job-pairs, generates a schedule evaluation matrix. The matrix is the input data to a transportation problem, the solution of which gives near-optimal jobsequence and makespan. The performance of the algorithm is discussed.     

New Methods for Resolving Conflicting Requests with Examples from Medical Residency Scheduling

In scheduling medical residents, the objective is often to maximize resident satisfaction across the space of feasible schedules, relative to the many hard constraints that ensure appropriate patient coverage, adequate training opportunities, etc. A common metric of resident satisfaction is the number of time‐off requests that are granted. Simply maximizing this total, however, may lead to undesirable schedules since some requests have higher priority than others. For example, it might be better to grant one resident's request for a family member's wedding in place of two residents’ requests to attend a rugby game. Another approach is to assign a weight to each request and maximize the total weight of granted requests, but determining weights that accurately represent residents’ and schedulers’ preferences can be quite challenging. Instead, we propose to identify the exhaustive collection of maximally feasible and minimally infeasible sets of requests which can then be used by schedulers to select their preferred solution. Specifically, we have developed two algorithms, which we call Sequential Request Selection Via Cuts (Sequential RSVC) and Simultaneous Request Selection Via Cuts (Simultaneous RSVC), to identify these sets by solving two sequences of optimization problems. We present these algorithms along with computational results based on a real‐world problem of scheduling residents at the University of Michigan C.S. Mott Pediatric Emergency Department. Although we focus our exposition on the problem of resident scheduling, our approach is applicable to a broad class of problems with soft constraints.     

Solution Procedures for the Lot-Streaming Problem

Lot streaming is the process of splitting a job into sublots so its operations can be overlapped and its progress accelerated. We present a computationally efficient procedure for solving the m-machine, two-sublot problem, and we discuss the bottleneck insights that emerge from the analysis. We also examine heuristic approaches for more than two sublots and discuss computational results for these procedures.     

USING A LATE-START RESOURCE-CONSTRAINED PROJECT SCHEDULE TO IMPROVE PROJECT NET PRESENT VALUE*

Although literature on the achievement of monetary objectives in a resource-constrained project environment is limited, the maximization of project net present value (NPV) is an important criterion of project success. This paper presents a procedure for developing a late-start resource-constrained project schedule using the critical path method-material requirements planning. Using an extensive set of problems from the literature, we show that this procedure yields a higher NPV and lower average duration than schedules derived with heuristics that schedule each activity as early as possible. In addition, while the late-start schedule on average was significantly longer than the optimal-duration resource-constrained schedule, no significant difference occurred in the average NPVs of the two scheduling methods.     

An Evaluation of Tour Scheduling Heuristics with Differences in Employee Productivity and Cost

This study focuses on the manpower tour scheduling problem using data from a lockbox system of a commercial bank. The lockbox system uses employees who differ in productivity, hourly cost, number of available working hours per week, and days-off constraints. These specific problem characteristics require a more general problem formulation and solution procedure for the manpower tour scheduling problem than addressed in previous research. Four heuristic methods for solving the problem (three developed here and a simple round-up procedure) are tested on a set of forty problems. The results of this study show the effort to develop sophisticated heuristic methods for this class of problems is well justified.     

Sequencing Rules for Productivity Improvements in Underground Coal Mining*

In this paper, we report on a unique two-machine, dynamic sequencing problem that was involved in a project designed to improve the productivity of underground coal mining operations. It was discovered that mine output was dependent on the particular sequence of faces the continuous miner and bolter worked. The problem is characterized by two unique features. First, the problem is unique because of the geological and safety constraints that must be satisfied by the sequence. Second, the scheduling problem is dynamic because the available job sets change as work progresses, and the production times change as coal is mined. Three heuristic approaches were developed and tested using mine parameters. The best heuristic had a worst case scenario of being within 2.7 percent of the optimal sequence and only a 1.1 percent chance of determining a better sequence. This heuristic resulted in an 8.1 percent productivity improvement.     

A simulated annealing algorithm for job shop scheduling

In this paper, the job shop scheduling problem is considered with the objective of minimization of makespan time. We first reviewed the literature on job shop scheduling using meta-heuristics. Then a simulated annealing algorithm is presented for scheduling in a job shop. To create neighbourhoods, three perturbation schemes, viz. pairwise exchange, insertion, and random insertion are used, and the effect of them on the final schedule is also compared. The proposed simulated annealing algorithm is compared with existing genetic algorithms and the comparative results are presented. For comparative evaluation, a wide variety of data sets are used. The proposed algorithm is found to perform well for scheduling in the job shop.