John Mittenthal

Matchup Scheduling with Multiple Resources, Release Dates and Disruptions

This paper considers the rescheduling of operations with release dates and multiple resources when disruptions prevent the use of a preplanned schedule. The overall strategy is to follow the preschedule until a disruption occurs. After a disruption, part of the schedule is reconstructed to match up with the preschedule at some future time. Conditions are given for the optimality of this approach. A practical implementation is compared with the alternatives of preplanned static scheduling and myopic dynamic scheduling. A set of practical test problems demonstrates the advantages of the matchup approach. We also explore the solution of the matchup scheduling problem and show the advantages of an integer programming approach for allocating resources to jobs.

Simulation optimization using simulated annealing

Abstract The purpose of this study is to investigate the feasibility of using a simulated annealing algorithm in conjunction with a simulation model to find the optimal parameter levels at which to operate a system. In particular, we discuss an effort to use simulated annealing to find a combination of input parameter values for a model which optimizes a nonconvex, nonconcave objective function of the input parameters. In the absence on an optimal annealing schedule, we demonstrate that multiple runs of the simulated annealing algorithm can result in an optimal or near-optimal solution to the problem.

Single‐machine scheduling subject to stochastic breakdowns

We provide several examples of one‐machine problems in which the minimization of expected cost subject to stochastic breakdowns of the machine can be successfully attacked analytically. In particular for the weighted flow‐time model, we derive strong bounds on the difference between the optimal static policy and the WSPT policy and discuss an example in which the WSPT policy is not optimal.

Stochastic single machine scheduling with quadratic early-tardy penalties

We address the problem of scheduling n jobs on a single machine, which is subject to random breakdowns, to minimize an expected sum of nonregular penalty functions. A simple recourse model is considered when the penalty function is the squared deviation of job completion times from a common due date, and a deterministic equivalent objective function is developed. Characterizations of optimal schedules for this quadratic objective function are established both when the common due date is a decision variable and when it is given and fixed. Most importantly, the V-shaped nature of optimal schedules is investigated for a class of Poisson processes, {N(t), t > 0}, describing the number of breakdowns in the interval (0, t). In addition, relationships to a class of bicriteria models are demonstrated.

Scheduling on a two-machine flowshop subject to random breakdowns with a makespan objective function

Abstract Two-machine flowshop scheduling problems have been discussed in the literature extensively under the assumption that machines are continuously available. We address the problem of minimizing makespan in a two-machine flowshop when the machines are subject to random breakdowns. We first show that it is sufficient to consider the same sequence of the jobs on each machine. After providing an elimination criterion for minimizing makespan with probability 1, we show that under appropriate conditions Johnsons algorithm stochastically minimizes makespan.

A hybrid simulated annealing approach for single machine scheduling problems with non-regular penalty functions

Abstract An algorithm is presented for single machine scheduling problems which have V-shaped optimal schedules. The algorithm is a hybrid of a greedy approach, followed by a simulated annealing search of the V-shaped sequence solution space. A number of non-regular objective functions, both with and without a common due date, are considered. In all test problems, the algorithm gives better solutions than the heuristics previously presented in the literature.

Scheduling on M parallel machines subject to random breakdowns to minimize expected mean flow time

The problem of scheduling n jobs on m parallel machines is considered when the machines are subject to random breakdowns and job processing times are random variables. An objective function of mean flow time is developed for a general parallel machine system, and an expression of its expected value is derived. The problem is transformed into a deterministic unrelated parallel machine scheduling model with modified processing times when the number of breakdowns is modeled as a generalized Poisson process.

Optimization Of An Automated Manufacturing System Simulation Model Using Simulated Annealing

The purpose of this study is to investigate the feasibility of using a simulated annealing algorithm in conjunction with a simulation model to find the optimal parameter levels at which to operate the system being simulated. In particular, we discuss an effort to use simulated annealing to find a combination of input parameter values for an automated manufacturing system which optimizes a nonconvex, nonconcave objective function of the input parameters.This paper contains a brief description of an automated manufacturing system used to assemble three products. The problem objective is to maximize profit as a function of the levels of three parameters - batch size of arriving products, distribution of products in the batches, and machine output buffer size. Simulated annealing is then used to search for the optimal combination of input parameter levels. By experimenting with the simulated annealing parameters, the algorithm parameters are chosen such that the annealing program will consistently find the global optimum after evaluating approximately 36% of the input variable combinations.

A TSSP + 1 decomposition strategy for the vehicle routing problem

Abstract The basic, capacity-constrained vehicle routing problem (VRP) is to determine a set of capacity-feasible vehicle routes with minimum total travel cost so that all customers are visited by exactly one vehicle. In this paper, we introduce a new decomposition strategy for the VRP which separates the decisions of a dispatcher from those of the individual drivers. The dispatcher is responsible for assigning a reward value to each of the customer cities so that each customer will be visited by exactly one vehicle. Based on the assigned reward values together with the given travel costs, each vehicle driver is responsible for choosing which customers to visit and determining an individual feasible route. The drivers problem is modeled as a Traveling Salesman Subset-tour Problem with one additional constraint (TSSP + 1). The TSSP + 1 decomposition is based on aagrangian relaxation and is capable of producing valid lower bounds for the VRP. The best bound attainable is shown to be at least as good as the bound obtained by solving the linear programming relaxation of the classic set partitioning formulation of the VRP. To tet the practical value of the decomposition, we present a decomposition-based heuristic and examine its performance on a collection of problems from the literature.