Matthew Rosenshine

Analysis of a Standing Order Inventory System with Emergency Orders

The advent of relatively sophisticated information systems has made it possible for many businesses that keep inventories to know their needs very rapidly. However, the producers of these inventories have not all made comparable advances in scheduling production to meet the rapidly changing orders placed by their increasingly sophisticated customers. As a result, leadtimes have been growing rather than decreasing. Since in most cases the company needing the inventory cannot control the leadtime, it must either accept it or look for ways to mitigate its effect. This paper evaluates one way to cope with the problem of large or growing leadtimes.

Scheduling arrivals to queues

Abstract An algorithm is developed to determine the schedule for n arrivals to a single server exponential first come, first served service which will minimize the sum of customer waiting and server availability costs. The algorithm results in a n − 1 dimensional objective function which has been shown to be convex for n ⩽ 4 and is suspected to be convex for n ⩾ 5. The difficulty in demonstrating convexity for n ⩾ 5 is indicated.

PLANNING TIMELY ARRIVALS TO A STOCHASTIC PRODUCTION OR SERVICE SYSTEM

A stochastic planning problem of determining the optimal arrival times for N customers, each to be assigned to one of K equal time slots, is considered. The objective is to minimize the total system cost, which is composed of the customer waiting cost and the server availability cost. This optimal arrival schedule is examined for a single server system with either exponential or Erlang-fc service time distribution. Two versions of this planning arrival problem are considered, a dynamic version and a static version. The dynamic problem requires planning decisions to be made at the beginning of each time slot, while in the static problem all decisions must be made at the beginning of the first time slot. The dynamic problem is solved by dynamic programming. The structure of the optimal dynamic policy is identified and used to solve the dynamic problem efficiendy. A branch-and-bound algorithm, which uses the solution to the dynamic problem, is developed to solve the static problem. The results can be used to...

THE DEPARTURE PROCESS FOR THE M/M/1 QUEUE

The problem of determining the probability of j departures during the time interval (0, t) from an M/M/1 queue empty at t = 0 is considered. A closedform solution is obtained. It is shown that this solution is unique and invariant under interchanging the arrival rate and service rate. Finally, sample computational representations of the solution are developed and results of a simple computation are provided.

Analysis of robot positioning error

Positioning errors of robots used for material handling and assembly can be sufficiently large to cause problems. These errors are due to imperfect repeatability of the robots, and their effects can be ameliorated or exacerbated by tolerances on the workpieces and on the jigs and fixtures. In this paper, a model for characterizing the positioning errors of robots is developed. A statistical analysis of positioning error data is performed to make inferences about the stochastic nature of the robotic system. The basic issue is whether the positioning errors of the robot are state dependent or state invariant.

The Application of Semi-Markov Decision Processes to Queueing of Aircraft for Landing at an Airport

Socially optimal control of access to the landing queue of an airport is investigated in this paper. Semi-Markov decision process models, M / M /1 and M / E k /1, for several classes of customers are used to determine how access should be controlled. Only commercial jet aircraft are considered and they are divided up into five classes based on aircraft type. Data from the Greater Pittsburgh International Airport are used to determine the parameters of the service time distribution. Data from several published sources are used to develop the cost, reward, and arrival rate parameters for each of the classes. Results are developed and presented for both models.

Approximate Solutions for Some Two-Stage Tandem Queues, Part 1: Individual Arrivals at the Second Stage

The analysis of tandem queues in which the output of each stage immediately becomes the input to the next is, in general, quite difficult. Although the analytic solution for the steady-state departure distribution from an M/M/N queue is well-known and that of an M/G/1 queue can be obtained if the analyst is willing to view it through a “Laplacian curtain,” the list of existing analytic solutions is not long. Some analytic “tricks” exist, but their utility is usually limited to the single-server queue. The treatment of tandem queues not fitting into these categories has been largely left to simulation. Yet this approach has its drawbacks. It is expensive and involves difficulties in designing and analyzing the simulation experiment. Approximation techniques are beginning to emerge as a wiser, faster, cheaper, and less troublesome alternative to simulation. In this paper we develop approximate solutions for average steady-state queue length in four different but related tandem queues that arise in connectio...

Scheduling for a combination of made-to-stock and made-to-order jobs in a job shop

This paper deals with selecting a heuristic rule for concurrent scheduling of mixtures of due-date and non-due-date jobs. The measure of performance for the mixture of jobs is chosen to be mean flowtime subject to the constraint that due dates are satisfied. To handle varying levels of due-date tightness, three types of schedules are introduced. Dispatching rules for two of the three types of schedules were selected by simulation. Decision rules for determining the best schedules in appropriate situations are suggested.

A heuristic for determining the optimal order in a tandem queue

Abstract This paper presents a heuristic for determining the optimal order of the stations in a nonblocking tandem queue. Specifically, we argue that the first two customers can almost represent the entire arrival stream for comparing expected flow time for different orders of the stations. The heuristic was extensively tested by simulation. The heuristic yielded the optimal order 92% of the time for two-station problems, 85% for three-station problems and 65% for four-station problems. The results of the heuristic were found to be close to optimal orders.

Queueing Theory: The State-of-the-Art

Abstract Approximately seven years ago T. L. Saaty wrote, “If one also takes the trouble to examine the (queueing) literature, …, he might get the idea that all those contributing to the understanding of congestion phenomena are interested in doing something about them …” This survey of the state-of-the-art in queueing theory directs attention to two areas—theory and applications—attempting to indicate their evolution to their present states. The appropriateness of Saatys comment now is assessed, and based on this assessment some recommendations about what needs to be done are presented. The notion implied in the foregoing quotation, that if the queueing theorists were really interested in doing something about real-world problems they could, is subjected to scrutiny.