Uttarayan Bagchi

Simultaneous minimization of mean and variation flow time and waiting in single machine systems

In this paper, we consider bicriterion scheduling problems involving job completion times and job waiting times in a nonpreemptive single machine environment. As an example, we seek to determine a schedule that yields both a low mean and a low variation of completion time. Such a schedule is attractive when the system has the dual objectives of minimizing in-process inventory and providing different jobs the same quality of service. Similarly, we seek a schedule that performs well on both the mean and variation of waiting time. As the measure of variation, we use the sum of absolute pairwise differences. We present an efficient algorithm for minimizing the variation of waiting time. Next, we assume that the total scheduling cost is a function of the mean and variation of completion time alone, and is linear. We give an efficient algorithm for minimizing this total cost. Finally, we consider parametric analysis of this cost function and present simple procedures for generating all or some of the optimal sc...

Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date

We consider a single-machine scheduling problem in which all jobs have the same due date and penalties are assessed for both early and late completion of jobs. However, earliness and tardiness are penalized at different rates. The scheduling objective is to minimize either the weighted sum of absolute deviations (WSAD) or the weighted sum of squared deviations (WSSD). For each objective we consider two versions of the problem. In the unconstrained version an increase in the due date does not yield any further decrease in the objective function. We present a constructive algorithm for the unconstrained WSAD problem and show that this problem is equivalent to the two-parallel, nonidentical machine, mean flow-time problem. For the unconstrained WSSD and the constrained WSAD and WSSD problems we propose implicit enumeration procedures based on several dominance conditions. We also report on our computational experience with the enumeration procedures.

The effect of lead-time variability: The case of independent demand

Abstract We show in this study, through analysis and examples, the impact on stockouts and stockout risk if the variability of lead time in independent demand systems is ignored. In calculating safety stocks, we recommend that the compound distribution of demand during lead time, or a good approximation to it, be used. We motivate the article by a case study on lead-time variability at the U.S. Air Force and show the impact of lead-time variability by means of numerical examples and by marginal analysis. Having established that it is essential to consider lead-time variability, we take advantage of theoretical developments and show how to calculate reorder points and safety stocks in some common situations. It is important to use the proper form for the compound distribution of demand during lead time. A normal approximation to it will often yield significant errors. This is because the true distribution is usually very much skewed to the right.

Experimental investigation of real-time scheduling in flexible manufacturing systems

This paper presents a new two-phase (TP) approximate method for real-time scheduling in a flexible manufacturing system (FMS). This method combines a reduced enumeration schedule generation algorithm with a 0–1 optimization algorithm. In order to make the combined algorithm practicable, heuristic rules are introduced for the selection of jobs to be scheduled. The relative performance of the TP method vis-a-vis conventional heuristic dispatching rules such as SPT, LPT, FCFS, MWKR, and LWKR is investigated using combined process-interaction/discrete-event simulation models. An efficient experimental procedure is designed and implemented using these models, and the statistical analysis of the results is presented. For the particular case investigated, the conclusions are very encouraging. In terms of mean flow time, the TP method performs significantly better than any other tested heuristic dispatching rules. Also, the experimental results show that using global information significantly improves the FMS performance.

Improved lower bounds for minimizing the sum of completion times of n jobs over m machines in a flow shop

Abstract The paper considers the classic n job, m machine scheduling problem where the objective is to minimize the sum of completion times. A procedure is presented for obtaining m − 1 new machine based lower bounds. The result is an improved overall lower bound.

Effect of increasing component commonality on service level and holding cost

We investigate the effect of increasing component commonality in an assemble-to-order system. Numerical investigation of two end products that share up to three components, and whose demands are identically distributed according to either the exponential or the geometric distribution, shows that increasing component commonality results in increasing marginal returns when the criteria are aggregate service level and aggregate stock requirement. For arbitrary end-product demands and general service measures, it is shown that the optimal holding cost for a given service level is concave in the level of commonality.

Dynamic, Non-Preemptive Priority Queues with General, Linearly Increasing Priority Function

This paper considers a single server queueing system that services customers from P non-preemptive priority classes. We assume independent identically distributed exponential interarrival and general service times for each class of customer. We also assume that a customers priority in the queue is determined not only by its class, but also by the length of time it has spent in the queue; the priority for each class can be a general linearly increasing priority function. Our development gives an expression for the expected waiting time of each customer class, and gives bounds on this expression. We demonstrate the calculation of the bounds by several numerical examples, and discuss the sensitivity of the bounds to priority function parameters and system utilization. We also show that, even under the most conservative assumptions, the bounds are remarkably tight. Furthermore, for the special case of an M/M/1 system with identical service time distributions, these bounds can be substantially improved if the ordinal ranking of expected waiting times is known a priori. The results of this research enable systems designers to anticipate and consequently to control system behavior for systems with general linearly increasing priority disciplines.

The Effect of RFID On Inventory Management and Control

Our thesis is that the evolution of information technology (IT) facilitates the flow of information, which in turn may reduce the variance of an inventory system, and hence its cost. We use radio-frequency identification (RFID) as a paradigm. RFID is the latest application of IT to tracking goods and services or anything for that matter, including human beings. It is an evolution from bar code and palette technology, and, in this chapter, we present the argument that RFID is superior in reducing the mean and variance of inventory cycle times. As inventory cost is a function of these (among other variables, such as unit holding and shortage costs), we show that RFID reduces this cost. Also, because RFID leads to rapid transmission of data, it would help avoid excessive inventories and shortages, further reducing total inventory cost. We argue that RFID is superior to existing identification technologies according to mean-variance stochastic dominance. We discuss the ethical implications and the societal trade-offs inherent in RFID, as society must decide how much of its privacy it is willing to curtail in the pursuit of lower prices versus physical security.

Lower bounds for single-machine scheduling problems

This article addresses deterministic, nonpreemptive scheduling of n jobs with unequal release times on a single machine to minimize the sum of job completion times. This problem is known to be NP-hard. The article compares six available lower bounds in the literature and shows that the lower bound based on the optimal solution to the preemptive version of the problem is the dominant lower bound.

Technical Note-An Improved Lower Bound for Minimizing Weighted Completion Times with Deadlines

We consider the NP-hard, one-machine scheduling problem whose objective is to minimize the weighted sum of completion times, subject to meeting deadlines. We propose a new lower bound that dominates the bounds found in the literature.