George L. Vairaktarakis

Integrated Scheduling of Production and Distribution Operations

Motivated by applications in the computer and food catering service industries, we study an integrated scheduling model of production and distribution operations. In this model, a set of jobs (i.e., customer orders) are first processed in a processing facility (e.g., manufacturing plant or service center) and then delivered to the customers directly without intermediate inventory. The problem is to find a joint schedule of production and distribution such that an objective function that takes into account both customer service level and total distribution cost is optimized. Customer service level is measured by a function of the times when the jobs are delivered to the customers. The distribution cost of a delivery shipment consists of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment. We study two classes of problems under this integrated scheduling model. In the first class of problems, customer service is measured by the average time when the jobs are delivered to the customers; in the second class, customer service is measured by the maximum time when the jobs are delivered to the customers. Two machine configurations in the processing facility--single machine and parallel machine--are considered. For each of the problems studied, we provide an efficient exact algorithm, or a proof of intractability accompanied by a heuristic algorithm with worst-case and asymptotic performance analysis. Computational experiments demonstrate that the heuristics developed are capable of generating near-optimal solutions. We also investigate the possible benefit of using the proposed integrated model relative to a sequential model where production and distribution operations are scheduled sequentially and separately. Computational tests show that in many cases a significant benefit can be achieved by integration.

Robust scheduling of a two-machine flow shop with uncertain processing times

This paper focuses on manufacturing environments where job processing times are uncertain. In these settings, scheduling decision makers are exposed to the risk that an optimal schedule with respect to a deterministic or stochastic model will perform poorly when evaluated relative to actual processing times. Since the quality of scheduling decisions is frequently judged as if processing times were known a priori, robust scheduling, i.e., determining a schedule whose performance (compared to the associated optimal schedule) is relatively insensitive to the potential realizations of job processing times, provides a reasonable mechanism for hedging against the prevailing processing time uncertainty. In this paper we focus on a two-machine flow shop environment in which the processing times of jobs are uncertain and the performance measure of interest is system makespan. We present a measure of schedule robustness that explicitly considers the risk of poor system performance over all potential realizations of job processing times. We discuss two alternative frameworks for structuring processing time uncertainty. For each case, we define the robust scheduling problem, establish problem complexity, discuss properties of robust schedules, and develop exact and heuristic solution approaches. Computational results indicate that robust schedules provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance

Machine scheduling with deliveries to multiple customer locations

One important issue in production and logistics management is the coordination of activities between production and delivery. In this paper, we develop a single-machine scheduling model that incorporates routing decisions of a delivery vehicle which serves customers at different locations. The objective is to minimize the sum of job arrival times. The problem is NP-hard in the strong sense in general. We develop a polynomial time algorithm for the case when the number of customers is fixed. More efficient algorithms are developed for several special cases of the problem. In particular, an algorithm is developed for the single-customer case with a complexity lower than the existing ones.

Robust multi-item newsboy models with a budget constraint

Abstract In this paper we present robust newsboy models with uncertain demand. The traditional approach to describing uncertainty is by means of probability density functions. In this paper we present an alternative approach using deterministic optimization models. We describe uncertainty using two types of demand scenarios; namely interval and discrete scenarios. For interval demand scenarios we only require a lower and an upper bound for the uncertain demand of each item, while for discrete demand scenarios we require a set of likely demand outcomes for each item. Using the above scenarios to describe demand uncertainty, we develop several minimax regret formulations for the multi-item newsboy problem with a budget constraint. For the problems involving interval demand scenarios, we develop linear time optimal algorithms. We show that the corresponding models with discrete demand scenarios are NP -hard and that they are solvable by dynamic programming. Finally, we extend the above results to the case of mixed scenarios where the demand of some of the items is described by interval scenarios and the demand of the remaining items is described by discrete scenarios.

Workforce planning in mixed model assembly systems

Serial assembly systems are formed by arranging several production cells or stations in series. We study a popular class of serial assembly lines where all stations have the same production cycle. We address a workforce planning problem for such lines which finds applications in labor-intensive operations in automobile, fire engine, aircraft, and PC board assembly. The problem presented can be applied to lines that produce several variations of a basic stable design; i.e., mixed model transfer lines. Given a set of n jobs, we want to find a sequence that minimizes the maximum workforce requirements over all production cycles. An optimal polynomial algorithm for the two-station line is presented, and the three-station case is proved to be strongly 𝒩𝒫-complete. Several heuristic algorithms that produce upper and lower bounds are developed for the general problem. Worst case behavior of the upper bounds, as well as average performance of lower and upper bounds, are reported. Computational results show that s...

Optimization tools for design and marketing of new/improved products using the house of quality

Abstract Quality function deployment (QFD) has helped many firms realize significant reduction in product design costs and development time. The QFD process includes ranking customer preferences, rating the competitors, and parts deployment for the new/improved product. Prior to this research, such activities have been performed based on expert opinion, or the “best-in-class” approach. We develop and solve optimization models for the identification of consensus rankings and ratings, that take into account the priorities and perceptions of all the customers in a target market. Then, based on the consensus rankings, we identify a parts mix for the new/improved product that satisfies a budget constraint and matches or exceeds the performance expectations of all customers surveyed in the target market. Finally, we show how the QFD charts can be used to identify competitors that are falsely perceived as superior, as well as areas where the firms marketing strategies have had the desired effects. Such insights are useful in developing the future marketing strategy of the firm.

Test case generators and computational results for the maximum clique problem

In the last years many algorithms have been proposed for solving the maximum clique problem. Most of these algorithms have been tested on randomly generated graphs. In this paper we present different test problem generators that arise from a variety of practical applications, as well as graphs with known maximum cliques. In addition, we provide computational experience with two exact algorithms using the generated test problems.

The use of flowlines to simplify routing complexity in two-stage flowshops

Flexible manufacturing systems are often designed as flowshops supported by automated material handling devices that facilitate routing among any two processors of adjacent stages. This routing structure is complex, and results in excessive capital investment and costs of management. In this paper we propose a decomposition of two-stage flowshops into smaller independent flowlines that allow for unidirectional routing only. We solve optimally the problem of minimizing makespan on two parallel flowlines, by means of a Dynamic Programming algorithm (DP). Based on DP we develop lower bounds on the throughput performance of environments that consist of more than two flowlines. We present several heuristic algorithms and report their optimality gaps. Using these algorithms, we show that the decomposition of two stage flowshops with complicated routing into flowline-like designs with unidirectional routing is associated with minor losses in throughput performance, and hence significant savings in material handling costs.

Coordination of Outsourced Operations to Minimize Weighted Flow Time and Capacity Booking Costs

A set of manufacturers outsources certain operations to a single third party following the announcement of a booking price for each available day of production. Knowing these costs, manufacturers book available production days in a first-come-first-serve order to optimize their individual cost. The cost for each manufacturer consists of booking and work-in-progress costs, as expressed by the weighted flow time. When window booking is completed, the third party identifies a schedule that minimizes the total cost incurred by all manufacturers. This coordination reduces the total cost but may result in higher costs for a subset of manufacturers. For this reason, the third party devises a savings sharing scheme with which the monetary benefit for each manufacturer is greater. In this article we present algorithms for the problem considered, as well as savings-sharing schemes that make coordination a better alternative for all parties. The highlight of our experiments is that the costs of the production chain can be reduced by an average of 32% if one-third of the members let the third party cover their increased work-in-progress cost in exchange for 38%--53% of the total savings.

The Value of Processing Flexibility in Multipurpose Machines

We study a scheduling problem in a multipurpose machine environment where every job can be processed by a subset of the machines operated in parallel, with the objective of minimizing makespan. We develop lower bounds, heuristic algorithms, and a branch-and-bound procedure. We perform an extensive computational experiment to assess how much flexibility is enough to render the multipurpose machine system equally efficient to an equivalent system of parallel identical machines. We find that very small amounts of flexibility appropriately distributed across processors provide nearly the same makespan performance as a system of fully flexible parallel machines.