A dynamic allocation heuristic for centralized safety stock

An inventory system that consists of a depot (central warehouse) and retailers (regional warehouses) is considered. The system is replenished regularly on a fixed cycle by an outside supplier. Most of the stock is direct shipped to the retailer locations but some stock is sent to the central warehouse. At the beginning of any one of the periods during the cycle, the central stock can then be completely allocated out to the retailers. In this paper we propose a heuristic method to dynamically (as retailer inventory levels change with time) determine the appropriate period in which to do the allocation. As the optimal method is not tractable, the heuristic's performance is compared against two other approaches. One presets the allocation period, while the other provides a lower bound on the expected shortages of the optimal solution, obtained by assuming that we know ahead of time all of the demands, period by period, in the cycle. The results from extensive simulation experiments show that the dynamic heuristic significantly outperforms the “preset” approach and its performance is reasonably close to the lower bound. Moreover, the logic of the heuristic is appealing and the calculations, associated with using it, are easy to carry out. Sensitivities to various system parameters (such as the safety factor, coefficient of variation of demand, number of regional warehouses, external lead time, and the cycle length) are presented. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A multi‐objective model for bank ATM networks

In this paper we present an application of the core solution concepts for multi‐objective games to a bank ATM network model. In these games, the worth of a coalition is given by a subset of vectors of the k‐dimensional space rather than by a scalar. The paper investigates how an ATM network model based on multi‐objective cooperative game theory could be used as an alternative way of setting interchange fees paid by the customer's bank to the one that owns the ATM. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

A robust policy for serial agile production systems

One of the major problems in modeling production systems is how to treat the job arrival process. Restrictive assumptions such as Markovian arrivals do not represent real world systems, especially if the arrival process is generated by job departures from upstream workstations. Under these circumstances, cost‐effective policies that are robust with respect to the nature of the arrival process become of interest. In this paper, we focus on minimizing the expected total holding and setup costs in a two‐stage produce‐to‐order production system operated by a cross‐trained worker. We will show that if setup times are insignificant in comparison with processing times, then near‐optimal policies can be generated with very robust performances with respect to the arrival process. We also present conditions under which these near‐optimal policies can be obtained by using only the arrival and service rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Predictability of operational processes over finite horizon

Operational processes are usually studied in terms of stochastic processes. The main information measure used for predictability of stochastic processes is the entropy rate, which is asymptotic conditional entropy, thus not suitable for application over a finite horizon. We use the conditional entropy to study the predictability of stochastic processes over the finite horizon. It is well‐known that the conditional entropies of stationary processes decrease as the processes evolve, implying that, on average, their pasts become more informative about prediction of their future outcomes. Some important operational processes such as martingale, models for maintenance policies, nonhomogeneous Poisson, and mixed Poisson processes are nonstationary. We show that as a nonstationary process evolves, it may provide more information or less information about the future state of the system. We develop results for comparing the predictability of stochastic processes. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Makespan minimization in the two‐machine flowshop batch scheduling problem

In this paper we consider a practical scheduling problem commonly arising from batch production in a flexible manufacturing environment. Different part‐types are to be produced in a flexible manufacturing cell organized into a two‐stage production line. The jobs are processed in batches on the first machine, and the completion time of a job is defined as the completion time of the batch containing it. When processing of all jobs in a batch is completed on the first machine, the whole batch of jobs is transferred intact to the second machine. A constant setup time is incurred whenever a batch is formed on any machine. The tradeoff between the setup times and batch processing times gives rise to the batch composition decision. The problem is to find the optimal batch composition and the optimal schedule of the batches so that the makespan is minimized. The problem is shown to be strongly NP‐hard. We identify some special cases by introducing their corresponding solution methods. Heuristic algorithms are also proposed to derive approximate solutions. We conduct computational experiments to study the effectiveness of the proposed heuristics. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 128–144, 2000     

Implicit enumeration based algorithms for postoptimizing zero-one programs

It has been shown by G. Roodman that useful postoptimization capabilities for the 0-1 integer programming problem can be obtained from an implicit enumeration algorithm modified to classify and collect all fathomed partial solutions. This paper extends the the approach as follows: 1) Improved parameter ranging formulas are obtained by higher resolution classification criteria. 2) Parameters may be changed so as to tighten the original problem, in addition to relaxing it. 3) An efficient storage structure is presented to cope with difficult data collection task implicit in this approach. 4) Finally, computer implementation is facilitated by the elaboration of a unified set of algorithms.     

A risk function for the stochastic modeling of electric capacity expansion

We present a stochastic optimization model for planning capacity expansion under capacity deterioration and demand uncertainty. The paper focuses on the electric sector, although the methodology can be used in other applications. The goals of the model are deciding which energy types must be installed, and when. Another goal is providing an initial generation plan for short periods of the planning horizon that might be adequately modified in real time assuming penalties in the operation cost. Uncertainty is modeled under the assumption that the demand is a random vector. The cost of the risk associated with decisions that may need some tuning in the future is included in the objective function. The proposed scheme to solve the nonlinear stochastic optimization model is Generalized Benders' decomposition. We also exploit the Benders' subproblem structure to solve it efficiently. Computational results for moderate‐size problems are presented along with comparison to a general‐purpose nonlinear optimization package. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:662–683, 2001     

Product commonality in multiple‐period,make‐to‐stock systems

It is well known that replacing several products by a single common product can reduce required safety stock levels due to the benefits of risk pooling. Recent research utilizing single‐period models has investigated the cost savings (or losses) from doing so. This paper uses a very general multiple‐period model, with general demand distributions, any number of products, and the objective of minimizing production, holding, and shortage costs. Two scenarios are considered—one that utilizes a common product and one that does not. Prior results utilizing single‐period models indicate that even if the common product is more expensive than the products it replaces, there are many circumstances under which it is still worthwhile to employ. Surprisingly, this paper will show that this is almost never the case in a multiple‐period model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 737–751, 1999     

A genetic algorithm methodology for complex scheduling problems

This paper considers the scheduling problem to minimize total tardiness given multiple machines, ready times, sequence dependent setups, machine downtime and scarce tools. We develop a genetic algorithm based on random keys representation, elitist reproduction, Bernoulli crossover and immigration type mutation. Convergence of the algorithm is proved. We present computational results on data sets from the auto industry. To demonstrate robustness of the approach, problems from the literature of different structure are solved by essentially the same algorithm. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 199–211, 1999