A note on minimizing the expected makespan in flowshops subject to breakdowns

Consider a two machine flow shop and n jobs. The processing time of job j on machine i is equal to the random variable X_ij One of the two machines is subject to breakdown and repair. The objective is to find the schedule that minimizes the expected makespan. Two results are shown. First, ifP(X_2j ≧ X_1j) = 1 for all j and the random variables X₁₁, X₁₂,…, X_1n are likelihood ratio ordered, then the SEPT sequence minimizes the expected makespan when machine 2 is subject to an arbitrary breakdown process; if P(X_1j≧X_2j) = 1 and X₂₁, X₂₂,….,X_2n are likelihood ratio ordered, then the LEPT sequence minimizes the expected makespan when machine 1 is subject to an arbitrary breakdown process. A generalization is presented for flow shops with m machines. Second, consider the case where X_1j and X_2j are i.i.d. exponentially distributed with rate λ_j. The SEPT sequence minimizes the expected makespan when machine 2 is subject to an arbitrary breakdown process and the LEPT sequence is optimal when machine 1 is subject to an arbitrary breakdown process. © 1995 John Wiley & Sons, Inc.     

A bayesian approach to environmental stress screening

The article presents a Bayesian analysis for the environmental stress screening problem. The decision problem of deriving optimal stress screen durations is solved. Given a screen duration, the optimal stress level can also be determined. Indicators of the quality of a screen of any duration are derived. A statistical model is presented which allows a posterior density for the rate of early failures of the production process to be calculated. This enables the user to update his opinion about the quality of the process. © 1994 John Wiley & Sons, Inc.     

Equipment replacement under technological change

For infinite-horizon replacement economy problems it is common practice to truncate the problem at some finite horizon. We develop bounds on the error due to such a truncation. These bounds differ from previous results in that they include both revenues and costs. Bounds are illustrated through a numerical example from a real case in vehicle replacement. © 1994 John Wiley & Sons, Inc.     

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

A perfect lot-tree procedure for the discounted dynamic lot-size problem with speculation

This article considers the dynamic lot-size problem under discounting, allowing a speculative motive for holding inventory. A forward procedure is developed that determines the first lot-size decision in a rolling horizon environment by using forecast data of the minimum possible number of future periods. © 1992 John Wiley & Sons, Inc.     

A shifting bottleneck heuristic for minimizing the total weighted tardiness in a job shop

We present a shifting bottleneck heuristic for minimizing the total weighted tardiness in a job shop. The method decomposes the job shop into a number of single‐machine subproblems that are solved one after another. Each machine is scheduled according to the solution of its corresponding subproblem. The order in which the single machine subproblems are solved has a significant impact on the quality of the overall solution and on the time required to obtain this solution. We therefore test a number of different orders for solving the subproblems. Computational results on 66 instances with ten jobs and ten machines show that our heuristic yields solutions that are close to optimal, and it clearly outperforms a well‐known dispatching rule enhanced with backtracking mechanisms. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 1–17, 1999     

Value added analysis for army equipment modernization

This paper describes the Value Added Analysis methodology which is used as part of the U.S. Army's Planning, Programming, Budgeting, and Execution System to assist the Army leadership in evaluating and prioritizing competing weapon system alternatives during the process of building the Army budget. The Value Added Analysis concept uses a family of models to estimate an alternative system's contribution to the Army's effectiveness using a multiattribute value hierarchy. A mathematical optimization model is then used to simultaneously determine an alternative's cost‐benefit and to identify an optimal mix of weapon systems for inclusion in the Army budget. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 233–253, 1999     

The LP/POMDP marriage: Optimization with imperfect information

A new technique for solving large‐scale allocation problems with partially observable states and constrained action and observation resources is introduced. The technique uses a master linear program (LP) to determine allocations among a set of control policies, and uses partially observable Markov decision processes (POMDPs) to determine improving policies using dual prices from the master LP. An application is made to a military problem where aircraft attack targets in a sequence of stages, with information acquired in one stage being used to plan attacks in the next. © 2000 John Wiley & Sons, Inc., Naval Research Logistics 47: 607–619, 2000     

Pareto-optimality in classical inventory problems

In this paper the inventory problem with backorders both deterministic and stochastic is studied using trade-off analysis in the context of vector optimization theory. The set of Pareto-optimal solutions is geometrically characterized in both the constrained and unconstrained cases. Moreover, a new way of utilizing Pareto-optimality concepts to handle classical inventory problems with backorders is derived. A new analysis of these models is done by means of a trade-off analysis. New solutions are shown, and an error bound for total inventory cost is provided. Other models such as multi-item or stochastic lead-time demand inventory problems are addressed and their Pareto-optimal solution sets are obtained. An example is included showing the additional applicability of this kind of analysis to handle parametric problems. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 83–98, 1998