The multiplicative representation for multiple objectives optimization with an application for arms procurement

Multiple Objectives Optimization is much seen in combination with linear functions and even with linear programming, together with an adding of the objectives by using weights. With distance functions, normalization instead of weights is used. It is also possible that together with an additive direct influence of the objectives on the utility function a mutual utility of the objectives exists under the form of a multiplicative representation. A critical comment is brought on some representations of this kind. A full‐multiplicative form may offer other opportunities, which will be discussed at length in an effort to exclude weights and normalization. This theoretical approach is followed by an application for arms procurement. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 327–340, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10014     

Resequencing with parallel queues to minimize the maximum number of items in the overflow area

This article treats an elementary optimization problem, where an inbound stream of successive items is to be resequenced with the help of multiple parallel queues in order to restore an intended target sequence. Whenever early items block the one item to be currently released into the target sequence, they are withdrawn from their queue and intermediately stored in an overflow area until their actual release is reached. We aim to minimize the maximum number of items simultaneously stored in the overflow area during the complete resequencing process. We met this problem in industry practice at a large German automobile producer, who has to resequence containers with car seats prior to the assembly process. We formalize the resulting resequencing problem and provide suited exact and heuristic solution algorithms. In our computational study, we also address managerial aspects such as how to properly avoid the negative effects of sequence alterations. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 401–415, 2016     

Optimal operating policies in a commodity trading market with the manufacturer's presence

With the help of the Internet and express delivery at relatively low costs, trading markets have become increasingly popular as a venue to sell excess inventory and a source to obtain products at lower prices. In this article, we study the operational decisions in the presence of a trading market in a periodic‐review, finite‐horizon setting. Prices in the trading market change periodically and are determined endogenously by the demand and supply in the market. We characterize the retailers'optimal ordering and trading policies when the original manufacturer and the trading market co‐exist and retailers face fees to participate in the trading market. Comparing with the case with no trading fees, we obtain insights into the impact of trading fees and the fee structure on the retailers and the manufacturer. Further, we find that by continually staying in the market, the manufacturer may use her pricing strategies to counter‐balance the negative impact of the trading market on her profit. Finally, we extend the model to the case when retailers dynamically update their demand distribution based on demand observations in previous periods. A numerical study provides additional insights into the impact of demand updating in a trading market with the manufacturer's competition. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Determination of burn‐in parameters and residual life for highly reliable products

Today, many products are designed and manufactured to function for a long period of time before they fail. Determining product reliability is a great challenge to manufacturers of highly reliable products with only a relatively short period of time available for internal life testing. In particular, it may be difficult to determine optimal burn‐in parameters and characterize the residual life distribution. A promising alternative is to use data on a quality characteristic (QC) whose degradation over time can be related to product failure. Typically, product failure corresponds to the first passage time of the degradation path beyond a critical value. If degradation paths can be modeled properly, one can predict failure time and determine the life distribution without actually observing failures. In this paper, we first use a Wiener process to describe the continuous degradation path of the quality characteristic of the product. A Wiener process allows nonconstant variance and nonzero correlation among data collected at different time points. We propose a decision rule for classifying a unit as normal or weak, and give an economic model for determining the optimal termination time and other parameters of a burn‐in test. Next, we propose a method for assessing the product's lifetime distribution of the passed units. The proposed methodologies are all based only on the product's initial observed degradation data. Finally, an example of an electronic product, namely contact image scanner (CIS), is used to illustrate the proposed procedure. © 2002 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

The building evacuation problem with shared information

In this article, the Building Evacuation Problem with Shared Information (BEPSI) is formulated as a mixed integer linear program, where the objective is to determine the set of routes along which to send evacuees (supply) from multiple locations throughout a building (sources) to the exits (sinks) such that the total time until all evacuees reach the exits is minimized. The formulation explicitly incorporates the constraints of shared information in providing online instructions to evacuees, ensuring that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. Arc travel time and capacity, as well as supply at the nodes, are permitted to vary with time and capacity is assumed to be recaptured over time. The BEPSI is shown to be NP‐hard. An exact technique based on Benders decomposition is proposed for its solution. Computational results from numerical experiments on a real‐world network representing a four‐story building are given. Results of experiments employing Benders cuts generated in solving a given problem instance as initial cuts in addressing an updated problem instance are also provided. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Estimating failure time distribution and its parameters based on intermediate data from a Wiener degradation model

Instead of measuring a Wiener degradation or performance process at predetermined time points to track degradation or performance of a product for estimating its lifetime, we propose to obtain the first‐passage times of the process over certain nonfailure thresholds. Based on only these intermediate data, we obtain the uniformly minimum variance unbiased estimator and uniformly most accurate confidence interval for the mean lifetime. For estimating the lifetime distribution function, we propose a modified maximum likelihood estimator and a new estimator and prove that, by increasing the sample size of the intermediate data, these estimators and the above‐mentioned estimator of the mean lifetime can achieve the same levels of accuracy as the estimators assuming one has failure times. Thus, our method of using only intermediate data is useful for highly reliable products when their failure times are difficult to obtain. Furthermore, we show that the proposed new estimator of the lifetime distribution function is more accurate than the standard and modified maximum likelihood estimators. We also obtain approximate confidence intervals for the lifetime distribution function and its percentiles. Finally, we use light‐emitting diodes as an example to illustrate our method and demonstrate how to validate the Wiener assumption during the testing. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A general model of heterogeneous system lifetimes and conditions for system burn‐in

Burn‐in is a technique to enhance reliability by eliminating weak items from a population of items having heterogeneous lifetimes. System burn‐in can improve system reliability, but the conditions for system burn‐in to be performed after component burn‐in remain a little understood mathematical challenge. To derive such conditions, we first introduce a general model of heterogeneous system lifetimes, in which the component burn‐in information and assembly problems are related to the prediction of system burn‐in. Many existing system burn‐in models become special cases and two important results are identified. First, heterogeneous system lifetimes can be understood naturally as a consequence of heterogeneous component lifetimes and heterogeneous assembly quality. Second, system burn‐in is effective if assembly quality variation in the components and connections which are arranged in series is greater than a threshold, where the threshold depends on the system structure and component failure rates. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 364–380, 2003.     

Supply chain coordination with shelf‐space and retail price dependent demand and heterogeneous retailers

We consider supply chain coordination in which a manufacturer supplies some product to multiple heterogeneous retailers and wishes to coordinate the supply chain via wholesale price and holding cost subsidy. The retail price is either exogenous or endogenous. The market demand is described by the market share attraction model based on all retailers'shelf‐spaces and retail prices. We obtain optimal solutions for the centralized supply chain, where the optimal retail pricing is a modified version of the well‐known cost plus pricing strategy. We further get feasible contracts for the manufacturer to coordinate the hybrid and decentralized supply chains. The manufacturer can allocate the total profit free to himself and the retail market via the wholesale price when the retail price is exogenous, but otherwise he cannot. Finally, we point out that different characteristics of the retail market are due to different powers of the manufacturer, and the more power the manufacturer has, the simpler the contract to coordinate the chain will be. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Dynamic inventory management with cash flow constraints

In this article, we consider a classic dynamic inventory control problem of a self‐financing retailer who periodically replenishes its stock from a supplier and sells it to the market. The replenishment decisions of the retailer are constrained by cash flow, which is updated periodically following purchasing and sales in each period. Excess demand in each period is lost when insufficient inventory is in stock. The retailer's objective is to maximize its expected terminal wealth at the end of the planning horizon. We characterize the optimal inventory control policy and present a simple algorithm for computing the optimal policies for each period. Conditions are identified under which the optimal control policies are identical across periods. We also present comparative statics results on the optimal control policy. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008