Supporting acquisition decisions through effective experimental design

Weapon acquisition is a very expensive process, especially in today's cost reduction environment. Techniques must be used to conduct operational testing using a minimum of resources while not sacrificing the adequacy and credibility of the test. A coordinated use of a combat simulation and a design of experiment procedure, the Taguchi method, shows promise as an acquisition strategyThis research focused on the Javelin medium antitank system which just completed operational testing in the Fall of 1993 and was intended to give the Javelin Project Manager's office information regarding the probable outcome of critical design characteristics prior to the test. Using the Taguchi method, many different design parameters were analyzed at several different levels of performance The method reduced the number of trials required to obtain a desired level of statistical significance while still obtaining the necessary data for each parameter. Once the required number of trials were identified, the Janus combat model simulated the operational test trials.Results suggest what weapon parameters are critical to the specific measures of effectiveness of survivability, lethality, and engagement range. In a broader view, this tandem use of an experimental design technique and a combat simulation can provide acquisition managers with insights on critical system parameters prior to actual testing.     

Estimation of more than one parameters in stratified sampling with fixed budget

In a multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. A compromise criterion is needed to work out a usable allocation which is optimum, in some sense, for all the characteristics. When auxiliary information is also available the precision of the estimates of the parameters can be increased by using it. Furthermore, if the travel cost within the strata to approach the units selected in the sample is significant the cost function remains no more linear. In this paper an attempt has been made to obtain a compromise allocation based on minimization of individual coefficients of variation of the estimates of various characteristics, using auxiliary information and a nonlinear cost function with fixed budget. A new compromise criterion is suggested. The problem is formulated as a multiobjective all integer nonlinear programming problem. A solution procedure is also developed using goal programming technique.     

Posynomial geometric programming with parametric uncertainty

Geometric programming provides a powerful tool for solving nonlinear problems where nonlinear relations can be well presented by exponential or power function. This paper develops a procedure to derive the lower and upper bounds of the objective of the posynomial geometric programming problem when the cost and constraint parameters are uncertain. The imprecise parameters are represented by ranges, instead of single values. An imprecise geometric program is transformed to a family of conventional geometric programs to calculate the objective value. The derived result is also in a range, where the objective value would appear. The ability of calculating the bounds of the objective value developed in this paper might help lead to more realistic modeling efforts in engineering design areas.     

Scalable methodology for supply chain inventory coordination with private information

This paper considers the problems of coordinating serial and assembly inventory systems with private information where end-item demands are known over a finite horizon. In a private information environment, the objective function and cost parameters of each facility are regarded as private information that no other facilities in the system have access to. The solution approach decomposes the problem into separable subproblems such that the private information is partitioned as required. Global optimality is sought with an iterative procedure in which the subproblems negotiate the level of material flows between facilities. At the core of the solution procedure is a supplier–buyer link model that can be used as a building block to form other supply chain configurations. Experimental results show that the proposed methodology provides promising results when compared to competing methodologies that disregard information privacy.     

Optimal service contract under cost information symmetry/asymmetry

Service outsourcing has become a hot topic in both industry and academy. This paper studies the contract design problems for a service seller who consigns the service to a vendor. The vendor’s service cost parameter may or may not completely be known by the seller, which constitutes the cases of information symmetry or asymmetry. In both cases, the optimal contracts are developed to maximize the seller’s expected profit, with the consideration of contractible and non-contractible service qualities. The properties of the contract parameters are explored, along with the analysis of information rent and value of cost information. Moreover, we find that non-contractible service quality is not an issue for the service seller under cost information symmetry since a revenue-sharing type of contract can guarantee the seller’s profit. However, this result does not hold under cost information asymmetry and thus non-contractibility of the service quality indeed costs the seller.     

Bounds on the value of information in uncertain decision problems

The cost of obtaining good information regarding the various probability distributions needed for the solution of most stochastic decision problems is considerable. It is important to consider questions such as: (1) what minimal amounts of information are sufficient to determine optimal decision rules; (2) what is the value of obtaining knowledge of the actual realization of the random vectors; and (3) what is the value of obtaining some partial information regarding the actual realization of the random vectors. This paper is primarily concerned with questions two and three when the decision maker has an a priori knowledge of the joint distribution function of the random variables. Some remarks are made regarding results along the lines of question one. Mention is made of assumptions sufficient so that knowledge of means, or of means, variances, co-variances and n-moments are sufficient for the calculation of optimal decision rules. The analysis of the second question leads to the development of bounds on the value of perfect information. For multiperiod problems it is important to consider when the perfect information is available. Jensen's inequality is the key tool of the analysis. The calculation of the bounds requires the solution of nonlinear programs and the numerical evaluation of certain functions. Generally speaking, tighter bounds may be obtained only at the expense of additional information and computational complexity. Hence, one may wish to compute some simple bounds to decide upon the advisability of obtaining more information. For the analysis of the value of partial information it is convenient to introduce the notion of a signal. Each signal represents the receipt of certain information, and these signals are drawn from a given probability distribution. When a signal is received, it alters the decision maker's perception of the probability distributions inherent in his decision problem. The choice between different information structures must then take into account these probability distributions as well as the decision maker's preference function. A hierarchy of bounds may be determined for partial information evaluation utilizing the tools of the multiperiod perfect information case. However, the calculation of these bounds is generally considerably more dicult than the calculation of similar boulids in the perfect information case. Most of the analysis is directed towards problems in which the decision maker has a linear utility function over profits, costs or some other numerical variable. However, some of the bounds generalize to the case when the utility function is strictly increasing and concave.     

Multi-choice stochastic transportation problem involving extreme value distribution

In this paper a multi choice stochastic transportation problem is considered where the supply and demand parameters of the constraints follow extreme value distribution. Some of the cost coefficients of the objective function are multi-choice type. At first all the probabilistic constraints are transformed into deterministic constraints. Further using the binary variables, multi-choice type cost coefficients are handled. Then the transformed problem is considered as a deterministic multi-choice transportation problem. Finally, a numerical example is presented to illustrate the solution procedure.     

Economic selection of process mean for single-vendor single-buyer supply chain

Process mean selection for a container-filling process is an important decision in a single-vendor single-buyer supply chain. Since the process mean determines the vendor’s conforming and yield rates, it influences the vendor–buyer decisions regarding the production lot size and number of shipments delivered from the vendor to buyer. It follows, therefore, that these decisions should be determined simultaneously in order to control the supply chain total cost. In this paper, we develop a model that integrates the single-vendor single-buyer problem with the process mean selection problem. This integrated model allows the vendor to deliver the produced lot to buyer in number of unequal-sized shipments. Moreover, every outgoing item is inspected, and each item failing to meet a lower specification limit is reprocessed. Further, in order to study the benefits of using this integrated model, two baseline cases are developed. The first of which considers a hierarchical model where the vendor determines the process mean and schedules of production and shipment separately. This hierarchical model is used to show the impact of integrating the process mean selection with production/inventory decisions. The other baseline case is studied in the sensitivity analysis where the optimal solution for a given process is compared to the optimal solution when the variation in the process output is negligible. The integrated model is expected to lead to reduction in reprocessing cost, minimal loss to customer due to the deviation from the optimum target value, and consequently, providing better products at reduced cost for customers. Also, a solution procedure is devised to find the optimal solution for the proposed model and sensitivity analysis is conducted to investigate the effect of the model key parameters on the optimal solution.     

An incentive model for closed-loop supply chain under the EPR law

Motivated by the collection outsourcing phenomena under Extended Producer Responsibility (EPR), this paper studies a contract design problem for a manufacturer who consigns the used product collection to a collector, while the manufacturer only has incomplete information on the collector's cost. On the basis of the incentive theory, optimal contracts are developed to minimize the cost and satisfy the collection constraints prescribed by EPR. Properties of the contract parameters are derived, and issues such as information rent and information value are also explored. The impacts of EPR are analysed by comparing whether or not EPR law is implemented, and more managerial insights are further obtained through numerical examples.     

Statistical tests involving several independent gamma distributions

Statistical tests are developed regarding linear combinations of the parameters of several independent gamma populations. The tests are based on a generalized minimum chi-square procedure. On utilizing these, one can test hypotheses regarding the means or the scale parameters when the shape parameters are unknown. In these tests there is no need to assume the equality of the shape parameters of the underlying populations. Tests for comparing coefficients of variation of several gamma populations have also been developed. For the two population case, a power comparison of these tests with some existing tests is also presented. Two examples are provided to explain the procedure.     

Sensitivity analyses for preventive-maintenance models

Models for determining preventive-maintenance strategies usuallymake assumptions of constancy regarding lifetime distributions,cost functions, temporal effects, down-time durations, and preventive-maintenanceintervals. In practice, extraordinary sources of variabilityarise, leading to inaccurate information about parameters, probabilities,predictions, and decisions. This paper examines these errors,using simulation studies for delayed renewal processes withWeibull lifetime distributions. These sensitivity analyses demonstratethe importance of allowing for extraordinary sources of variabilitywhen deciding on optimal strategies for preventive maintenance.     

Time-cost trade-off analysis of project networks in fuzzy environments

This paper proposes a novel approach for time-cost trade-off analysis of a project network in fuzzy environments. Different from the results of previous studies, in this paper the membership function of the fuzzy minimum total crash cost is constructed based on Zadeh’s extension principle and fuzzy solutions are provided. A pair of two-level mathematical programs parameterized by possibility level α is formulated to calculate the lower and upper bounds of the fuzzy minimum total crash cost at α. By enumerating different values of α, the membership function of the fuzzy minimum total crash cost is constructed, and the corresponding optimal activity time for each activity is also obtained at the same time. An example of time-cost trade-off problem with several fuzzy parameters is solved successfully to demonstrate the validity of the proposed approach. Since the minimum total crash cost is expressed by a membership function rather than by a crisp value, the fuzziness of parameters is conserved completely, and more information is provided for time-cost trade-off analysis in project management. The proposed approach also can be applied to time-cost trade-off problems with other characteristics.     

An integrated vendor–buyer inventory model with order-processing cost reduction and permissible delay in payments

Trade credit plays an important role in financing for many businesses and industries. For the buyers, purchased inventory can be considered to be financed in whole or in part with permissible delay in payments during the purchasing process. On the other hand, both the vendor and buyer take part in order-processing cost reduction by applying information technologies, such as EDI (electronic data interchange). The order-processing cost can also be reduced by adding certain capital investments, and this will affect the lot size decisions. This article develops an integrated inventory model to determine the optimal inventory policy under conditions of order-processing cost reduction and permissible delay in payments, and shows that the total annual variable cost function possesses some kinds of convexities. A solution procedure is provided to determine the optimal order policy. Finally, a numerical example is presented to illustrate the solution procedure.     

Heuristic procedures for a stochastic batch service problem

This paper considers a multi-class batch service problem that involves a class-dependent waiting cost and a service cost in determining customer batch sizes. Unlike a fixed service cost used widely in standard models, the service cost considered in this work is incurred only if the total service time is over the capacity. We formulate this problem as an infinite horizon Markov decision process, and exploit its structural properties to establish theoretical results, including bounds on the optimal action space. We use the results to improve the value iteration procedure. Furthermore, we design heuristic algorithms for large problems. The numerical experiments demonstrate that the class-dependent waiting cost has a considerable influence on the optimal customer batch size. Finally, we evaluate the efficiency of the proposed value iteration procedure and the quality of the heuristic solutions.     

Discrete Markov ballistic missile defense system modeling

Expected value is a common and useful baseline used to compare different multi-layered missile defense strategies or fire doctrines (number of interceptors fired at one target). However, expected value by itself does not render enough information to the military or national security researchers regarding the probability distribution of the effectiveness of the entire missile defense system. The objective of this paper is to provide relevant probability distribution functions (pdf) for ballistic missile defense (BMD) planning and cost-effective analyzing. To achieve this goal, discrete time Markov process is utilized to model multi-layered BMD system. Most issues of the multi-layered BMD system are covered in this model, including multi-reentry vehicles, discrimination probabilities and accompanying risk and waste of defensive resources, probability to engage all of the hostile objects, and required inventory levels. The effectiveness of a multi-layered BMD system is expressed in the pdf form of the number of warheads or missiles penetrating the BMD system. This paper also suggests that by changing fire doctrines and comparing the resulting effectiveness against cost the BMD system might be optimized. Since Markov process modeling requires initial state, military intelligence and information will be necessary to generate the initial state.     

An alternative procedure for selecting a good value for the parameter <Emphasis Type="Italic">c</Emphasis> in RBF-interpolation

The impact of the scaling parameter c on the accuracy of interpolation schemes using radial basis functions (RBFs) has been pointed out by several authors. Rippa (Adv Comput Math 11:193–210, 1999) proposes an algorithm based on the idea of cross validation for selecting a good such parameter value. In this paper we present an alternative procedure, that can be interpreted as a refinement of Rippa’s algorithm for a cost function based on the euclidean norm. We point out how this method is related to the procedure of maximum likelihood estimation, which is used for identifying covariance parameters of stochastic processes in spatial statistics. Using the same test functions as Rippa we show that our algorithm compares favorably with cross validation in many cases and discuss its limitations. Finally we present some computational aspects of our algorithm.     

Efficient synchronization of structurally adaptive coupled Hindmarsh–Rose neurons

The use of spikes to carry information between brain areas implies complete or partial synchronization of the neurons involved. The degree of synchronization reached by two coupled systems and the energy cost of maintaining their synchronized behavior is highly dependent on the nature of the systems. For non-identical systems the maintenance of a synchronized regime is energetically a costly process. In this work, we study conditions under which two non-identical electrically coupled neurons can reach an efficient regime of synchronization at low energy cost. We show that the energy consumption required to keep the synchronized regime can be spontaneously reduced if the receiving neuron has adaptive mechanisms able to bring its biological parameters closer in value to the corresponding ones in the sending neuron.     

不同补贴对象下闭环供应链信息共享价值研究

在一个制造商和一个零售商组成的二级闭环供应链中,为研究政府补贴下供应链需求信息共享对决策的影响及共享价值,针对两种补贴对象,构建并求解无信息共享和信息共享博弈模型,并进行仿真验证.研究表明:1)两种补贴对象下,制造商均能从信息共享中获益,零售商仅在绿色成本和回收成本较低时才会从信息共享中获益;绿色成本和回收成本稍高时,设计基于谈判势力的信息补偿机制能有效促进零售商共享信息.2)产品绿色度和回收率随预测需求量的提高而提高,批发价和零售价仅在回收成本较低时,才会随预测需求量的提高而提高.3)在仅补贴一方情况下,当补贴对象为低补贴一方时,两个主体所获的信息共享价值大;若对两者的补贴均较低,两个主体均希望补贴对象为零售商;若对两者的补贴均较高,零售商不愿共享需求信息.     

An integrated inventory model under conditions of order processing cost reduction and permissible delay in payments

This article develops an integrated inventory model to determine the optimal policy under conditions of order processing cost reduction and permissible delay in payments. Both the vendor and the buyer participate in order processing cost reduction by applying information technologies. The order processing cost can be reduced by certain expenditures and will affect lot-size decisions. Simultaneously, the existence of the credit period serves to reduce the cost of holding stock to the buyer, because it reduces the amount of capital invested in stock for the duration of the credit period. The article derives the total cost function and shows that the function possesses some kinds of convexities. A solution procedure is provided to determine the optimal order policy. Finally, numerical examples are presented to illustrate the solution procedure.