Sensitivity analysis on responsive pricing and production under imperfect demand updating

This paper examines three types of sensitivity analysis on a firm's responsive pricing and responsive production strategies under imperfect demand updating. Demand has a multiplicative form where the market size updates according to a bivariate normal model. First, we show that both responsive production and responsive pricing resemble the classical pricing newsvendor with posterior demand uncertainty in terms of the optimal performance and first‐stage decision. Second, we show that the performance of responsive production is sensitive to the first‐stage decision, but responsive pricing is insensitive. This suggests that a “posterior rationale” (ie, using the optimal production decision from the classical pricing newsvendor with expected posterior uncertainty) allows a simple and near‐optimal first‐stage production heuristic for responsive pricing. However, responsive production obtains higher expected profits than responsive pricing under certain conditions. This implies that the firm's ability to calculate the first‐stage decision correctly can help determine which responsive strategy to use. Lastly, we find that the firm's performance is not sensitive to the parameter uncertainty coming from the market size, total uncertainty level and information quality, but is sensitive to uncertainty originating from the procurement cost and price‐elasticity.     

Risk pooling in a two-period,two-echelon inventory stocking and allocation problem

The object of this article is to investigate the risk-pooling effect of depot stock in two-echelon distribution system in which the depot serves n retailers in parallel, and to develop computationally tractable optimization procedures for such systems. The depot manager has complete information about stock levels and there are two opportunities to allocate stock to the retailers within each order cycle. We identify first- and second-order aspects to the risk-pooling effect. In particular, the second-order effect is the property that the minimum stock available to any retailer after the second allocation converges in probability to a constant as the number of retailers in the system increases, assuming independence of the demands. This property is exploited in the development of efficient procedures to determine near-optimal values of the policy parameters.     

Estimation of the survival function of a repairable standby series system

This article deals with the statistical analysis of an N-component series system supported by an active standby and one repair facility. Assuming that the life and repair times of the components are independent exponential random variables, the probability distribution of the first passage to the system failure time is shown to be a convolution of two independent exponential distributions. Three observation schemes are considered to obtain the maximum likelihood estimates of the survival function. Information matrices are supplied. Numerical results based on Monte Carlo simulation are presented. It is noted that component level information (failure rate, repair rate) is not necessary for estimating the survival function of the system.     

Stochastic linear fractional programming with the ratio of independent Cauchy variates

In this article is studied a stochastic linear fractional programming problem, in which the parameters of both the numerator and the denominator are assumed to be mutually independent Cauchy variates. The deterministic equivalent of the problem is obtained and is shown to be a linear fractional program. A numerical example is also added for illustration.     

Search and the introduction of improved technologies

Modeling R&D as standard sequential search, we consider a monopolist who can implement a sequence of technological discoveries during the technology search process: he earns revenue on his installed technology while he engages in R&D to find improved technology. What is not standard is that he has a finite number of opportunities to introduce improved technology. We show that his optimal policy is characterized by thresholds ξ_i(x): introduce the newly found technology if and only if it exceeds ξ_i(x) when x is the state of the currently installed technology and i is the number of remaining introductions allowed. We also analyze a nonstationary learning‐by‐doing model in which the monopolist's experience in implementing new technologies imparts increased capability in generating new technologies. Because this nonstationary model is not in the class of monotone stopping problems, a number of surprising results hold and several seemingly obvious properties of the stationary model no longer hold. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

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.     

Class scheduling algorithms for Navy training schools

The problem of developing good schedules for Navy C-Schools has been modeled as a combinatorial optimization problem. The only complicating feature of the problem is that classes must be grouped together into sequences known as pipelines. An ideal schedule will have all classes in a pipeline scheduled in consecutive weeks. The objective is to eliminate the nonproductive time spent by sailors at C-Schools who are waiting for the next class in a pipeline. In this investigation an implicit enumeration procedure for this problem was developed. The key component of our algorithm is a specialized greedy algorithm which is used to obtain a good initial incumbent. Often this initial incumbent is either an optimal schedule or a near optimal schedule. In an empirical analysis with the only other competing software system, our greedy heuristic found equivalent or better solutions in substantially less computer time. This greedy heuristic was extended and modified for the A-School scheduling problem and was found to be superior to its only competitor. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 533–551, 1998     

Attrition modeling in the presence of decoys: An operations-other-than-war motivation

Under various operational conditions, in particular in operations other than war (OOTW) or peacekeeping, an intervening force, here Blue, must occasionally engage in attrition warfare with an opposing force, here Red, that is intermingled with noncombatants. Desirably, Red armed actives are targeted, and not the unarmed noncombatants. This article describes some simple Lanchesterian attrition models that reflect a certain capacity of Blue to discriminate noncombatants from armed and active Red opponents. An explicit extension of the Lanchester square law results: Blue's abstinence concerning the indiscriminate shooting of civilians mixed with Red's is essentially reflected in a lower Blue rate of fire and less advantageous exchange rate. The model applies to other situations involving decoys, and reflects the value of a discrimination capability. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44 : 507–514, 1997