Scheduling customer arrivals to a stochastic service system

An efficient algorithm for determining the optimal arrival schedule for customers in a stochastic service system is developed. All customers arrive exactly when scheduled, and service times are modeled as iid Erlang random variables. Costs are incurred at a fixed rate per unit of time each customer waits for service, and an additional cost is incurred for every unit of time the server operates beyond a scheduled closing time. The objective is to minimize total operating cost. This type of problem arises in many operational contexts including transportation, manufacturing, and appointment‐based services. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 549–559, 1999     

Multicriteria efficiency with arbitrary finite sets and cyclic preferences

It is shown that when X is an arbitrary finite subset of an n-factor product set and preference relations on each factor or criterion are assumed only to be asymmetric, efficient (undominated) points always exist in the set P of probability distributions on X when the preference relations are extended to probability distributions on the factors according to SSB utility theory. Thus, arbitrary finite structures and potentially cyclic preferences do not present a problem for the theory of efficiency under the convexification-extension procedure.     

A duality model for a generalized minmax program

We consider a generalized minmax programming problem, and establish, under certain weaker convexity assumptions, the Fritz John sufficient optimality conditions for such a problem. A dual program is introduced and using those optimality conditions duality theorems are proved relating the dual and the primal. Duality for the generalized fractional programming problem is considered as an application of the results proved.     

Cost allocation in continuous-review inventory models

A centralized inventory system serves a number of stores with common ownership, and thus reliable and timely information sharing. Each of them pays a share of the inventory cost, and the reward structure leaves the owners of individual stores rewarded for their individual performance. Appropriate selection of a cost allocation method is important if such a centralized system is to last. In this work we propose three necessary criteria—stability (core of a related cooperative game), justifiability (consistency of benefits with costs), and polynomial computability. For a concrete example we demonstrate that common allocation procedures may not meet all three tests, and we present a method that that meets all three criteria. This kind of cost allocation analysis helps the common management to evaluate the trade-offs in choosing an allocation scheme for the cost of inventory centralization. © 1996 John Wiley & Sons, Inc.     

Modeling the fatigue life of longitudinal elements

Functional equations enable us to arrive at a simple consensus model for fatigue life of longitudinal elements based on engineering principles. The model is then applied to two representative data sets. By the application of proportional hazards techniques and subsequent likelihood analysis, simple parsimonious Weibull models are derived. Inter alia attention is given to the desirability of deriving models exhibiting plausible asymptotic independence. © 1996 John Wiley & Sons, Inc.     

Coordination of pricing and inventory control across products

We consider the joint pricing and inventory‐control problem for a retailer who orders, stocks, and sells two products. Cross‐price effects exist between the two products, which means that the demand of each product depends on the prices of both products. We derive the optimal pricing and inventory‐control policy and show that this policy differs from the base‐stock list‐price policy, which is optimal for the one‐product problem. We find that the retailer can significantly improve profits by managing the two products jointly as opposed to independently, especially when the cross‐price demand elasticity is high. We also find that the retailer can considerably improve profits by using dynamic pricing as opposed to static pricing, especially when the demand is nonstationary. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Tests for transient means in simulated time series

We present a family of tests to detect the presence of a transient mean in a simulation process. These tests compare variance estimators from different parts of a simulation run, and are based on the methods of batch means and standardized time series. Our tests can be viewed as natural generalizations of some previously published work. We also include a power analysis of the new tests, as well as some illustrative examples. © 1994 John Wiley & Sons, Inc.     

Application of perturbation analysis to a class of periodic review (s,S) inventory systems

In this article we apply perturbation analysis (PA), combined with conditional Monte Carlo, to obtain derivative estimators of the expected cost per period with respect to s and S, for a class of periodic review (s, S) inventory systems with full backlogging, linear holding and shortage costs, and where the arrivals of demands follow a renewal process. We first develop the general form of four different estimators of the gradient for the finite-horizon case, and prove that they are unbiased. We next consider the problem of implementing our estimators, and develop efficient methodologies for the infinite-horizon case. For the case of exponentially distributed demand interarrival times, we implement our estimators using a single sample path. Generally distributed interarrival times are modeled as phase-type distributions, and the implementation of this more general case requires a number of additional off-line simulations. The resulting estimators are still efficient and practical, provided that the number of phases is not too large. We conclude by reporting the results of simulation experiments. The results provide further validity of our methodology and also indicate that our estimators have very low variance. © 1994 John Wiley & Sons, Inc.