A note on the “value” of bounds on EVPI in stochastic programming

The existing literature concentrates on determining sharp upper bounds for EVPI in stochastic programming problems. This seems to be a problem without an application. Lower bounds, which we view as having an important application, are only the incidental subject of study and in the few instances that are available are obtained at an extremely high cost. In order to suggest a rethinking of the course of this research, we analyze the need for bounds on EVPI in the context of its significance in decision problems.     

On the optimal allocation of crewmen aboard a warship

In the temporarily isolated situation in which a warship finds itself during a mission. not only spare parts, but also “spare” crewmen in various categories of specialization must he on board. Mathematical models for the probabilities of mission survival for personnel and for personnel and materiel jointly are proposed. A practical example is worked out: the optimal allocation of spare crewmen to different categories of specialization is calculated.     

A simulation–optimization method: Its convergence and utility

An optimization method is given for solving problems where a portion of the explicit mathematical form is unknown but can be evaluated. The solution scheme is an iterative process utilizing optimization and subsystem evaluation (such as via simulation). Conditions for the convergence of the iterative process are given. Several published application articles are noted as using this basic methodology. The method is superior to most other numerical optimization procedures. However, the class of problems for which the method is applicable is restricted to problems with enough known structure to generate a convergent iterative procedure. Three numerical examples are given and comparisons made with several other methods of optimizing unknown systems.     

Optimal admission pricing and service rate control of an M[x]/M/s queue with reneging

In this article we consider the optimal control of an M^[X]/M/s queue, s ≧ 1. In addition to Poisson bulk arrivals we incorporate a reneging function. Subject to control are an admission price p and the service rate μ. Thus, through p, balking response is induced. When i customers are present a cost h(i,μ,p) per unit time is incurred, discounted continuously. Formulated as a continuous time Markov decision process, conditions are given under which the optimal admission price and optimal service rate are each nondecreasing functions of i. In Section 4 we indicate how the infinite state space may be truncated to a finite state space for computational purposes.     

Parameter estimation for the EOQ lot-size model: Minimax and expected value choices

This article provides formulas for estimating the parameters to be used in the basic EOQ lot-size model. The analysis assumes that the true values of these parameters are unknown over known ranges and perhaps nonstationary over time. Two measures of estimator “goodness” are derived from EOQ sensitivity analysis. Formulas are given for computing the minimax choice and the minimum expected value choice for the parameter estimates using both measures of estimator “goodness”. A numerical example is included.     

An analysis of single item inventory systems with returns

Inventory systems with returns are systems in which there are units returned in a repairable state, as well as demands for units in a serviceable state, where the return and demand processes are independent. We begin by examining the control of a single item at a single location in which the stationary return rate is less than the stationary demand rate. This necessitates an occasional procurement of units from an outside source. We present a cost model of this system, which we assume is managed under a continuous review procurement policy, and develop a solution method for finding the policy parameter values. The key to the analysis is the use of a normally distributed random variable to approximate the steady-state distribution of net inventory. Next, we study a single item, two echelon system in which a warehouse (the upper echelon) supports N(N ? 1) retailers (the lower echelon). In this case, customers return units in a repairable state as well as demand units in a serviceable state at the retailer level only. We assume the constant system return rate is less than the constant system demand rate so that a procurement is required at certain times from an outside supplier. We develop a cost model of this two echelon system assuming that each location follows a continuous review procurement policy. We also present an algorithm for finding the policy parameter values at each location that is based on the method used to solve the single location problem.     

Optimal ordering policies when anticipating parameter changes in EOQ systems

The classical Economic Order Quantity Model requires the parameters of the model to be constant. Some EOQ models allow a single parameter to change with time. We consider EOQ systems in which one or more of the cost or demand parameters will change at some time in the future. The system we examine has two distinct advantages over previous models. One obvious advantage is that a change in any of the costs is likely to affect the demand rate and we allow for this. The second advantage is that often, the times that prices will rise are fairly well known by announcement or previous experience. We present the optimal ordering policy for these inventory systems with anticipated changes and a simple method for computing the optimal policy. For cases where the changes are in the distant future we present a myopic policy that yields costs which are near-optimal. In cases where the changes will occur in the relatively near future the optimal policy is significantly better than the myopic policy.     

Scheduling of stochastic tasks on two parallel processors

We consider the problem of scheduling n tasks on two identical parallel processors. We show both in the case when the processing times for the n tasks are independent exponential random variables, and when they are independent hyperexponentials which are mixtures of two fixed exponentials, that the policy of performing tasks with longest expected processing time (LEPT) first minimizes the expected makespan, and that in the hyperexponential case the policy of performing tasks with shortest expected processing time (SEPT) first minimizes the expected flow time. The approach is simpler than the dynamic programming approach recently employed by Bruno and Downey.     

On a single-server queue with state-dependent service

This paper discusses a class of queueing models in which the service time of a customer al a single server facility is dependent on the queue size at the onset of its service. The Laplace transform for the wait in queue distribution is derived and the utilization of the server is given when the arrival is a homogeneous Poisson process.