Vehicle fleet refueling strategies to maximize operational range

The focus of this research is on self-contained missions requiring round-trip vehicle travel from a common origin. For a single vehicle the maximal distance that can be reached without refueling is defined as its operational range. Operational range is a function of a vehicle's fuel capacity and fuel consumption characteristics. In order to increase a vehicle's range beyond its operational range replenishment from a secondary fuel source is necessary. In this article, the problem of maximizing the range of any single vehicle from a fleet of n vehicles is investigated. This is done for four types of fleet configurations: (1) identical vehicles, (2) vehicles with identical fuel consumption rates but different fuel capacities, (3) vehicles which have the same fuel capacity but different fuel consumption rates, and (4) vehicles with both different fuel capacities and different consumption rates. For each of the first three configurations the optimal refueling policy that provides the maximal range is determined for a sequential refueling chain strategy. In such a strategy the last vehicle to be refueled is the next vehicle to transfer its fuel. Several mathematical programming formulations are given and their solutions determined in closed form. One of the major conclusions is that for an identical fleet the range of the farthest vehicle can be increased by at most 50% more than the operational range of a single vehicle. Moreover, this limit is reached very quickly with small values of n. The performance of the identical fleet configuration is further investigated for a refueling strategy involving a multiple-transfer refueling chain, stochastic vehicle failures, finite refueling times, and prepositioned fleets. No simple refueling ordering rules were found for the most general case (configuration 4). In addition, the case of vehicles with different fuel capacities is investigated under a budget constraint. The analysis provides several benchmarks or bounds for which more realistic structures may be compared. Some of the more complex structures left for future study are described.     

Decision rules for attacking targets of opportunity

Frequently in warfare, a force is required to attack a perishable enemy target system - a target system where the targets are detected seemingly at random, and if not immediately attacked, will shortly escape from detection. A conflicting situation arises when an attack element detects a target of relatively low value and has to decide whether to expend his resources on that particular target or to wait for a more lucrative one, hoping one will be found. This paper provides a decision rule giving the least valued target that should be attacked as well as the resources that should be expended as a function of the attack element's remaining mission time.     

Inequalities for mixed integer programs with structure

Mixed integer programming problems arising in practice often contain special structures such as imbedded networks and multiple choice constraints. Easily derived inequalities are given that can be used to reduce the range of admissible solutions for such problems.     

Selection of the optimal setup policy

A model is developed taking into consideration all the costs (namely cost of sampling, cost of not detecting a change in the process, cost of a false indication of change, and the cost of readjusting detected changes) incurred when a production process, using an unscheduled setup policy, utilizes fraction-defective control charts to control current production. The model is based on the concept of the expected time between detection of changes calling for setups. It is shown that the combination of unscheduled setups and control charts can be utilized in an optimal way if those combinations of sample size, sampling interval, and extent of control limits from process average are used that provide the minimum expected total cost per unit of time. The costs of a production process that uses unscheduled setups in conjunction with the appropriate optimal control charts are compared to the costs of a production process that uses scheduled setups at optimum intervals in conjunction with its appropriate control charts. This comparison indicates the criteria for selecting production processes with scheduled setups using optimal setup intervals over unscheduled setups. Suggestions are made to evaluate the optimal process setup strategy and the accompanying optimal decision parameters, for any specific cost data, by use of computer enumeration. A numerical example for assumed cost and process data is provided.     

Toward optimal bidding strategies

In this paper we investigate a form of rational behavior in response to an oligopoly pricing problem where only one buyer is involved. We investigate the problem from the standpoint of the seller who wants to maximize his gain from the transaction. In particular, we deal with the problem of one seller's response to an invitation to submit a sealed (i. e., noncooperative) bid to a government or other dominant purchasing agency for supplying a specified bundle of goods and services for which either (1) no other demand exists, or (2) the terms or quantities involved cannot, at least in the short run, be obtained from another source. Although treated from a normative standpoint, i. e., what bid the supplier should make, the paper also has implications for the buyer's behavior and oligopoly-monopsony pricing in a more general sense.     

A heuristic network procedure for the assembly line balancing problem

Proposed is a Heuristic Network (HN) Procedure for balancing assembly lines. The procedure uses simple heuristic rules to generate a network which is then traversed using a shortest route algorithm to obtain a heuristic solution. The advantages of the HN Procedure are: a) it generally yields better solutions than those obtained by application of the heuristics, and b) sensitivity analysis with different values of cycle time is possible without having to regenerate the network. The rationale for its effectiveness and its application to problems with paralleling are presented. Computational experience with the procedure on up to 50 task test problems is provided.     

An approximative algorithm for the fixed charge problem

This paper describes an approximate solution method for solving the fixed charge problem. This heuristic approach is applied to a set of test problems to explore the margin of error. The results indicate that the proposed fixed charge simplex algorithm is capable of finding optimal or near optimal solutions to moderate sized fixed charge problems. In the absence of an exact method, this heuristic should prove useful in solving this fundamental nonlinear programming problem.     

An inventory problem with obsolescence

A stochastic single product convex cost inventory problem is considered in which there is a probability, π_j, that the product will become obsolete in the future period j. In an interesting paper, Barankin and Denny essentially formulate the model, but do not describe some of its interesting and relevant ramifications. This paper is written not only to bring out some of these ramifications, but also to describe some computational results using this model. The computational results show that if obsolescence is a distinct possibility in the near future, it is quite important that the probabilities of obsolescence be incorporated into the model before computing the optimal policies.