Average-case analysis of the bin-packing problem with general cost structures

We consider a version of the famous bin-packing problem where the cost of a bin is a concave function of the number of items in the bin. We analyze the problem from an average-case point of view and develop techniques to determine the asymptotic optimal solution value for a variety of functions. We also describe heuristic techniques that are asymptotically optimal. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 673–686, 1997     

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.     

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 manpower planning/capital budgeting model (MAPCAB)

A deterministic resource allocation model is developed to optimize defense effectiveness subject to budget, manpower, and risk constraints. The model consists of two major submodels connected by a heuristic. The first is a mathematical program which optimizes the multiperiod weapon mix subject to the constraint set. The second is a manpower supply model based on a transition matrix in which individual transitions are functions of personnel related budgets and historical transition rates. The heuristic marries the submodels through an iterative process leading to improved solutions. An example is provided which demonstrates how systems are undercosted and overprocured if manpower supply is not properly reflected relative to manpower demand.     

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.     

The value of information sharing in a two‐stage supply chain with production capacity constraints

We consider a simple two‐stage supply chain with a single retailer facing i.i.d. demand and a single manufacturer with finite production capacity. We analyze the value of information sharing between the retailer and the manufacturer over a finite time horizon. In our model, the manufacturer receives demand information from the retailer even during time periods in which the retailer does not order. To analyze the impact of information sharing, we consider the following three strategies: (1) the retailer does not share demand information with the manufacturer; (2) the retailer does share demand information with the manufacturer and the manufacturer uses the optimal policy to schedule production; (3) the retailer shares demand information with the manufacturer and the manufacturer uses a greedy policy to schedule production. These strategies allow us to study the impact of information sharing on the manufacturer as a function of the production capacity, and the frequency and timing in which demand information is shared. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003