Bonus-malus systems (BMSs) are widely used in actuarial sciences. These systems are applied by insurance companies to distinguish the policyholders by their risks. The most known application of BMS is in automobile third-party liability insurance. In BMS, there are several classes, and the premium of a policyholder depends on the class he/she is assigned to. The classification of policyholders over the periods of the insurance depends on the transition rules. In general, optimization of these systems involves the calculation of an appropriate premium scale considering the number of classes and transition rules as external parameters. Usually, the stationary distribution is used in the optimization process. In this article, we present a mixed integer linear programming (MILP) formulation for determining the premium scale and the transition rules. We present two versions of the model, one with the calculation of stationary probabilities and another with the consideration of multiple periods of the insurance. Furthermore, numerical examples will also be given to demonstrate that the MILP technique is suitable for handling existing BMSs.

A computer model which selects least cost herbicide programs given a minimum desired level of weed control could provide growers with economical weed management options. Using an integer programming approach, a herbicide selection model was developed for corn production under Pennsylvania conditions. Models for three rotations (corn-soybean, corn-corn, and corn-alfalfa) under three tillage systems (conventional tillage, reduced tillage, and no-till) that evaluated 21 soil-applied and 13 postemergence herbicide options for 24 weeds were developed. Each model minimizes the cost of a herbicide program subject to a desired level of weed control. By selecting the weed species to be controlled and the level of control desired, customized herbicide programs can be generated. The models can also be used to evaluate the cost of changing the level of control desired for an individual weed species or set of weeds.

Buffelgrass (Pennisetum ciliare) is a fire-prone, African bunchgrass spreading rapidly across the southern Arizona desert. This article introduces a model that simulates buffelgrass spread over a gridded landscape over time to evaluate strategies to control this invasive species. Weed-carrying capacity, treatment costs, and damages vary across grid cells. Damage from buffelgrass depends on its density and proximity to valued resources. Damages include negative effects on native species (through spatial competition) and increased fire risk to land and buildings. We evaluate recommended “rule of thumb” control strategies in terms of their ability to prevent weed establishment in newly infested areas and to reduce damage indices over time. Two such strategies—potential damage weighting and consecutive year treatment—used in combination, provided significant improvements in long-term control over no control and over a strategy of minimizing current damages in each year. Results suggest specific recommendations for deploying rapid-response teams to prevent establishment in new areas. The long-run population size and spatial distribution of buffelgrass is sensitive to the priority given to protecting different resources. Land managers with different priorities may pursue quite different control strategies, posing a challenge for coordinating control across jurisdictions.

The problem of finding structures with minimum stabbing number has received considerableattention from researchers. Particularly, [10]study the minimum stabbing number of perfect matchings (mspm), spanning trees(msst) and triangulations (mstr) associated to set of points in theplane. The complexity of the mstr remains open whilst the other two are known tobe 𝓝𝓟-hard. This paper presents integer programming(ip) formulations for these three problems, that allowed us to solve them tooptimality through ip branch-and-bound (b&b) or branch-and-cut(b&c) algorithms. Moreover, these models are the basis for the developmentof Lagrangian heuristics. Computational tests were conducted with instances taken from theliterature where the performance of the Lagrangian heuristics were compared with that ofthe exact b&b and b&c algorithms. The results reveal that theLagrangian heuristics yield solutions with minute, and often null, duality gaps forinstances with several hundreds of points in small computation times. To our knowledge,this is the first computational study ever reported in which these three stabbing problemsare considered and where provably optimal solutions are given.

Linear programming techniques can be used in constructing schedules but theirapplication is not trivial. This in particular holds true if a trade-offhas to be made between computation time and solution quality. However,it turns out that – whenhandled with care – mixed integer linear programs may provide effectivetools. This is demonstrated in the successful approach to the benchmarkconstructed for the 2007 ROADEF computation challenge on scheduling problemsfurnished by France Telecom.

An algorithm for enumerating all nondominated vectors of multiple objectiveinteger linear programs is presented. The method tests different regionswhere candidates can be found using an auxiliary binary problem for trackingthe regions already explored. An experimental comparision with our previousefforts shows the method has relatively good time performance.

The minimum cost multiple-source unsplittable flow problem isstudied in this paper. A simple necessary condition to get asolution is proposed. It deals with capacities and demands and canbe seen as a generalization of the well-known semi-metriccondition for continuous multicommdity flows. A cutting planealgorithm is derived using a superadditive approach. Theinequalities considered here are valid for single knapsackconstraints. They are based on nondecreasing superadditivefunctions and can be used to strengthen the relaxation of anyinteger program with knapsack constraints. Some numericalexperiments confirm the efficiency of the inequalities introducedin the paper.

Public inoculation centers are examples of facilities providing service to customers whose demand is elastic to travel and waiting time. That is, people will not travel too far, or stay in line for too long to obtain the service. The goal, when planning such services, is to maximize the demand they attract, by locating centers and staffing them so as to reduce customers' travel time and time spent in queue. In the case of inoculation centers, the goal is to maximize the people that travel to the centers and stay in line until inoculated. We propose a procedure for the allocation of multiple servers to centers, so that this goal is achieved. An integer programming model is formulated. Since demand is elastic, a supply-demand equilibrium equation must be explicitly included in the optimization model, which then becomes nonlinear. As there are no exact procedures to solve such problems, we propose a heuristic procedure, based on Heuristic Concentration, which finds a good solution to this problem. Numerical examples are presented.

This paper describes the process planning techniques we developed for use in an Integrated Product and Process Design (IPPD) tool for the design and manufacture of microwave transmit/receive modules. Given a collection of data about the design of a microwave module, the IPPD tool uses a combination of AI planning and OR trade-off analysis to produce a collection of alternative designs and alternative process plans that have Pareto optimal values for manufacturing and purchasing lead time, process yield, cost, and number of suppliers. The IPPD tool provides facilities to enable the user to generate and examine these Pareto optimal alternatives in real time, in order to provide immediate feedback on how to modify the design to improve its cost and productivity.

Fractional programming consists in optimizing a ratio oftwo functions subject to some constraints. Different versions of thismodel, linear or nonlinear, have applications in various fields likecombinatorial optimization, stochastic programming, data bases, andeconomy. Three resolution methods are presented: direct solution,parametric approach and solution of an equivalent problem.

We examine connections between A-hypergeometric differential equations and the theory of integer programming. In the first part, we develop a ’hypergeometric sensitivity analysis‘ for small variations of constraint constants with creation operators and b-functions. In the second part, we study the indicial polynomial (b-function) along the hyperplane xi=0 via a correspondence between the optimal value of an integer programming problem and the roots of the indicial polynomial. Gröbner bases are used to prove theorems and give counter examples.

This paper shows how majorization and Schur-convex functions can be used to solve the problem of optimal allocation of components to parallel-series and series-parallel systems to maximize the reliability of the system. For parallel-series systems the optimal allocation is completely described and depends only on the ordering of component reliabilities. For series-parallel systems, we describe a partial ordering among allocations that can lead to the optimal allocation. Finally, we describe how these problems can be cast as integer linear programming problems and thus the results obtained in this paper show that when some linear integer programming problems are recast in a different way and the techniques of Schur functions are used, complete solutions can be obtained in some instances and better insight in others.