In this paper we develop a general approach to generate all efficient solutions of the Multi-Objective Integer Programming (MOIP) Problem. Our approach, which is based on identification of objective efficiency ranges, is an improvement over classical ε-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical ε-constraint method on the Bi-Objective Integer Programming problem for the sake of completeness and comment on its efficiency. Then present our method on Tri-Objective Integer Programming problem and then extend it to the general MOIP problem with k objectives. A numerical example considering Tri-Objective Assignment problem is also provided.

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of Özlen and Azizoğlu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.

The Asset Protection problem is encountered where an uncontrollable fire is sweeping across a landscape comprising important infrastructure assets. Protective activities by teams of firefighters can reduce the risk of losing a particular asset. These activities must be performed during a time-window for each asset determined by the progression of the fire. The nature of some assets is such that they require the simultaneous presence of more than one fire vehicle and its capabilities must meet the requirements of each asset visited. The objective is then to maximise the value of the assets protected subject to constraints on the number and type of fire trucks available. The solution times to this problem using commercial solvers preclude their use for operational purposes. In this work we develop an adaptive large neighbourhood search algorithm (ALNS) based on problem-specific attributes. Several removal and insertion heuristics, including some new algorithms, are applied. A new benchmark set is generated by considering the problem attributes. In tests with small instances the ALNS is shown to achieve optimal, or near optimal, results in a fraction of the time required by CPLEX. In a second set of experiments comprising larger instances the ALNS was able to produce solutions in times suitable for operational purposes. These solutions mean that significantly more assets can be protected than would be the case otherwise.

Incident management teams (IMTs) are responsible for managing the response to wildfires. One of the objectives of IMTs is the protection of assets and infrastructure. In this paper, we develop a mathematical model to assist IMTs in assigning resources to asset protection activities during wildfires. We present a mixed integer programming model for resource allocation with the aim of protecting the maximum possible total value of assets. The model allows for mixed vehicle types with interchangeable capabilities and with travel times determined by vehicle-specific speed and road network information. We define location-specific protection requirements in terms of vehicle capabilities. The formulated model extends classic variants of the team orienteering problem with time windows. The model capabilities are demonstrated using a hypothetical fire scenario impacting South Hobart, Tasmania, Australia. Computational testing shows that realistically sized problems can be solved within a reasonable time.

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