Allocation of tasks to specialized processors: A planning approach

This paper addresses the problem of scheduling randomly arriving tasks of different types at a diversified service system. Servers at such a system differ in that each may specialize in one task type, but can also perform others perhaps less rapidly and adequately than does a specialist. We consider the issue of how much redirection of tasks from specialists to non-specialists may be desirable in such a system and propose a static model in which tasks are randomly assigned to servers. Two scheduling strategies for individual servers are also considered: one in which each server performs the tasks assigned to him or her in order of their arrival and the second in which each server schedules his or her workload optimally. The problems for finding the best random assignment probabilities are formulated as mathematical programs. Results from a numerical example provide information that is both informative and useful in decision-making

Second best toll and capacity optimisation in network: solution algorithm and policy implications

This paper looks at the first and second-best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second-best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second-best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader’s decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal.We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity

A multi-model deployment planning problem. Final report

This report considers a multi-modal deployment planning problem in which movement requirements are allowed to originate from (supply) centers, ground transported to (sea or air) ports of embarkation, and, upon arrival at (sea or air) ports of debarkation, ground transported again to (demand) centers or destinations. This sequence of movements involves all three modes of transportation: air, land, and sea. The authors formulate this deployment problem as an integer program which has a columnar structure and allows for many different objectives. The complexity of this program along with optimality properties for its solutions are discussed. A heuristic solution procedure is also proposed

Allocation of tasks to specialised processors: a planning approach

This paper addresses the problem of scheduling randomly arriving tasks of different types at a diversified service system. Servers at such a system di€er in that each may specialize in one task type, but can also perform others perhaps less rapidly and adequately than does a specialist. We consider the issue of how much redirection of tasks from specialists to non-specialists may be desirable in such a system and propose a static model in which tasks are randomly assigned to servers. Two scheduling strategies for individual servers are also considered: one in which each server performs the tasks assigned to him or her in order of their arrival and the second in which each server schedules his or her workload optimally. The problems for finding the best random assignment probabilities are formulated as mathematical programs. Results from a numerical example provide information that is both informative and useful i