A network solution to a general vehicle scheduling problem

Dantzig and Fulkerson and later Bellmore et al. have shown that certain vehicle (tanker) scheduling problems can be formulated as minimum cost flow problems on a network. In this paper, the results of Dantzig and Fulkerson are extended to the case where more than one type of vehicle can be used in the determination of an optimal fleet. (In tanker scheduling terminology; how many small, medium and large tankers would form an optical fleet.) It is seen how the problem can be formulated as a modified transportation problem where flow in some arcs is conditioned to there being flow on certain other arcs. These “conditional” transportation problems were solved directly as linear programs and showed the peculiarity of terminating all integer in spite of having a constraint matrix, which does not satisfy the well known sufficient conditions for urimodularity. We discuss the implementation of the model and its empirical results.     

Prior analysis and scheduling of the 2011 Rugby Union ITM Cup in New Zealand

This paper describes work done for the New Zealand Rugby Union (NZRU) in preparation for their most important wholly domestic competition in 2011. This competition had to be played during a shorter timescale than usual because of the 2011 Rugby Union World Cup, and the NZRU were keen to ensure that they could incorporate the format they wanted into this timescale without unfortunate consequences. In addition, they wanted to introduce a novel feature into this tournament. Thus some detailed prior experimental, or ‘what-if’, analysis was necessary. This paper describes this analysis and its results. As a result of this analysis, the NZRU was persuaded to abandon one of its design ideas, but was able to proceed with others, enabling them to announce the detailed format of the competition in the confidence that it would work well in practice. Subsequent scheduling of the competition in this format proved successful, and the resulting schedule is shown together with detailed analysis of its notional costs. The paper demonstrates how important it can be for schedulers to be closely involved in tournament design in advance of the actual scheduling.     

Petrol delivery tanker assignment and routing: a case study in Hong Kong

In this paper, we present a case study on a tanker assignment and routing problem for petrol products in Hong Kong. A fleet of heterogeneous dangerous goods vehicles has been assigned to deliver several types of petroleum products to petrol stations with different tank capacities. Under the vendor-managed inventory system, the delivery company is responsible for controlling the station's inventory and replenishment. The operational characteristics and challenges such as geographic zoning, size of petrol stations, routing restrictions and so on are unique and have been described in this paper. A decision support system (DSS) combining heuristic clustering and optimal routing is employed to find the optimal fleet assignment and routing. Multiple objectives are considered simultaneously such that the number of tankers used could be minimized, the number of drops in trips is minimized, profit in terms of total products delivered is maximized and utilization of resources is maximized. The case illustrates the benefit and advantages of using the proposed DSS.     

Maritime crude oil transportation - A split pickup and split delivery problem

The maritime oil tanker routing and scheduling problem is known to the literature since before 1950. In the presented problem, oil tankers transport crude oil from supply points to demand locations around the globe. The objective is to find ship routes, load sizes, as well as port arrival and departure times, in a way that minimizes transportation costs. We introduce a path flow model where paths are ship routes. Continuous variables distribute the cargo between the different routes. Multiple products are transported by a heterogeneous fleet of tankers. Pickup and delivery requirements are not paired to cargos beforehand and arbitrary split of amounts is allowed. Small realistic test instances can be solved with route pre-generation for this model. The results indicate possible simplifications and stimulate further research.     

IMGD: an interactive method for multiobjective group decision aid

Multiobjective methods for group decision situations that are proposed in the literature do not generally model power and influence. On the other hand, papers dealing with influence and power in group decision support system (GDSS) are looking for the effects of GDSS on the distribution of power among the group members. This paper proposes an interactive method for group decision aid in multiobjective context integrating the concept of power and influence within the multiperson–multicriteria aspect. The method is designed to be used by a committee to solve a multiple criteria allocation problem. The method is tested on a resource allocation problem in the Municipality of Tunis.     

Modelling a multi-objective allocation problem in a government sponsored entrepreneur development programme

Typically the vendor allocation problem for a commercial company requires the buyer to allocate business between the selected vendor suppliers to meet its needs at minimum cost, taking account of its quality and delivery performance requirements. However in a government sponsored entrepreneur development programme, the allocation of business cannot only be made dependent on criteria that reflect the current ability of the vendor nor solely on criteria fulfilling the current needs of the buyer. It must also consider how it may aid the vendors to improve their business performance in the future and also on how it affects the development of that indigenous industry sector. Furthermore, conditions change from one year to the next so the problem is dynamic over time.This paper describes how a combination of Goal Programming model (GP) with pre-emptive priority ranking of goal constraints with a linear programming model facilitates allocation of businesses to entrepreneurs. In particular, the subject used in this paper is a Malaysia Government sponsored entrepreneur development programme for furniture maker, which administered by a commercial company. An innovative aspect of the work is the use of GP as a modelling rather than a solution technique. It is used to convert the conflicting multi-objectives that were expressed only in general policy terms to operational terms on which business could be allocated. The paper shows how it can be used to try to understand, and then formally model how managers use their judgement and experience in a complex multi-criteria situation. The paper goes on to show that using the formal model leads to more consistency in decision-making and an improvement in the achievement of the objectives. This is important as several different managers are having to make independent decisions on subsets of the vendors.     

Probabilistic simulation of offshore collisions

Collisions between tankers and offshore structures may result in serious problems such as oil pollution. It is therefore of interest to estimate the probability of a collision. This is done here by means of a simulation model using the GASP IV simulation program. The new method is based on a statistical prediction of the ship's path after some kind of critical failure affecting the manoeuvrability of the tanker has taken place.     

A methodology for sensitivity analysis in three-criteria problems: A case study in municipal management

This paper describes part of an on-going research project studying the issues of the application of Multicriteria Decision Aid Methodologies in real case-studies at the local level of the Portuguese Public Administration.In a first part, it address the complexity of decision situations in municipal management in general and the significance of decision analysis, namely multicriteria evaluation procedures, in conducting decision aid processes in that environment (Section 1).In a second part, a case study is described (Section 2), followed by its discussion in the ‘space of the weights’ in the context of different particular types of possible problem formulations (Section 3). For this purpose, an extension of Triangular Decision Technique is first proposed, followed by the presentation of a new Outranking approach, designated by ‘Outweigh’ analysis, which will permit the enrichment of the discussion.     

An interactive,computer-aided ship scheduling system

This paper is concerned with a fleet scheduling and inventory resupply problem faced by an international chemical operation. The firm uses a fleet of small ocean-going tankers to deliver bulk fluid to warehouses all over the world. The scheduling problem centers around decisions on routes, arrival/departure times, and inventory replenishment quantities. An interactive computer system was developed and implemented at the firm, and was successfully used to address daily scheduling issues as well as longer range planning problems. The purpose of this paper is to first present how the underlying decision problem was analyzed using both a network flow model and a mixed integer programming model, and then to describe the components of the decision support system developed to generate schedules. The use of the system in various decision making applications is also described.     

Optimal Loading of Tankers

This paper describes a method for maximising payloads carried by a fleet of road tankers. The tankers carry a range of products in multicompartment tanks. A case study demonstrates the method's potential to increase payload and remove the risk of overload penalties.     

An oil outflow model for tanker collisions and groundings

In this paper we have developed an oil outflow model for collision and grounding accidents of tankers. The collision model explicitly links input variables such as tanker hull design (single or double), displacement and speed, striking vessel displacement and speed, and the interaction angle of both vessels to output variables: longitudinal and transversal damage extents of the tanker. Overlaying these damage extents on the tank vessel’s design yields an oil outflow volume totaling the capacity of the damaged tank compartments. A similar model is developed for grounding accidents. A total of 80,000 simulation accident scenarios described in the National Research Council SR259 report published in 2001 served as the joint data set of input and output variables used in this “linking” process. The oil outflow model herein was designed keeping computational efficiency in mind to allow for its integration with a maritime transportation system (MTS) simulation. We shall demonstrate the use of the oil outflow model as a final analysis layer to evaluate double-hull effectiveness in a geographic context of an MTS simulation model developed for the oil transportation routes traversing the environmentally sensitive San Juan Islands area in Washington State.     

Cascading Knapsack Inequalities: reformulation of a crude oil distribution problem

In this paper we consider the problem in which crude oil is shipped from platforms to terminals using oil tankers at minimum transportation cost. This subproblem, which arises in petroleum supply chain models, can be surprisingly expensive to solve with a straightforward formulation involving inventory balances. We present a reformulation that has a special structure defined in this paper as Cascading Knapsack Inequalities. This is used as the basis for deriving tight reformulations for special cases with a limited number of classes of tankers. Numerical results are presented to demonstrate that significant computational savings can be accomplished with the proposed reformulations.     

Energy-aware workload management models for operation cost reduction in data centers

In the last century, the costs of powering datacenters have increased so quickly, that datacenter power bills now dwarf the IT hardware bills. Many large infrastructure programs have been developed in the past few years to reduce the energy consumption of datacenters, especially with respect to cooling requirements. Although these methods are effective in lowering the operation costs they do require large upfront investments. It is therefore not surprising that some datacenters have been unable to utilize the above means and as a result are still struggling with high energy bills. In this work we present a cheap addition to or an alternative to such investments as we propose the use of intelligent, energy efficient, system allocation mechanisms in place of current packaged system schedulers available in modern hardware infrastructure cutting server power costs by 40%. We pursue both the quest for (1) understanding the energy costs generated in operation as well has how to utilize this information to (2) allocate computing tasks efficiently in a cost minimizing optimization approach. We were able to underline the energy savings potential of our models compared to current state-of-the-art schedulers. However, since this allocation problem is complex (NP-hard) we investigated various model approximations in a trade-off between computational complexity and allocative efficiency. As a part of this investigation, we evaluate how changes in system configurations impact the goodness of our results in a full factorial parametric evaluation.     

Analysing consumer segments to budget for loyalty and promotion programmes and maximize market share

This paper seeks to provide a framework and benchmark for the allocation of marketing budget between promotion and loyalty programmes using an approach that combines a Markov-type market share model and the Lagrange multiplier method to maximize market share. The Lagrange multiplier method, that takes into account the market share and the loyalty effect observable in preceding periods along with the estimated promotional effects, permits the allocation to be optimized and future market share to be maximized. Then, loyalty-based consumer segment are used to explain why the budgeting exercise can achieve the maximization objective. To this end, the study uses consumer panel data concerning three categories, namely, adult milk powder, shampoo, and detergent. It extends previous research on loyalty-based segmentation by focusing on the budget allocation between the two options of loyalty enhancement and promotion programming. A Budget Allocation Grid for Loyalty-based Segmentation is proposed as an aid to understand budget allocation between loyalty and promotion programmes based on the relative sizes of exclusive-loyalty and variety-seeking segments.     

Hierarchical multi-objective decision systems for general resource allocation problems

We consider optimization methods for hierarchical power-decentralized systems composed of a coordinating central system and plural semi-autonomous local systems in the lower level, each of which possesses a decision making unit. Such a decentralized system where both central and local systems possess their own objective function and decision variables is a multi-objective system. The central system allocates resources so as to optimize its own objective, while the local systems optimize their own objectives using the given resources. The lower level composes a multi-objective programming problem, where local decision makers minimize a vector objective function in cooperation. Thus, the lower level generates a set of noninferior solutions, parametric with respect to the given resources. The central decision maker, then, parametric with respect to the given resources. The central decision maker, then, chooses an optimal resource allocation and the best corresponding noninferior solution from among a set of resource-parametric noninferior solutions. A computational method is obtained based on parametric nonlinear mathematical programming using directional derivatives. This paper is concerned with a combined theory for the multi-objective decision problem and the general resource allocation problem.The authors are indebted to Professor G. Leitmann for his valuable comments and suggestions.     

Prioritisation of an IT budget within a local authority

This paper describes the prioritisation of an IT budget within a department of a local authority. The decision problem is cast as a simple multiattribute evaluation but from two perspectives. First, as an exercise in group decision making. Here the emphasis is on a shared process wherein the object is to obtain consensus. The use of an explicit evaluation framework and the ability to interact with the evaluation data in real time via a simple spreadsheet model were found to improve the decision making. Second, the prioritisation is made analytically. The motivation is to determine the degree to which the rankings are the result of the structural characteristics of the projects themselves rather than of the differences in importance attached to the achievement of the goals represented by the project attributes. Three methods are used: Monte Carlo simulation of ranks, cluster analysis based on attributes and an approach based on entropy maximisation. It is found that in the case studied the structure inherent in the data is high and so the results of the analyses are robust. Finally, a procedure is suggested for the appropriate use of these analyses via a facilitator to aid prioritisation decisions.     

Operations research games: A survey

This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved. Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players. This interplay between optimisation and allocation is the main subject of the area of operations research games. It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.     

考虑外部效应与风险因素的多项目优化模型及应用

多项目的组合优化与资源分配优化,实质上是经济学中资源配置与利用问题.运用经济学与管理学的相关理论和定量研究方法,建立了外部效应估算模型、项目评价模型、风险估算模型、多项目组合优化模型和关于资源分配优化的两层决策模型.相关模型的应用实例研究,说明了该模型的有效性.     

Allocating the fixed cost as a complement of other cost inputs: A DEA approach

In cost allocation problem, traditional DEA approaches allocate the fixed cost among a group of decision making units (DMUs), and treat the allocated cost as an extra input of each DMU. If costs except for the fixed cost are regarded as inputs in the cost allocation problem, then it is obvious that the fixed cost is a complement of other inputs rather than an extra independent input. Therefore it is necessary to combine the allocated cost with other cost measures in cost allocation problem. Based on this observation, this paper investigates the relationship between the allocated cost and the DEA efficiency score and develops a DEA-based approach to allocate the fixed cost among various DMUs. An example of allocating advertising expenditure between a car manufacturer and its dealers is presented to illustrate the method proposed in this paper.