Stabilizing employment in a fluctuating resource economy

We consider a resource management problem in which the management objective is to minimize fluctuations in resource economics. Stabilizing management policies consist of memoryless state feedback control strategies for a class of discrete-time resource models which contain unknown but bounded fluctuations. The underlying theory is based on conditions developed for Lyapunov-type stability of sets. The design of the stabilizing policies is illustrated by a simulation example from resource economics. Specifically, employment of fishermen is stabilized by using a subsidizing and taxing policy in an open-access common-property fishery in which the value of the resource and the resource level fluctuate, and where entry and exit dynamics are determined by fluctuating revenues obtained from the fishery.This work was supported by NSF and AFOSR under Grant No. ECS-86-02524.The support by the Yrjö Jahnsson Foundation is greatly acknowledged.     

A MIXED CONTROL PROBLEM OF THE MANAGEMENT OF NATURAL RESOURCES

In this paper, we study the optimal solutions of a model of natural resource management which allows for both impulse and continuous harvesting policies. This type of model is known in the literature as mixed optimal control problem. In the resource management context, each type of control represents a different harvesting technology, which has a different cost. In particular, we want to know when the following conjecture made by Clark is an optimal solution to this mixed optimal control problem: if the harvesting capacity is unlimited, it is optimal to jump immediately to the steady state of the continuous time problem and then to stay there. We show that under a particular relationship between the continuous and the impulse profit function, the conjecture made by Clark is true. In other cases, however, it is either better to use only continuous control variables or to jump to resource levels which are smaller than the steady state and then let the resource grow back to the steady state. These results emphasize the importance of the cost functions in the modeling of natural resource management.     

Multi-stage stochastic programming models for provisioning cloud computing resources

We focus on the resource provisioning problem of a cloud consumer from an Infrastructure-as-a-Service type of cloud. The cloud provider offers two deployment options, which can be mixed and matched as appropriate. Cloud instances may be reserved for a fixed time period in advance at a smaller usage cost per hour but require a full commitment and payment for the entire contract duration. In contrast, on-demand instances reflect a pay-as-you-go policy at a premium. The trade-off between these two options is rooted in the inherent uncertainty in demand and price and makes it attractive to complement a base reserved capacity with on-demand capacity to hedge against the spikes in demand. This paper provides several novel multi-stage stochastic programming formulations to enable a cloud consumer to handle the cloud resource provisioning problem at a tactical level. We first formulate the cloud resource provisioning problem as a risk-neutral multi-stage stochastic program, which serves as the base model for further modeling variants. In our second set of models, we also incorporate a certain concept of system reliability. In particular, chance constraints integrated into the base formulation require a minimum service level met from reserved capacity, provide more visibility into the future available capacity, and smooth out expensive on-demand usage by hedging against possible demand fluctuations. An extensive computational study demonstrates the value of the proposed models by discussing computational performance, gleaning practical managerial insights from the analysis of the solutions of the proposed models, and quantifying the value of the stochastic solutions.     

Pricing surplus server capacity for mean waiting time sensitive customers

We consider a queueing model wherein the resource is shared by two different classes of customers, primary (existing) and secondary (new), under a service level based pricing contract. This contract between secondary class customers and resource manager specifies unit admission price and quality of service (QoS) offered. We assume that the secondary customers’ Poisson arrival rate depends linearly on unit price and service level offered while the server uses a delay dependent priority queue management scheme. We analyze the joint problem of optimal pricing and operation of the resource with the inclusion of secondary class customers, while continuing to offer a pre-specified QoS to primary class customers. Our analysis leads to an algorithm that finds, in closed form expressions, the optimal points of the resulting non-convex constrained optimization problem. We also study in detail the structure and the non-linear nature of these optimal pricing and operating decisions.     

Resource Allocation with Wobbly Functions

We consider resource allocation with separable objective functions defined over subranges of the integers. While it is well known that (the maximisation version of) this problem can be solved efficiently if the objective functions are concave, the general problem of resource allocation with functions that are not necessarily concave is difficult.In this article, we focus on a large class of problem instances, with objective functions that are close to a concave function or some other smooth function, but with small irregularities in their shape. It is described that these properties are important in many practical situations.The irregularities make it hard or impossible to use known, efficient resource allocation techniques. We show that, for this class of functions the optimal solution can be computed efficiently. We support our claims by experimental evidence. Our experiments show that our algorithm in hard and practically relevant cases runs up to 40–60 times faster than the standard method.     

A successive convex approximation method for multistage workforce capacity planning problem with turnover

Workforce capacity planning in human resource management is a critical and essential component of the services supply chain management. In this paper, we consider the planning problem of transferring, hiring, or firing employees among different departments or branches of an organization under an environment of uncertain workforce demands and turnover, with the objective of minimizing the expected cost over a finite planning horizon. We model the problem as a multistage stochastic program and propose a successive convex approximation method which solves the problem in stages and iteratively. An advantage of the method is that it can handle problems of large size where normally solving the problems by equivalent deterministic linear programs is considered to be computationally infeasible. Numerical experiments indicate that solutions obtained by the proposed method have expected costs near optimal.     

Resource capacity allocation to stochastic dynamic competitors: knapsack problem for perishable items and index-knapsack heuristic

In this paper we propose an approach for solving problems of optimal resource capacity allocation to a collection of stochastic dynamic competitors. In particular, we introduce the knapsack problem for perishable items, which concerns the optimal dynamic allocation of a limited knapsack to a collection of perishable or non-perishable items. We formulate the problem in the framework of Markov decision processes, we relax and decompose it, and we design a novel index-knapsack heuristic which generalizes the index rule and it is optimal in some specific instances. Such a heuristic bridges the gap between static/deterministic optimization and dynamic/stochastic optimization by stressing the connection between the classic knapsack problem and dynamic resource allocation. The performance of the proposed heuristic is evaluated in a systematic computational study, showing an exceptional near-optimality and a significant superiority over the index rule and over the benchmark earlier-deadline-first policy. Finally we extend our results to several related revenue management problems.     

A single-resource revenue management problem with random resource consumptions

We study a single-resource multi-class revenue management problem where the resource consumption for each class is random and only revealed at departure. The model is motivated by cargo revenue management problems in the airline and other shipping industries. We study how random resource consumption distribution affects the optimal expected profit and identify a preference acceptance order on classes. For a special case where the resource consumption for each class follows the same distribution, we fully characterize the optimal control policy. We then propose two easily computable heuristics: (i) a class-independent heuristic through parameter scaling, and (ii) a decomposition heuristic that decomposes the dynamic programming formulation into a collection of one-dimensional problems. We conduct extensive numerical experiments to investigate the performance of the two heuristics and compared them with several widely studied heuristic policies. Our results show that both heuristics work very well, with class-independent heuristic slightly better between the two. In particular, they consistently outperform heuristics that ignore demand and/or resource consumption uncertainty. Our results demonstrate the importance of considering random resource consumption as another problem dimension in revenue management applications.     

Dynamic resource allocation in a multi-product make-to-stock production system

We consider optimal policies for a production facility in which several (K) products are made to stock in order to satisfy exogenous demand for each. The single machine version of this problem in which the facility manufactures at most one product at a time to minimise inventory costs has been much studied. We achieve a major generalisation by formulating the production problem as one involving dynamic allocation of a key resource which drives the manufacture of all products under an assumption that each additional unit of resource allocated to a product achieves a diminishing return of increased production rate. A Lagrangian relaxation of the production problem induces a decomposition into K single product problems in which the production rate may be varied but is subject to charge. These reduced problems are of interest in their own right. Under mild conditions of full indexability the Lagrangian relaxation is solved by a production policy with simple index-like structure. This in turn suggests a natural index heuristic for the original production problem which performs strongly in a numerical study. The paper discusses the importance of full indexability and makes proposals for the construction of production policies involving resource idling when it fails.     

New computational results on the discrete time/cost trade-off problem in project networks

We describe a new exact procedure for the discrete time/cost trade-off problem in deterministic activity-on-the-arc networks of the CPM type, where the duration of each activity is a discrete, nonincreasing function of the amount of a single resource (money) committed to it. The objective is to construct the complete and efficient time/cost profile over the set of feasible project durations. The procedure uses a horizon-varying approach based on the iterative optimal solution of the problem of minimising the sum of the resource use over all activities subject to the activity precedence constraints and a project deadline. This optimal solution is derived using a branch-and-bound procedure which computes lower bounds by making convex piecewise linear underestimations of the discrete time/cost trade-off curves of the activities to be used as input for an adapted version of the Fulkerson labelling algorithm for the linear time/cost trade-off problem. Branching involves the selection of an activity in order to partition its set of execution modes into two subsets which are used to derive improved convex piecewise linear underestimations. The procedure has been programmed in Visual C ++ under Windows NT and has been validated using a factorial experiment on a large set of randomly generated problem instances.     

基于收益管理和仿真的第三方仓储资源分配

针对不确定市场需求条件下第三方仓储资源的能力规划与分配问题,构建随机数学规划模型,理论分析证明了最优资源分配量的存在性,并指出最优资源分配量是单位资源成本的递减函数、单位资源收益和单位损失成本的递增函数。鉴于解析求解的复杂性,基于收益管理思想,结合离散事件仿真技术和响应曲面法,提出一种新的分析求解框架:收益管理用于细分顾客、构建资源分配策略,仿真模型刻画系统随机特性并评估系统绩效指标,响应曲面法则优化分配策略并探寻绩效改进方向。案例研究和仿真实验结果显示,根据顾客类别分配仓储能力的策略优于传统的先到先服务策略,收益管理、响应曲面法与仿真的综合集成,能够提高系统收益,从而使本文所提方法体系得到了有效验证。     

Designing Conferences to Improve Resource Utilization and Participant Satisfaction

We look at a conference scheduling problem with the objective of maximizing the ability of participants to attend sessions of interest. This problem was addressed in an article by Eglese and Rand; conference scheduling has otherwise received little attention in management science literature. Related problems of class- and exam-scheduling have been extensively studied and published, yet few cases consider participant (e.g. student) preferences. Our formulation, which a variation of that used by Eglese and Rand, includes prioritized preferences for conference sessions, as well as schedule resource constraints. The purpose of this paper is to extend the previous work by exploring the impact of various scheduling decisions on participant satisfaction (measured by enrollment in desired sessions). We use a previously published algorithm to look at issues such as conference length and make general observations that may aid the conference-scheduling decision maker.     

Analysis of dynamical model for resource-based industry sustainable development

This paper aims at the sustainable development of resource-based industry. First, one-dimensional discrete dynamic model is formulated by considering exploitation and protection of renewable resource simultaneously, and then it is extended to two-dimensional dynamic model by assuming that government carries on the dynamic management to the exploitation speed of resource. The conditions of the existence and local stability of positive equilibrium are derived. The threshold of output is given which ensures the resource is stabilized at a fixed value. The global analysis of both models is represented by determining the feasible domain of attractor. The stability of positive fixed point at flip bifurcation and Neimark-Sacker bifurcation is respectively investigated with center manifold theorem and normal form. We also verify the given conclusions by the method of numerical analysis. In the end, we argued that if the government implements the dynamic quota management for resource exploitation, not only can we maintain a certain stock of resources so that people can get more resources permanently but also we can ensure a higher and wider output to meet the development of the industry.     

Influence of model management systems on decision making: empirical evidence and implications

Model management (MM) regards decision models as an important organisational resource deserving prudent management. Despite the remarkable volume of model management literature compiled over the past twenty-odd years, very little is known about how decision makers actually benefit from employing model management systems (MMS). In this paper, we report findings from an experiment designed to verify the idea that the adequacy of modeling support provided by a MMS influences the decision maker's problem solving performance and behaviour. We show that the decision makers who receive adequate modelling support from MMS outperform those without such support. Also, we provide empirical evidence that the MMS help turn the decision makers' perception of problem solving from a number crunching task into development of solution strategies, consequently changing their decision making behaviour.     

The resource constrained project scheduling problem with multiple crashable modes: A heuristic procedure

We present a heuristic procedure for a nonpreemptive resource constrained project scheduling problem in which the duration/cost of an activity is determined by the mode selection and the duration reduction (crashing) applied within the selected mode. This problem is a natural combination of the time/cost trade-off problem and the resource constrained project scheduling problem. The objective is to determine each activity's start (finish) time, mode and duration so that the total project cost is minimized. Total project cost is the sum of all activity costs and the penalty cost for completing the project beyond its due date. We introduce a multi-pass algorithm. We report computational results with a set of 100 test problems and demonstrate the efficacy of the proposed heuristic procedure.     

Complexity analysis of an assignment problem with controllable assignment costs and its applications in scheduling

We extend the classical linear assignment problem to the case where the cost of assigning agent j to task i is a multiplication of task i’s cost parameter by a cost function of agent j. The cost function of agent j is a linear function of the amount of resource allocated to the agent. A solution for our assignment problem is defined by the assignment of agents to tasks and by a resource allocation to each agent. The quality of a solution is measured by two criteria. The first criterion is the total assignment cost and the second is the total weighted resource consumption. We address these criteria via four different problem variations. We prove that our assignment problem is NP-hard for three of the four variations, even if all the resource consumption weights are equal. However, and somewhat surprisingly, we find that the fourth variation is solvable in polynomial time. In addition, we find that our assignment problem is equivalent to a large set of important scheduling problems whose complexity has been an open question until now, for three of the four variations.     

Fair resource allocation for different scenarios of demands

This paper considers a resource allocation problem, which objective is to treat fairly all the system users. Usually the requests cannot be entirely predicted, but the manager can forecast the request evolution, this leading to a set of possible scenarios. Such a problem arises for instance in network bandwidth allocation as well as in storage space management. It also appears in the management of computer systems, such as computational grids or in cloud computing, when teams share a common pool of machines. Problems of fair resource sharing arise among users with equal access right but with different needs.Here the problem is tackled by a multi-criteria model, where one criterion is associated to one scenario. A solution is a policy, which provides an allocation for each scenario. An algorithm is proposed and analysed that lists all solutions which are Pareto optimal with regard to the different possible user request scenarios. The algorithm is used offline, but can be adapted, with some additional hypothesis, to be used online.     

Allocation of advertising budget between multiple channels to support sales in multiple markets

We consider the allocation of a limited marketing budget between multiple channels in order to promote sales at multiple markets. The channels differ in their type, level of targetability (or reach), and costliness. We incorporate the “threshold effect” from each market in our resource allocation which requires some positive advertising investment in each market before much sales impact can be observed from it. The increased number of channels in recent years with the advent of digital advertising, along with the added complexity created by the threshold effect, necessitates the development of new allocation approaches. In this paper, we formulate the firm’s resource allocation decision as a nonlinear and nonseparable knapsack problem. We develop a branch and cut solution method which is enhanced by a heuristic approach. A set of numerical experiments illustrate the performance of our methods and evaluate the usefulness of two rule-of-thumb strategies commonly used in practice.     

Efficient Coordination by Optimal Allocation of Decision Rights for Participants on Electronic Financial Services Markets

Information technology (IT) is enabling large companies and particularly banking firms to create new forms of organizations. Both globalization of markets and stronger regulation throughout the world puts pressure on banking firms to either spend more money coordinating business activities in the traditional hierarchical ways or to employ new forms of organizations enabled by (lower costs of) IT. When facing uncertain demand in multiple horizontal markets, resource allocation problems occur. Accordingly, the location of decision authority in a multilevel hierarchical organization has profound impact on the performance of the firm. The firm has to design its coordination structure, which determines who makes the resource allocation decisions. Considering the tradeoff between pooling effects in the case of centralized decision-making and better assessment of local markets in the case of decentralized decision-making, the decision problem where to locate decision rights to maximize total profits has to be solved. In this paper we investigate for both independent and dependent demands the total profits for each of the possible coordination mechanisms: centralized decision-making, decentralized decision-making, and intermediate-level decision-making. It turns out that—depending on the crucial parameters of the firm—decentralized decision-making or centralized decision-making may be optimal. But in many relevant cases the optimal location of decision rights is at an intermediate level of the hierarchy. We illustrate the findings by considering the banking firm coordinating equity capital allocation by granting alternative decision rights to their employees as participants on electronic financial markets. Finally we discuss the generality of the approach and its applicability in other areas such as inventory management.     

OPTIMAL RECOVERY OF A SHARED RESOURCE STOCK: A DIFFERENTIAL GAME MODEL WITH EFFICIENT MEMORY EQUILIBRIA

We consider an optimal two-country management of depleted transboundary renewable resources. The management problem is modelled as a differential game, in which memory strategies are used. The countries negotiate an agreement among Pareto efficient harvesting programs. They monitor the evolution of the agreement, and they memorize deviations from the agreement in the past. If the agreement is observed by the countries, they continue cooperation. If one of the countries breaches the contract, then both countries continue in a noncooperative management mode for the rest of the game. This noncooperative option is called a threat policy. The credibility of the threats is guaranteed by their equilibrium property. Transfer or side payments are studied as a particular cooperative management program. Transfer payments allow one country to buy out the other from the fishery for the purpose of eliminating the inefficiency caused by the joint access to the resources. It is shown that efficient equilibria can be reached in a class of resource management games, which allow the use of memory strategies. In particular, continuous time transfer payments (e.g., a share of the harvest) should be used instead of a once-and-for-all transfer payment.