Linking stakeholder visions with resource allocation scenarios and multi-criteria assessment

Stakeholders and decision makers often develop visions of the ideal-type future as a response to complex societal problems and design their actions accordingly. However, these actors sometimes have a limited understanding as to whether their visions are feasible, what action is required and what the potential consequences are. This paper presents a methodology for linking visions with quantitative resource allocation scenarios which show different options in implementing the visions. The consequences are then appraised by multi-criteria assessment in order to find optimal and acceptable ways of implementation. As a result, stakeholders and decision makers learn about their visions and may even rethink them before decision making. The methodology thus couples visionary ideas with analytical information, providing a novel approach using quantitative techniques in a soft framework. The methodology is illustrated via a real-world case study concerning the future energy system in a small Swiss community.     

Stochastic programming based capacity planning for semiconductor wafer fab with uncertain demand and capacity

Capacity planning is a challenging problem in semiconductor manufacturing industry due to high uncertainties both in market and manufacturing systems, short product life cycle, and expensive capital invest. To tackle this problem, this paper proposes a scenario-based stochastic programming model which considers demand and capacity uncertainties via scenarios, where the overall equipment efficiency is employed to describe the uncertain capacity for the first time. Based on the decentralized structure of tool procurement, production, stockout, and inventory decision-making processes, recourse approximation strategies are presented with varying degree of information share. The computational experiments show that the resulting tool set is robust enough to cope with the changes in capacity with the expected profits being maximized for different scenarios, and the scheme can generate pretty good solutions in reasonable computational time.     

Centralized resource allocation for enhanced Russell models

This paper proposes a centralized resource allocation (CRA) model for the enhanced Russell model. All the DMUs can be easily projected onto the efficient frontier by solving only one model. This projection can be made by transforming the proposed model to a linear programming problem. In this paper, instead of non-radially increasing or decreasing the inputs or outputs individually, we increase or decrease non-radially all of the inputs and outputs at the same time. By solving a single model, we can provide targets for all DMUs. By the proposed approximation, different targets can be found for all DMUs, as compared to those obtained by the previous approximations. The proposed model can be developed to CRA models. Finally, an applied example emphasizes the importance of the proposed model.     

Centralized resource allocation with stochastic data

Data Envelopment Analysis (DEA) is a technique based on mathematical programming for evaluating the efficiency of homogeneous Decision Making Units (DMUs). In this technique inefficient DMUs are projected on to the frontier which constructed by the best performers. Centralized Resource Allocation (CRA) is a method in which all DMUs are projected on to the efficient frontier through solving just one DEA model. The intent of this paper is to present the Stochastic Centralized Resource Allocation (SCRA) in order to allocate centralized resources where inputs and outputs are stochastic. The concept discussed throughout this paper is illustrated using the aforementioned example.     

A single-resource allocation problem with Poisson resource requirements

We consider a stochastic resource allocation problem that generalizes the knapsack problem to account for random item weights that follow a Poisson distribution. When the sum of realized weights exceeds capacity, a penalty cost is incurred. We wish to select the items that maximize expected profit. We provide an effective solution method and illustrate the advantages of this approach via computational experiments.     

Decision model and analysis for investment interest expense deduction and allocation

Investment income tax planning requires informed, strategic choices. One must determine the amount of qualified dividends and net long-term capital gain to be included in investment income (against which investment interest expense can be deducted). This choice also determines the residual qualified dividends and net long-term capital gain which enjoy a reduced tax rate. Another important decision is whether all or some of this interest expense should be deducted in the current year or carried forward. This paper puts forward a new approach to formulate these questions as a generalized resource allocation problem which permits analysis of the interdependence between, and the tax consequences of, the above decisions. The commonly used approach – deducting investment interest expense sooner rather than later – we consider myopic since the benefit of deferring some of the deduction is not leveraged. Presented here is a tax planning guideline (a necessary and sufficient condition for optimality) to realize a more forward-looking strategy. We also show that, for certain income structures, the tax savings by deducting a one-dollar investment interest expense may be more than the tax rate on the dollar of investment income that is offset.     

A goal programming approach to strategic resource allocation in acute care hospitals

This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Toronto's Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.     

Stochastic optimization models for a single-sink transportation problem

In this paper, we study a single-sink transportation problem in which the production capacity of the suppliers and the demand of the single customer are stochastic. Shipments are performed by capacitated vehicles, which have to be booked in advance, before the realization of the production capacity and the demand. Once the production capacity and the demand are revealed, there is an option to cancel some of the booked vehicles against a cancellation fee; if the quantity shipped from the suppliers using the booked vehicles is not enough to satisfy the demand, the residual quantity is purchased from an external company. The problem is to determine the number of vehicles to book in order to minimize the total cost. We formulate a two-stage and a multistage stochastic mixed integer linear programming models to solve this problem and test them on a real case provided by Italcementi, the primary Italian cement producer and the fifth largest cement producer in the world. We test the influence of different scenario-tree structures on the solutions of the problem, as well as sensitivity of the results with respect to the cancellation fee.     

Tracking models and the optimal regret distribution in asset allocation

We present a tracking model for asset allocation that tracks desired investment goals. The model is shown to be optimal with respect to an investor's ‘regret distribution’, the cumulative distribution of the difference between the revenue under perfect foresight and that possible without foresight. Relationships with Markowitz mean/variance models are also explored.     

Structuring resource allocation decisions: A framework for building multi-criteria portfolio models with area-grouped options

Multi-criteria portfolio modelling has been extensively employed as an effective means to allocate scarce resources for investment in projects when considering costs, benefits and risks. Some of these modelling approaches allow the grouping of projects into organisational areas, thus also supporting the decision of resource allocation among organisational units in a way that is collectively efficient for the organisation. However, structuring in practice a portfolio model using this latter type of approach is not a trivial task. How should areas be defined? Where should new projects be included? How should one define the criteria to evaluate performance? As far as we know, there is very little indication in the operational research and decision sciences literatures on how to structure this type of model. This paper suggests different ways to structuring portfolio models where projects are divided into areas and evaluated by multiple criteria, and illustrates their use in two action-research projects. Drawing on these experiences it then suggests a general framework for the structuring of such models in practice. Directions for future research are also identified.     

Quantitative models for sustainable supply chain management: Developments and directions

Sustainability, the consideration of environmental factors and social aspects, in supply chain management (SCM) has become a highly relevant topic for researchers and practitioners. The application of operations research methods and related models, i.e. formal modeling, for closed-loop SCM and reverse logistics has been effectively reviewed in previously published research. This situation is in contrast to the understanding and review of mathematical models that focus on environmental or social factors in forward supply chains (SC), which has seen less investigation. To evaluate developments and directions of this research area, this paper provides a content analysis of 134 carefully identified papers on quantitative, formal models that address sustainability aspects in the forward SC. It was found that a preponderance of the publications and models appeared in a limited set of six journals, and most were analytically based with a focus on multiple criteria decision making. The tools most often used comprise the analytical hierarchy process or its close relative, the analytical network process, as well as life cycle analysis. Conclusions are drawn showing that numerous possibilities and insights can be gained from expanding the types of tools and factors considered in formal modeling efforts.     

Dynamic job assignment: A column generation approach with an application to surgery allocation

We consider the assignment of jobs to heterogeneous agents in a dynamic system with a rolling time horizon. An example is a hospital operating theatre where the jobs are surgeries and the agents are the surgeons. The paper is presented in the context of surgery allocation and the system is characterized as follows: Patients are grouped into categories and they arrive continually following a stochastic process. Patients in each group have specific time limits within which they need treatment and if it cannot be accommodated then the patients are outsourced. The service level is the percentage of patients in each group treated within the time limit. Surgery durations are stochastic and depend on the surgeon conducting the surgeries. Each surgeon has limited time available and expected overtime is penalized by a non-decreasing convex function. We develop a column generation approach for the assignment of already arrived patients and tentative future patients to surgeons on specific days. It balances the conflicting objectives of including as many arrived patients as possible within their time limits, maximizing the service level of future patients, and minimizing the expected overtime of surgeons. A computational study is conducted with the model embedded in a rolling time horizon frame. The study indicates that the assignment of patients based on our model increases system performance in terms of service level and reduced overtime compared to a First-Come-First-Served (FCFS) policy when the arrival rates of patients are medium to high compared to the capacity of the system.     

Optimal resource allocation in survey designs

Resource allocation is a relatively new research area in survey designs and has not been fully addressed in the literature. Recently, the declining participation rates and increasing survey costs have steered research interests towards resource planning. Survey organizations across the world are considering the development of new mathematical models in order to improve the quality of survey results while taking into account optimal resource planning. In this paper, we address the problem of resource allocation in survey designs and we discuss its impact on the quality of the survey results. We propose a novel method in which the optimal allocation of survey resources is determined such that the quality of survey results, i.e., the survey response rate, is maximized. We demonstrate the effectiveness of our method by extensive numerical experiments.     

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.     

Stochastic programming for optimizing bidding strategies of a Nordic hydropower producer

From the point of view of a price-taking hydropower producer participating in the day-ahead power market, market prices are highly uncertain. The present paper provides a model for determining optimal bidding strategies taking this uncertainty into account. In particular, market price scenarios are generated and a stochastic mixed-integer linear programming model that involves both hydropower production and physical trading aspects is developed. The idea is to explore the effects of including uncertainty explicitly into optimization by comparing the stochastic approach to a deterministic approach. The model is illustrated with data from a Norwegian hydropower producer and the Nordic power market at Nord Pool.     

Integrated fleet mix and routing decision for hazmat transportation: A developing country perspective

In developing countries, truck purchase cost is the dominant criteria for fleet acquisition-related decisions. However, we contend that other cost factors such as loss due to the number of en route truck stoppages based on a truck type and recovery cost associated with a route choice decision, should also be considered for deciding the fleet mix and minimizing the overall costs for long-haul shipments. The resulting non-linear model, with integer variables for the number and type of trucks, and the route choices, is solved via genetic algorithm. Using real data from a bulk liquid hazmat transporter, the trade-offs between the cost of travel, loss due to number of truck stoppages, and the long-term recovery cost associated with the risk of exposure due to a hazmat carrier accident are discussed. The numerical experiments show that when factors related to public safety and truck stoppages are taken into account for transportation, the lowest total cost and optimal route choice do not align with the cheapest truck type option; rather, the optimal solution corresponds to another truck type and route with total costs significantly less than the total costs associated with the cheapest truck type. Our model challenges the current truck purchasing strategy adopted in developing countries using the cheapest truck criteria.     

Donation management for menu planning at soup kitchens

The food industry is confronted with a pressure to reduce waste and to make agreements on donating surplus food to charitable organizations. Charitable organizations such as food banks and soup kitchens can use these donations in preparing food parcels or meals for their clients. For soup kitchens, donation management is strongly influencing menu planning, and conversely, menu planning considerations have a strong impact on donation management decisions. To make the best use of (mostly highly perishable) food donations, we develop an MILP model for integrated donation management and menu planning that proposes a menu plan and suggests which (part of the) donations to accept. The combination of menu planning and donation management is essential for soup kitchens, but has not been studied before.The model is used to assess the impact of contracts on a strategic or tactical level, and captures operational decision making due to the integration of donation management and menu planning. To deal with meal variety considerations and to resemble planning practices, the developed model is solved in a rolling horizon. The results show that (i) the use of donations reduces overall costs for the soup kitchen; (ii) despite the short shelf life of donations, most donations can be used efficiently; and (iii) meal variety can be easily ensured and food donations increase this variety. In addition to the benefits for soup kitchens, the approach has implications for waste reduction in food supply chains, by structural/contractual donations of surplus food by retailers.     

A stochastic programming model for scheduling call centers with global Service Level Agreements

We consider the issue of call center scheduling in an environment where arrivals rates are highly variable, aggregate volumes are uncertain, and the call center is subject to a global service level constraint. This paper is motivated by work with a provider of outsourced technical support services where call volumes exhibit significant variability and uncertainty. The outsourcing contract specifies a Service Level Agreement that must be satisfied over an extended period of a week or month. We formulate the problem as a mixed-integer stochastic program. Our model has two distinctive features. Firstly, we combine the server sizing and staff scheduling steps into a single optimization program. Secondly, we explicitly recognize the uncertainty in period-by-period arrival rates. We show that the stochastic formulation, in general, calculates a higher cost optimal schedule than a model which ignores variability, but that the expected cost of this schedule is lower. We conduct extensive experimentation to compare the solutions of the stochastic program with the deterministic programs, based on mean valued arrivals. We find that, in general, the stochastic model provides a significant reduction in the expected cost of operation. The stochastic model also allows the manager to make informed risk management decisions by evaluating the probability that the Service Level Agreement will be achieved.     

A piecewise linearization framework for retail shelf space management models

Managing shelf space is critical for retailers to attract customers and optimize profits. This article develops a shelf-space allocation optimization model that explicitly incorporates essential in-store costs and considers space- and cross-elasticities. A piecewise linearization technique is used to approximate the complicated nonlinear space-allocation model. The approximation reformulates the non-convex optimization problem into a linear mixed integer programming (MIP) problem. The MIP solution not only generates near-optimal solutions for large scale optimization problems, but also provides an error bound to evaluate the solution quality. Consequently, the proposed approach can solve single category-shelf space management problems with as many products as are typically encountered in practice and with more complicated cost and profit structures than currently possible by existing methods. Numerical experiments show the competitive accuracy of the proposed method compared with the mixed integer nonlinear programming shelf-space model. Several extensions of the main model are discussed to illustrate the flexibility of the proposed methodology.