Multi-period Resource Allocation Research Articles

A data-driven optimization approach for multi-period resource allocation in cholera outbreak control

Cholera, a water-borne bacteria infectious disease, shows clear spatial variation in its transmission pattern. It is thus important to incorporate understanding on the spatial variability of its transmission when making transmission prediction and intervention decisions. However, for an emerging cholera outbreak, transmission dynamics models are often uncertain as model parameters are indeterminate and epidemic state can only be partially observed. Hence, ensuing intervention decisions have to be made under uncertainty and thus the resultant optimization problem is challenging. In this paper, we study a multi-period location-specific resource allocation problem for cholera outbreak intervention with periodically acquired state information from different locations and increasingly understood transmission parameters over time. We formulate the problem as a nonlinear optimization model on a set of ordinary-differential-equations governing location-specific disease transmission dynamics. We propose a data-driven optimization approach to determine the optimal strategy of intervention resource allocation at each period and each community in a rolling-horizon manner. At each period, we integrate single-period model parameter fitting and scenario-based stochastic programming to make decisions under uncertainty with newly acquired system understanding. We conduct comparative studies to assess the performance of our data-driven optimization approach and offer insights into intervention resource allocation policy development. We conclude that our data-driven optimization approach is effective to multi-period decision problems under system dynamics with indeterminate parameters.

Novel methods for resource allocation in humanitarian logistics considering human suffering

Abstract Deprivation cost is often used as a key economic metric of human suffering associated with emergency logistics. An improved approach is proposed for effective and equitable critical resource allocation within emergency logistics that considers human suffering by using this economic representation. A dynamic programming model is constructed for a multi-period resource allocation dispatch problem extracted to represent the disaster response phase, with special attention paid to the human suffering resulting from the delivery delay. Extensive numerical experiments are conducted to validate the computational performance and solution quality of the dynamic programming method. Based on the best solutions, an optimal delivery pattern with a cyclically sequenced feature is identified and its sufficient condition is provided as well. Furthermore, a piecewise linear method is proposed to accommodate large-scale instances that cannot be applied to the “Cyclic Delivery Approach”.

The dynamic vehicle allocation problem with application in trucking companies in Brazil

This paper deals with the dynamic vehicle allocation problem (DVAP) in road transportation of full truckloads between terminals. The DVAP involves multi-period resource allocation and consists of defining the “movements” of a fleet of vehicles that transport goods between terminals with a wide geographical distribution. These movements may be of fully laden vehicles, unladen vehicles for repositioning or vehicles held at a terminal to meet future demands. Emphasis is given to the characterization of the problem in real situations, the mathematical modeling of the problem and the use of exact and heuristic methods to solve it, including GRASP and simulated annealing metaheuristics. Results based on a case study of a transportation company in Brazil are presented and analyzed, showing that the approach can be effective in supporting practical decisions.

Multi-period resource allocation for estimating project costs in competitive bidding

In competitive bidding for project contracts, contractors estimate the cost of completing a project and then determine the bid price. Accordingly, the bid price is markedly affected by the inaccuracies in the estimated cost. To establish a profit-making strategy in competitive bidding, it is crucial for contractors to estimate project costs accurately. Although allocating a large amount of resources to cost estimates allows contractors to prepare more accurate estimates, there is usually a limit to available resources in practice. To the best of our knowledge, however, none of the existing studies have addressed the resource allocation problem for estimating project costs in competitive bidding. To maximize a contractor’s expected profit, this paper develops a multi-period resource allocation method for estimating project costs in a sequential competitive bidding situation. Our resource allocation model is posed as a mixed integer linear programming problem by making piecewise linear approximations of the expected profit functions. Numerical experiments examine the characteristics of the optimal resource allocation and demonstrate the effectiveness of our resource allocation method.

Otimização na alocação dinâmica de veículos no transporte rodoviário de cargas completas entre terminais

Este artigo trata do problema da alocação dinâmica (multiperíodos) de veículos (PADV) no transporte rodoviário de cargas completas entre terminais. O PADV pertence à classe de problemas de alocação de recursos multiperíodos e consiste em definir "movimentos" de uma frota de veículos que realiza viagens entre terminais geograficamente dispersos que interagem entre si. Esses movimentos podem ser: veículos carregados com carga completa, vazios para reposicionamento ou mantidos em um terminal de um período para outro como provisão para o atendimento de demandas futuras. A ênfase é dada na caracterização do problema em situações reais, na modelagem matemática do problema e na sua solução utilizando um método exato e métodos aproximados, incluindo uma heurística GRASP. Resultados baseados em um estudo de caso de uma transportadora brasileira são apresentados e analisados mostrando que a abordagem pode ser efetiva para apoiar decisões na prática.

Computational solution of capacity planning models under uncertainty

The traditional supply chain network planning problem is stated as a multi-period resource allocation model involving 0–1 discrete strategic decision variables. The MIP structure of this problem makes it fairly intractable for practical applications, which involve multiple products, factories, warehouses and distribution centres (DCs). The same problem formulated and studied under uncertainty makes it even more intractable. In this paper we consider two related modelling approaches and solution techniques addressing this issue. The first involves scenario analysis of solutions to “wait and see” models and the second involves a two-stage integer stochastic programming (ISP) representation and solution of the same problem. We show how the results from the former can be used in the solution of the latter model. We also give some computational results based on serial and parallel implementations of the algorithms.

Multiperiod resource allocation with a smoothing objective

We consider a multiperiod resource allocation problem, where a single resource is allocated over a finite planning horizon of Tperiods. Resource allocated to one period can be used to satisfy demand of that period or of future periods, but backordering of demand is not allowed. The objective is to allocate the resource as smoothly as possible throughout the planning horizon. We present two models: the first assumes that the allocation decision variables are continuous, whereas the second considers only integer allocations. Applications for such models are found, for example, in subassembly production planning for complex products in a multistage production environment. Efficient algorithms are presented to find optimal allocations for these models at an effort of O( T 2 ). Among all optimal policies for each model, these algorithms find the one that carries the least excess resources throughout the planning horizon.

Multiperiod allocation of substitutable resources

We consider multiperiod resource allocation problems, where excess resources in one period can be used in subsequent periods and certain substitutions among the resources are feasible. The major issues addressed here are: (i) determine whether there ase sufficient resources to sustain specified levels for the various activities, and if so, (ii) find a feasible allocation scheme. We address these issues by finding a maximal flow in a related network. Assuming that the substitutional relations are transitive, the related network is relatively small; each resource is represented by a single node and only part of the possible substitutions are represented by arcs. Having an efficient method is important as often these issues must be repeatedly addressed as part of more complex algorithms, such as those for minimax resource allocation problems. We also present a more general allocation problem for which the issues above are addressed by finding a maximal flow in a related multiperiod transportation problem. The resulting network is, however, significantly larger than the former one. Potential applications for these multiperiod allocation problems are found, for example, in the manufacturing of high-tech products.

A Multiperiod Minimax Resource Allocation Problem with Substitutable Resources

In this paper we consider a multiperiod resource allocation model in which the resources are storable and substitutable. A specific application of this model relates to the multiperiod production planning for electronic circuit board assembly factories. In this case, resources are electronic components, which are storable, that is, excess components in one period can be used in subsequent periods. Components that can be used in the same function on a circuit board are considered substitutable. Substitutability between components, however, may be dependent upon the specific circuit board on which they reside. Given that there are certain production requirements for the circuit boards, and that some components are in short supply, our algorithm (a) revises the production levels of the affected circuit boards, and (b) efficiently allocates the available components according to the revised production, so as to minimize the maximum weighted deviation from the original production plans. The weights reflect the relative importance of the circuit boards. The objective function uses cumulative production levels and cumulative demands to allow for back-scheduling. We present a primal-dual algorithm that is very efficient. An implementation of the algorithm compares favorably with a standard linear programming code. We solved a problem with 300 components, 20 different circuit boards (average of 10 functions/board) for 10 time periods (approximately 30,000 variables) in less than one minute on a VAX 11/785. We also discuss upper and lower bound extensions, and a lexicographic algorithm to ensure that less critical resources are also allocated effectively.

Valuing a Depletable Resource Endowment in an Open Economy

Valuing a Depletable Resource Endowment in an Open Economy

Multiperiod Resource Allocation with Variable Technology

Planning the allocation of scarce resources to competing activities over multiple time periods is one of the most important problems facing decision makers in modern organizations. Much of the previous research in this area has concentrated on the use of linear programming procedures and has assumed that the technology through which scarce resource inputs are transformed into competing activity outputs is fixed. A more realistic assumption in many situations is that certain technology coefficients are likely to vary over the planning horizon as a function of activity levels in previous periods. In this paper, a multiperiod resource allocation model with variable technology is formulated. Enriching a more traditional fixed technology model to include variable technology results in a nonlinear model which is more realistic, but is also more difficult to solve. A heuristic procedure that is both straightforward and intuitively appealing is developed for obtaining good feasible solutions to the variable technology model. The solution procedure requires little additional computational effort beyond solving the associated, less realistic fixed technology model.

A Note on the Application of Dynamic Correction to the Optimization of a Multiperiod Resource Allocation Problem

In this note, Luss's approach to optimization of a multiperiod resource allocation problem is employed to include carry-over effects of the controllable variable on future periods and also to include the carry-over effect from previous periods.

A Note on the Application of Dynamic Correction to the Optimization of a Multiperiod Resource Allocation Problem

A Note on the Application of Dynamic Correction to the Optimization of a Multiperiod Resource Allocation Problem

Optimization of a Multiperiod Resource Allocation Model

In this paper we examine multiperiod resource allocation problems, such as allocating a given marketing budget among T periods. The return functions of each period are assumed to be concave functions of the effective effort variable, which is composed of the expenditures in all previous periods and the present one. Assuming that the effect of an amount spent in period t is decreasing by a fixed rate in successive periods, necessary and sufficient conditions for a non-boundary optimal policy are derived. Under these conditions the optimal policy which maximizes total returns is obtained.