Technical Note—Allocation of Effort Resources among Competing Activities

Luss, Hanan; Gupta, S. K.

doi:10.1287/opre.23.2.360

Cited by 172 publications

(57 citation statements)

References 3 publications

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“…We solve the network flow subproblem as a multicommodity network flow problem, and use an algorithm described by Luss and Gupta (1975) to solve the resource allocation subproblem. Further details of the subgradient algorithm and its implementation to solve this problem are available in Nicholas (2009, pp.…”

Section: Fast Effective Transmitter Placement In Wireless Mesh Networkmentioning

confidence: 99%

Fast, Effective Transmitter Placement in Wireless Mesh Networks

Nicholas¹,

Alderson²

2012

Military Oper Res

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W ireless mesh networks are systems of interconnected wireless access points that provide digital services to client devices via radio transmission. We consider the challenges of a communications planner who must quickly design a wireless mesh network, as might be expected during combat operations or in support of humanitarian assistance and disaster relief operations. We seek a network that maximizes client coverage area subject to constraints on network service, the technical characteristics of the available access points, and radio propagation over terrain. We create a nondifferentiable, nonconvex, nonlinear optimization problem and use a sampling algorithm to quickly find good solutions. We validate our formulation and solutions via numerical experiments and several field tests, and we demonstrate that our technique can generate network topologies capable of functioning in real-world scenarios.We construct a corresponding decision support tool that allows a communications planner to design working wireless mesh network topologies quickly, with no guesswork, and requiring very little expertise. The tool runs on a laptop, supports virtually any type of access point, uses terrain information freely downloadable from the Internet, and does not require any additional software or solver licenses.

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Section: Fast Effective Transmitter Placement In Wireless Mesh Networkmentioning

confidence: 99%

Fast, Effective Transmitter Placement in Wireless Mesh Networks

Nicholas¹,

Alderson²

2012

Military Oper Res

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“…The use of such functions complicates solving the allocation problem outlined in section 2.4, as there is no closed form Solution. However, because the allocation problem can be solved by applying an algorithm proposed by Luss and Gupta (1975 ), the general approach to establishing profit maximizing sales territory alignment remains more or less the same.…”

Section: Consideration Of Travel Timesmentioning

confidence: 99%

COSTA: Contribution Optimizing Sales Territory Alignment

Skiera

Albers

1998

Marketing Science

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. The alignment of sales territories represents a major problem in salesforce management with considerable impact on profit. The common approach to this alignment is the balancing approach, which establishes territories balanced as well as possible with respect to one or more attributes such as potential or work-load. Unfortunately, this approach does not necessarily guarantee an alignment that maximizes profit. As a consequence, it does not allow evaluation of the profit implications of any alignment proposal in comparison with the existing one. Because of this, several authors have already proposed nonlinear integer optimization models that attempt to directly maximize profit by simultaneously considering the problems of selling time allocation across accounts as well as the assignment of accounts to territories. However, these models proved to be too large to be mathematically solvable, such that the authors have either simplified the problem or proposed application of heuristic Solution procedures. The latter is based on the principle of equating the marginal profit of time for each salesperson. We show here that an optimal Solution does not possess the property of equal marginal profits of time. We thus propose a new approach, COSTA, for the derivation of contribution optimizing sales territory aügnments. COSTA is based on sales response functions at the level of sales coverage units incorporating selling time as independent variable and using a new concept designed to take travel times into account. This makes it possible to simultaneously solve the allocation and assignment problem. Furthermore, COSTA provides the structure for evaluating the effects on profit of different salesforce sizes and different locations of the salespersons. The suitability of COSTA for practical problems is supported by a real-world application in which COSTA improved an existing territory alignment by 5.8% in terms of profit contribution. Terms of use: Documents in

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“…(Problem) φj strictly convex; linear equality (aj = 1); lj = 0 (Origin) Parallel subproblem in a RHS allocation algorithm for a problem with additional linear generalized upper bound (GUB) constraints (Methodology) Derived from the ranking algorithm from [Bod69]; replaces sorting by work with two heaps; no complexity analysis; also discusses the reoptimization of the sorted list, and discusses the invertibility of φ j and proposes a numerical approximation scheme (cites [Zip80b]) (Citations) Related work ([Bod69, LuG75, OhK80, Zip80b, BiH81, Roh79])-see [Roh82] for the published version of the latter; data structures ([Knu68, AHU74]) (Notes) The paper [Roh82] contains a discussion on the productivity of the activities, measured in terms of the quantity φj(x * j )/x * j , and relates this number to the value of φ j (0) for some special return functions given in [ChC58b,LuG75] [Bru84] P. Brucker, An O(n) algorithm for quadratic knapsack problems [Zie82]; initial interval given from the least/most costly items relative storage requirements, followed by a Newton/regula falsi step; proposes an algorithm based on the continued use of such steps, but without a formal convergence analysis > 0); lj = 0, uj = ∞ (Methodology) Improves the initial bounds from [VeK88]; cites [HMMS60,Lew81] for the origins of such bounds; also presents a Newton-type algorithm (denoted the "implicit algorithm") for obtaining µ * , which utilizes the bounding formula iteratively; the algorithm utilizes an initial ranking of inventory cost/storage requirement ratios, just as in [Zie82,VeK88]; convergence is claimed (referring to it being a Newton method) but not established [Gla96] P. Glasserman, Allocating production capacity among multiple products (Problem) φj(xj) = cj /γj (xj), γ −1 j convex; linear equality (aj = 1); lj > 0, uj = ∞ (Origin) Choice of base-stock levels and capacity allocations for a minimal total backorder or holding cost, in an inventory system with several items (Methodology) Simple heuristic decision rules (Citations) Similar analyses for other sequencing problems: [Kle76,Ana89]; optimization algorithms: [LuG75, Zip80b, IbK88] (Notes) Shows that simple rules exist (such as one that maximizes the time between stockouts) that behave asymptotically optimally, in the sense that as the number of orders tend to infinity the allocation policy tend to be optimal.…”

Section: Introductionmentioning

confidence: 99%

“…[KoL98] M. S. Kodialam and H. Luss, Algorithms for separable nonlinear resource allocation problems (Problem) φj strictly increasing; gj strictly decreasing; φ j /g j strictly increasing and invertible; lj = 0; uj = ∞; Slater CQ (Origin) Same; application mentioned: the service constrained problem (Methodology) Two Lagrange multiplier algorithms: (a) ranking (denoted RANK)à la [LuG75] (and [Tan88] for a minimax version); and (b) bisection search (denoted EVALUATE)à la [Zip80b] (and [Lus91] for a minimax version); also presents a pegging algorithm (denoted RELAX)à la [BiH81], cf. Section 3.2, and a combination with RANK (denoted RELAX/RANK) in which sorting is first performed, then followed by the division of the problem into two roughly equal parts, each of which is solved with RELAX and RANK, respectively (cites [Ein81,Lus92] (Notes) Extends the three algorithms in a natural manner to the general bounded case, citing [LuG75,BiH81,GSAB93], but without an analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3.2, and a combination with RANK (denoted RELAX/RANK) in which sorting is first performed, then followed by the division of the problem into two roughly equal parts, each of which is solved with RELAX and RANK, respectively (cites [Ein81,Lus92] (Notes) Extends the three algorithms in a natural manner to the general bounded case, citing [LuG75,BiH81,GSAB93], but without an analysis. Conclude through numerical experiments (n = 10 4 ) that pegging (RELAX) is best when the multiplier valueμ is available explicitly (followed by RANK and EVALUATE), otherwise EVALUATE is much better; RANK however suffers much when lacking explicit solutions, since inversions are needed at every iteration.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A survey on the continuous nonlinear resource allocation problem

Patriksson

2008

European Journal of Operational Research

184

137

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Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research.

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Technical Note—Allocation of Effort Resources among Competing Activities

Cited by 172 publications

References 3 publications

Fast, Effective Transmitter Placement in Wireless Mesh Networks

Fast, Effective Transmitter Placement in Wireless Mesh Networks

COSTA: Contribution Optimizing Sales Territory Alignment

A survey on the continuous nonlinear resource allocation problem

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