The stochastic knapsack problem

Ross, Keith W.; Tsang, D.H.K.

doi:10.1109/cdc.1988.194387

Cited by 71 publications

(134 citation statements)

References 9 publications

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“…Ross and Tsang (1989), for example, develop a stochastic knapsack model for allocation of servers to arriving customers in a model relevant to telecommunications networks and rental car fleet management. Savin et al (2000) provide an analysis of a multi-class environment in the rental business.…”

Section: Literature Reviewmentioning

confidence: 99%

A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes

Deshpande¹,

Cohen

Donohue³

2003

Management Science

227

222

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Motivated by a study of the logistics systems used to manage consumable service parts for the U.S. military, we consider a static threshold-based rationing policy that is useful when pooling inventory across two demand classes characterized by different arrival rates and shortage (stockout and delay) costs. The scheme operates as a (Q, r) policy with the following feature. Demands from both classes are filled on a first-comefirst-serve basis as long as on-hand inventory lies above a threshold level K. Once on-hand inventory falls below this level, low priority (i.e., low shortage cost) demand is backordered while high priority demand continues to be filled. We analyze this static policy first under the assumption that backorders are filled according to a special threshold clearing mechanism. Structural results for the key performance measures are established to enable an efficient solution algorithm for computing stock control and rationing parameters (i.e., Q, r, and K). Numerical results confirm that the solution under this special threshold clearing mechanism closely approximates that of the priority clearing policy. We next highlight conditions where our policy offers significant savings over traditional 'round-up' and 'separate stock' policies encountered in the military and elsewhere. Finally, we develop a lower bound on the cost of the optimal rationing policy. Numerical results show that the performance gap between our static threshold policy and the optimal policy is small in environments typical of the military and high technology industries.

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Section: Literature Reviewmentioning

confidence: 99%

A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes

Deshpande¹,

Cohen

Donohue³

2003

Management Science

227

222

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“…In these papers, value distributions were considered known and constant, making dynamic programming a viable solution. Another variant of the knapsack problem is found in [21] where a deterministic knapsack is used, however, with objects arriving to and departing from the knapsack at random times. The optimization problem considered was to accept/block arriving objects so that the average value of the knapsack content is maximized.…”

Section: State Of the Artmentioning

confidence: 99%

Solving Stochastic Nonlinear Resource Allocation Problems Using a Hierarchy of Twofold Resource Allocation Automata

Granmo

Oommen

2010

IEEE Trans. Comput.

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Abstract-In a multitude of real-world situations, resources must be allocated based on incomplete and noisy information. However, in many cases, incomplete and noisy information render traditional resource allocation techniques ineffective. The decentralized Learning Automata Knapsack Game (LAKG) was recently proposed for solving one such class of problems, namely the class of Stochastic Nonlinear Fractional Knapsack Problems. Empirically, the LAKG was shown to yield a superior performance when compared to methods which are based on traditional parameter estimation schemes. This paper presents a completely new online Learning Automata (LA) system, namely the Hierarchy of Twofold Resource Allocation Automata (H-TRAA). In terms of contributions, we first of all, note that the primitive component of the H-TRAA is a Twofold Resource Allocation Automaton (TRAA) which possesses novelty in the field of LA. Second, the paper contains a formal analysis of the TRAA, including a rigorous proof for its convergence. Third, the paper proves the convergence of the H-TRAA itself. Finally, we demonstrate empirically that the H-TRAA provides orders of magnitude faster convergence compared to the LAKG for simulated data pertaining to two-material unit-value functions. Indeed, in contrast to the LAKG, the H-TRAA scales sublinearly. Consequently, we believe that the H-TRAA opens avenues for handling demanding real-world applications such as the allocation of sampling resources in large-scale web accessibility assessment problems. We are currently working on applying the H-TRAA solution to the web-polling and sample-size detection problems applicable to the world wide web.

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“…A detailed coverage of these problems can be found in Caraway et al (1993), Steinberg and Parks (1979), Henig (1990), Morita et al (1989), Papastravrou et al (1996), Tamaki (1986), Righter (1989), Ross and Tsang (1989); see Kleywegt and Papastavrou (1998). Balas and Zemel (1980), proposed an algorithm for large knapsack problems.…”

Section: Introductionmentioning

confidence: 99%