Using 3D-printing in disaster response:the two-stage stochastic 3D-printing knapsack problem

In this paper, we will shed light on when to pack and use 3D-printers in disaster response operations. For that, we introduce a new type of problem, which we call the two-stage stochastic 3D-printing knapsack problem. We provide a two-stage stochastic programming formulation for this problem, for which both the first and the second stage are NP-hard integer linear programs. We reformulate this formulation to an equivalent integer linear program, which can be efficiently solved by standard solvers. Our numerical results illustrate that for most situations using a 3D-printer is beneficial. Only in extreme circumstances, where the quality of printed items is extremely low, the size of the 3D-printer is extremely large compared to the knapsack size, when there is no time to print the items, or when demand for items is low, packing no 3D-printers is the best option. In this paper, we will shed light on when to pack and use 3D-printers in disaster response operations. For that, we introduce a new type of problem, which we call the two-stage stochastic 3D-printing knapsack problem. We provide a two-stage stochastic programming formulation for this problem, for which both the first and the second stage are NP-hard integer linear programs. We reformulate this formulation to an equivalent integer linear program, which can be efficiently solved by standard solvers. Our numerical results illustrate that for most situations using a 3D-printer is beneficial. Only in extreme circumstances, where the quality of printed items is extremely low, the size of the 3D-printer is extremely large compared to the knapsack size, when there is no time to print the items, or when demand for items is low, packing no 3D-printers is the best option

Probabilistic resource pooling games

We study a setting with a single type of resource and with several players, each associated with a single resource (of this type). Unavailability of these resources comes unexpectedly and with player-specific costs. Players can cooperate by reallocating the available resources to the ones that need the resources most and let those who suffer the least absorb all the costs. We address the cost savings allocation problem with concepts of cooperative game theory. In particular, we formulate a probabilistic resource pooling game and study them on various properties. We show that these games are not necessarily convex, do have non-empty cores, and are totally balanced. The latter two are shown via an interesting relationship with Böhm-Bawerk horse market games. Next, we present an intuitive class of allocation rules for which the resulting allocations are core members and study an allocation rule within this class of allocation rules with an appealing fairness property. Finally, we show that our results can be applied to a spare parts pooling situation

A note on maximal covering location games

In this note we introduce and analyse maximal covering location games. As the core may be empty, several sufficient conditions for core non-emptiness are presented. For each condition we provide an example showing that when the condition is not satisfied, core non-emptiness is not guaranteed

Pooling of critical, low-utilization resources with unavailability

\u3cp\u3eWe consider an environment in which several independent service providers can collaborate by pooling their critical, low-utilization resources that are subject to unavailability. We examine the allocation of the joint profit for such a pooled situation by studying an associated cooperative game. For this game, we will prove non-emptiness of the core, present a population monotonic allocation scheme and show convexity under some conditions. Moreover, four allocation rules will be introduced and we will investigate whether they satisfy monotonicity to availability, monotonicity to profit, situation symmetry and game symmetry. Finally, we will also investigate whether the payoff vectors resulting from those allocation rules are members of the core.\u3c/p\u3

A note on maximal covering location games

\u3cp\u3eIn this note we introduce and analyze maximal covering location games. As the core may be empty, several sufficient conditions for core non-emptiness are presented. For each condition we provide an example showing that when the condition is not satisfied, core non-emptiness is not guaranteed.\u3c/p\u3