Optimal continuous order quantity (s,S) policies; the 45-degrees algorithm

The most recent optimization algorithm for (s,S) order policies with continuous demand was developed by Federgruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead of discretization. Zheng and Federgruen (1991) developed an even more efficient algorithm for computing discrete order quantity (s,S) inventory policies. Since the continuous case prohibits enumeration, this algorithm does not apply to continuous order quantity systems. In this paper an efficient algorithm for continuous order quantity (s,S) policies is developed. A marginal cost approach is used for determining the optimal s. Furthermore, we construct two aid functions (generated by the optimality conditions for s and S), and exploiting their special properties a simple and efficient algorithm is obtained. The algorithm converges monotonically, such that at every iteration a policy improvement is obtained. Since every iteration finds a local minimum of the expected average cost, the number of iterations is at most N, where N45-degrees algorithm;order quantity policies

Optimal Continuous Order Quantity (s,s) Policies

The most recent optimization algorithm for (s, S) order policies with continuous demand was developed by Federgruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead of discretization. Zheng and Federgruen (1991) developed an even more efficient algorithm for computing discrete order quantity (s, S) inventory policies. Since the continuous case prohibits enumeration, this algorithm does not apply to continuous order quantity systems. In this paper an efficient algorithm for continuous order quantity (s, S) policies is developed. A marginal cost approach is used for determining the optimal s. Furthermore, we construct two aid functions (generated by the optimality conditions for s and S) , and exploiting their special properties a simple and efficient algorithm is obtained. The algorithm converges monotonically, such that at every iteration a policy improvement is obtained. Since every iteration finds a local minimum of the expected average cost, the number of iterations is at most N, where N < ? represents the number of local minimums. The algorithm also applies to discrete order quantity systems, in which case it basically reduces to the algorithm of Zheng and Federgruen (with the difference that in general our algorithm will take larger than unit steps, since we are not using enumeration)

Optimal continuous order quantity (s,S) policies - the 45-degrees algorithm

The most recent optimization algorithm for (s,S) order policies with continuous demand was developed by Federgruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead of discretization. Zheng and Federgruen (1991) developed an even more efficient algorithm for computing discrete order quantity (s,S) inventory policies. Since the continuous case prohibits enumeration, this algorithm does not apply to continuous order quantity systems. In this paper an efficient algorithm for continuous order quantity (s,S) policies is developed. A marginal cost approach is used for determining the optimal s. Furthermore, we construct two aid functions (generated by the optimality conditions for s and S), and exploiting their special properties a simple and efficient algorithm is obtained. The algorithm converges monotonically, such that at every iteration a policy improvement is obtained. Since every iteration finds a local minimum of the expected average cost, the number of iterations is at most N, where N<infinity represents the number of local minimums. The algorithm also applies to discrete order quantity systems, in which case it basically reduces to the algorithm of Zheng and Federgruen (with the difference that in general our algorithm will take larger than unit steps, since we are not using enumeration

Exploiting Non-Causal CPU-State Information for Energy-Efficient Mobile Cooperative Computing

Scavenging the idling computation resources at the enormous number of mobile devices can provide a powerful platform for local mobile cloud computing. The vision can be realized by peer-to-peer cooperative computing between edge devices, referred to as co-computing. This paper considers a co-computing system where a user offloads computation of input-data to a helper. The helper controls the offloading process for the objective of minimizing the user's energy consumption based on a predicted helper's CPU-idling profile that specifies the amount of available computation resource for co-computing. Consider the scenario that the user has one-shot input-data arrival and the helper buffers offloaded bits. The problem for energy-efficient co-computing is formulated as two sub-problems: the slave problem corresponding to adaptive offloading and the master one to data partitioning. Given a fixed offloaded data size, the adaptive offloading aims at minimizing the energy consumption for offloading by controlling the offloading rate under the deadline and buffer constraints. By deriving the necessary and sufficient conditions for the optimal solution, we characterize the structure of the optimal policies and propose algorithms for computing the policies. Furthermore, we show that the problem of optimal data partitioning for offloading and local computing at the user is convex, admitting a simple solution using the sub-gradient method. Last, the developed design approach for co-computing is extended to the scenario of bursty data arrivals at the user accounting for data causality constraints. Simulation results verify the effectiveness of the proposed algorithms.Comment: Submitted to possible journa