Abstract: According to examples, an apparatus may include a processor and a memory on which are stored machine readable instructions that when executed by the processor, cause the processor to identify a plurality of tasks, identify a plurality of resources configured to execute the tasks, and decompose the plurality of tasks into multiple groups of tasks based on a plurality of rules applicable to the multiple groups of tasks. The instructions may also cause the processor to, for each group in the multiple groups of tasks, model the group of tasks and a subset of the plurality of resources as a respective resource allocation problem and assign a respective node of a plurality of nodes to solve the resource allocation problem.

Abstract: A set of SKUs is divided into a plurality of different Mean Field clusters, and a tracker (or sensor) is identified for each cluster. Product decisions for each Mean Field cluster are generated based on the tracker (or sensor) and each Mean Field cluster is then deconstructed to obtain product decisions for individual SKUs in the Mean Field cluster.

Abstract: According to examples, an apparatus may include a processor and a memory on which are stored machine readable instructions that when executed by the processor, cause the processor to identify a plurality of tasks, identify a plurality of resources configured to execute the tasks, and decompose the plurality of tasks into multiple groups of tasks based on a plurality of rules applicable to the multiple groups of tasks. The instructions may also cause the processor to, for each group in the multiple groups of tasks, model the group of tasks and a subset of the plurality of resources as a respective resource allocation problem and assign a respective node of a plurality of nodes to solve the resource allocation problem.

Abstract: According to examples, an apparatus may include a processor that is to generate a plurality of candidate fulfillment plans regarding delivery of items over a network, in which each of the candidate fulfillment plans is generated using a respective decision variable of an array of values. The processor may also calculate an evaluation value for each of the candidate fulfillment plans, in which the evaluation value for a candidate fulfillment plan is a measure of a compliance of the candidate fulfillment plan with a plurality of factors pertaining to the delivery of the items. The processor may further output instructions regarding delivery of the items over the network according to the candidate fulfillment plan that corresponds to a maximized compliance with the plurality of factors among the calculated evaluation values to maximize compliance with the plurality of factors in the delivery of the items.

Abstract: Technologies are described to provide parameter estimation for a probabilistic forecaster in inventory management. A forecaster model may be generated based on observed delivery data, demand data, and a state of a delivery system managed by an inventory management service or an enterprise resource planning service. A probability of the state of the delivery system transitioning to a subsequent state of the delivery system may be determined based on an estimation of one or more parameters using a linear regression model. In some examples, the forecaster model may be derived from the discretized version of the linear Fokker-Planck equations using maximum log-likelihood estimate with optimization through a fast marching algorithm. In other examples, Lagrange multipliers may be used to determine initial constraints on the parameters. An optimal inventory level to be maintained may be computed based on the determined probability.

Abstract: A set of conditional rules (or transformations) that are effective for an article under analysis is identified. The set of rules is compressed into a single rule which is applied to a first quantity identifier that identifies a first quantity of the article, to obtain a second quantity. An order generation system generates an order based on the second quantity.

Abstract: A set of SKUs is divided into a plurality of different Mean Field clusters, and a tracker (or sensor) is identified for each cluster. Product decisions for each Mean Field cluster are generated based on the tracker (or sensor) and each Mean Field cluster is then deconstructed to obtain product decisions for individual SKUs in the Mean Field cluster. An interrogation system operates an interpretation of rules that were used to generate the product discussion.

Abstract: An optimization solver divides time-indexed historical data into intervals that have temporal boundaries. A discrete coefficient evaluator calculates coefficient values in a forecasting model at the temporal boundaries of the training data. An incremental parameter evaluator evaluates incremental parameter changes between the temporal boundaries in the training data. The incremental parameter evaluator updates the parameter values, based upon the incremental changes in the parameters, so that the updated parameter values can be used by the discrete coefficient evaluator for evaluating coefficient values at a next temporal boundary. The trained forecasting modes is deployed in a system to forecast phenomena.

Abstract: A set of SKUs is divided into a plurality of different Mean Field clusters, and a tracker (or sensor) is identified for each cluster. Product decisions for each Mean Field cluster are generated based on the tracker (or sensor) and each Mean Field cluster is then deconstructed to obtain product decisions for individual SKUs in the Mean Field cluster.