Enterprise AI workstation system based on private large model
By building an enterprise AI workstation system based on a private large model, the problems of system fragmentation, insufficient model adaptation, and inefficient collaboration have been solved, achieving efficient data exchange and decision support, and improving model accuracy and response speed.
Patent Information
- Application Number
- CN202511084511.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-04
- Publication Date
- 2025-11-18
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Existing enterprise AI workstation systems suffer from problems such as system fragmentation, insufficient adaptation of private large models to business scenarios, inefficient collaboration between AI digital employees and robots, and lagging business decision-making.
The enterprise AI workstation system based on a private big model includes a hardware base layer, an enterprise private big model layer, an AI digital employee and robot collaboration layer, and an operational decision support layer. Through technologies such as heterogeneous computing power clusters, distributed storage, multimodal interaction, security auditing, intelligent collaborative scheduling, and full data fusion, it achieves data interoperability, model adaptation, and decision support.
It achieved a 95% data interoperability rate, a 92% accuracy rate for private large model domain tasks, a 50ms response latency for cross-entity tasks, a 1% robot conflict rate, a 1-hour business analysis cycle, and a 40% increase in the adoption rate of decision recommendations.
Smart Images
Figure CN120975582A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of desktop computing platforms, and particularly relates to an enterprise AI workstation system based on a private large model. BACKGROUND
[0002] The enterprise AI workstation system refers to a high-performance desktop computing platform tailored for enterprises and professional teams for local development, training, fine-tuning, reasoning and deploying artificial intelligence models. It combines enterprise-level hardware, AI acceleration chips (such as NVIDIA RTX / DGX series), optimized software stack and security mechanisms, so that enterprises can complete the whole life cycle management of AI models locally, taking into account the three major needs of data security, cost control and flexible deployment.
[0003] The existing enterprise AI workstation system has the following key defects:
[0004] 1. System fragmentation: enterprise servers, computing resources and AI applications (such as financial software and scheduling systems) are independently deployed, with a data intercommunication rate of less than 30%, forming a "data island";
[0005] 2. Difficulty in landing private large models: general large models have poor adaptability to enterprise business scenarios, with an accuracy of less than 60%, and lack deep integration mechanisms with job processes and robot control;
[0006] 3. Low coordination efficiency: AI digital employees and intelligent robots belong to different systems, with a cross-subject task response delay of more than 1000ms and a multi-robot coordination conflict rate of more than 20%;
[0007] 4. Decision support lag: business data analysis relies on manual aggregation, with a decision suggestion generation cycle of more than 72 hours, making it difficult to respond to market changes in a timely manner.
[0008] Therefore, the present applicant has found a method to solve the above problems through beneficial exploration and research, and the technical solution to be introduced below is generated in this background. SUMMARY
[0009] The technical problem to be solved by the present application is to provide an enterprise AI workstation system based on a private large model to solve the problems of enterprise AI system fragmentation, insufficient adaptation of private large models to business scenarios, low efficiency of AI digital employees and robots in coordination, and lag in business decision-making, in view of the deficiencies of the prior art.
[0010] The technical problem to be solved by the present application can be implemented by using the following technical solution:
[0011] An enterprise AI workstation system based on a private large model comprises:
[0012] a hardware base layer for providing computing power, storing data, and providing a plurality of hardware interfaces to interface with intelligent robot terminals of different manufacturers;
[0013] a private enterprise large model layer for exclusive model inspection, multi-modal interaction, and security audit under the support of the hardware base layer;
[0014] an AI digital employee and robot collaboration layer for generating digital employees, intelligent collaboration scheduling, and adapting intelligent robot terminals under the support of the private enterprise large model layer; and
[0015] an operating decision support layer for full-data fusion, intelligent analysis, and decision suggestion generation.
[0016] In a preferred embodiment of the present application, the hardware base layer comprises:
[0017] a heterogeneous computing power cluster comprising a plurality of GPU servers, a plurality of CPU servers, and a plurality of FPGA acceleration cards;
[0018] a distributed storage module that adopts cold-hot data layered storage and supports encrypted storage of enterprise operating data, large model parameters, and robot logs; and
[0019] an edge interface unit deployed at a production service site, which comprises a plurality of hardware interfaces for interfacing with intelligent robot terminals of different manufacturers.
[0020] In a preferred embodiment of the present application, the GPU server adopts NVIDIA H20, the CPU server adopts Intel Xeon Platinum 8592, the heterogeneous computing power cluster provides at least 500 TFLOPS of AI computing power and supports private large model training, the single model training cycle is not greater than 72 hours, the real-time inference delay time is not greater than 10 ms, the capacity of the distributed storage system is not less than 200 TB, and the hardware interfaces of the edge interface unit include EtherCAT interfaces, USB3.0 interfaces, and RS485 interfaces, with a data transmission rate of not less than 1 Gbps.
[0021] In a preferred embodiment of the present application, the private enterprise large model layer comprises:
[0022] an exclusive training engine for fine-tuning a basic large model based on enterprise historical data and generating an industry-specific model;
[0023] A multi-modal interaction module for supporting text, voice, image input and output adapted to the job scene; and
[0024] A security audit unit for real-time monitoring of large model output and recording of training data sources and model iteration logs in compliance with relevant regulations.
[0025] In a preferred embodiment of the present application, the private large model fine-tuning algorithm of the exclusive training engine is a total loss function
[0026]
[0027] Where the parameters are defined: α = 0.7, β = 0.2, γ = 0.05, δ = 0.05; is a set of domain-related data; S = {4, 8, 12}: knowledge distillation layer index; Sim(.): cosine similarity function.
[0028] In a preferred embodiment of the present application, the AI digital employee and robot collaboration layer includes:
[0029] A digital employee generation and integration module for automatically generating new job digital employees based on private large models and job templates, and accessing existing AI applications through standardized API;
[0030] An intelligent collaborative scheduling engine for decomposing enterprise goals into digital employee tasks and robot tasks, and dynamically allocating resources based on reinforcement learning. When the robot power is ≤20% or the digital employee computing power is insufficient, task redistribution is triggered; and
[0031] A robot protocol adaptation unit with a private protocol analysis library of multiple manufacturers and unified conversion to ROS2DDS standard protocol.
[0032] In a preferred embodiment of the present application, the multi-agent collaborative scheduling algorithm used by the intelligent collaborative scheduling engine is:
[0033] Reinforcement learning strategy
[0034]
[0035] Real-time reward function
[0036]
[0037] Where the variables are: A CAE : Generalized advantage estimation (γ = 0.99, λ = 0.95); Path space of robot i; T prog: Task progress value (0-1); C risk : Collision risk coefficient (0-1).
[0038] In a preferred embodiment of the present application, the business decision support layer comprises:
[0039] Full-volume data fusion module, the full-volume data fusion module is used for collecting enterprise ERP, CRM, production system and robot sensor data, and forms a business data center through knowledge graph association;
[0040] Intelligent analysis engine, the intelligent analysis engine is used for outputting key indicator analysis based on time series prediction and causal inference; and
[0041] Decision suggestion generation module, the decision suggestion generation module is used for generating customized suggestions in combination with the boss management style.
[0042] In a preferred embodiment of the present application, the business decision causal inference algorithm used by the intelligent analysis engine is:
[0043] Causal effect estimation model:
[0044]
[0045] Wherein:
[0046]
[0047] A=GNN(H) (causal graph adjacency matrix)
[0048] The dynamic resource allocation algorithm used by the intelligent analysis engine is:
[0049] Quantum resource state:
[0050]
[0051] Task evolution operator:
[0052]
[0053] Optimal distribution:
[0054]
[0055] Due to the adoption of the above technical solutions, the present application has the following advantages:
[0056] 1. Integrated capability: breaking the system barriers, the data intercommunication rate is improved from 30% to 95%, and the enterprise IT architecture is simplified by 60%;
[0057] 2. Large model landing: The task accuracy in the private large model field is improved from 60% to 92%, which adapts to the actual scene of enterprises;
[0058] 3. Synergy efficiency: The response delay of cross-subject tasks is reduced from 1000ms to ≤50ms, and the robot conflict rate is reduced from 20% to ≤1%;
[0059] 4. Decision effectiveness: The business analysis cycle is shortened from 72 hours to 1 hour, and the adoption rate of recommendations is increased by 40%, helping enterprises respond quickly to the market. BRIEF DESCRIPTION OF DRAWINGS
[0060] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.
[0061] Figure 1 is the architecture diagram of the enterprise AI workstation system based on private large model of the present application.
[0062] Figure 2 is the private large model training flowchart of the present application.
[0063] Figure 3 is the intelligent collaboration scheduling time sequence diagram of the present application.
[0064] Figure 4 is the decision support logic diagram of the present application. DETAILED DESCRIPTION
[0065] In order to make the technical means, creative features, purposes and effects achieved by the present application easy to understand, the present application will be further described below in combination with specific drawings.
[0066] Referring to Figure 1 , the figure shows an enterprise AI workstation system based on private large model, which includes a hardware base layer 100, an enterprise private large model layer 200, an AI digital employee and robot collaboration layer 300, and a business decision support layer 400.
[0067] The hardware base layer 100 is used to provide computing power, store data, and provide multiple hardware interfaces to connect intelligent robot terminals of different manufacturers. Specifically, the hardware base layer 100 includes a heterogeneous computing power cluster 110, a distributed storage module 120, and an edge interface unit 130.
[0068] The heterogeneous computing cluster 110 includes at least 8 GPU servers, at least 4 CPU servers, and a plurality of FPGA acceleration cards, wherein the GPU servers adopt NVIDIA H20, the CPU servers adopt Intel Xeon Platinum 8592, provide at least 500 TFLOPS AI computing power, and support private large model training, and the single model training period is not greater than 72 hours, and the delay time of real-time inference is not greater than 10 ms.
[0069] The distributed storage module 120 adopts hot and cold data layered storage (hot data SSD, cold data HDD), and supports encrypted storage of enterprise operation data (finance, production, customers, etc.), large model parameters and robot logs. The encrypted storage can adopt an AES-256 algorithm. The capacity of the distributed storage module 120 is not less than 200 TB.
[0070] The edge interface unit 130 is deployed at the production service site, and includes a plurality of hardware interfaces for interfacing with intelligent robot terminals (AGV, mechanical arm, service robot, etc.) of different manufacturers. The hardware interfaces of the edge interface unit include an EtherCAT interface, a USB3.0 interface, and an RS485 interface, and the data transmission rate is not less than 1 Gbps.
[0071] The enterprise private large model layer 200 is used for exclusive model inspection, multi-modal interaction and security audit under the support of the hardware base layer. Specifically, the enterprise private large model layer 200 includes an exclusive training engine 210, a multi-modal interaction module 220, and a security audit unit 230.
[0072] The exclusive training engine 210 is used for fine-tuning a basic large model (such as LLaMA 3, Qwen 2) based on enterprise historical data (operation data in the past 3 years, post process documents), and generating an industry exclusive model (such as a manufacturing model containing a "lean production" knowledge base, and a service model containing a "customer stratification" rule), and the field task accuracy is ≥92%.
[0073] The private large model fine-tuning algorithm of the exclusive training engine 210 is as follows:
[0074] Total loss function
[0075]
[0076] Wherein the parameters are defined as follows:
[0077] α = 0.7, β = 0.2, γ = 0.05, δ = 0.05;
[0078] is a set of field-related data pairs;
[0079] S = {4, 8, 12}: knowledge distillation layer index;
[0080] Sim(.): cosine similarity function.
[0081] Referring to Figure 2 , a private large model training flowchart is given, which includes the following four steps:
[0082] 1. Data collection: collect enterprise historical data, and pre-process the collected data to select a base model;
[0083] 2. Fine-tuning: fine-tune the base large model according to the enterprise historical data;
[0084] 3. Evaluation: evaluate the fine-tuned base large model, and adjust the model parameters according to the evaluation results;
[0085] 4. Deployment: deploy the evaluated base large model online.
[0086] The multi-modal interaction module 220 is used to support text, voice, and image input (voice recognition accuracy ≥ 98.5%, image classification accuracy ≥ 97%), and output adaptive job scenarios, such as visual charts for decision-making suggestions for bosses, and text for AI customer service.
[0087] The security audit unit 230 is used to monitor the large model output in real time (sensitive word filtering accuracy ≥ 99.9%), and record the training data source and model iteration log, in accordance with relevant regulations such as the "Provisional Measures for the Management of Generative Artificial Intelligence Services".
[0088] The AI digital employee and robot collaboration layer 300 is used to generate digital employees, intelligent collaboration scheduling, and adaptive intelligent robot terminals under the support of the enterprise private large model layer. Specifically, the AI digital employee and robot collaboration layer 300 includes a digital employee generation and integration module 310, an intelligent collaboration scheduling engine 320, and a robot protocol adaptation unit 330.
[0089] The digital employee generation and integration module 310 is used to automatically generate new job digital employees (generation cycle ≤ 24 hours) based on private large models and job templates (such as "AI finance" containing "tax reporting-accounting-analysis" skill package), and access existing AI applications (such as deployed AI legal system) through standardized API (OpenAPI 3.0), with data intercommunication rate ≥ 95%;
[0090] The intelligent collaborative scheduling engine 320 is used to decompose enterprise goals (such as "10% increase in monthly production capacity") into digital employee tasks (AI scheduling) and robot tasks (AGV transfer), with a decomposition accuracy of ≥98%, and based on reinforcement learning (PPO algorithm) to dynamically allocate resources. When the robot power is ≤20% or the digital employee computing power is insufficient, trigger task reallocation (response time ≤50ms), and the multi-agent collaborative conflict rate ≤1%.
[0091] The multi-agent collaborative scheduling algorithm used by the intelligent collaborative scheduling engine 320 engine is:
[0092] Reinforcement learning strategy
[0093]
[0094] Real-time reward function
[0095]
[0096] Wherein the variable description is:
[0097] A GAE : Generalized advantage estimation (γ = 0.99, λ = 0.95);
[0098] Path space of robot i;
[0099] T prog : Task progress value (0-1);
[0100] C risk : Collision risk coefficient (0-1).
[0101] Referring to Figure 3 , the intelligent collaborative scheduling timing diagram is shown, and the intelligent collaborative scheduling specifically includes the following steps:
[0102] 1. The boss issues a production target, for example, a 10% increase in monthly production capacity;
[0103] 2. The production target is decomposed and a scheduling plan is generated and sent to the AI digital employee;
[0104] 3. The AI digital employee sends AGV path instructions to the robot cluster according to the scheduling plan, and the robot cluster performs corresponding actions according to the AGV path instructions and feeds back information such as power and position to the AI digital employee in real time;
[0105] 4. When the AI digital employee encounters a conflict during production, it can request resource reallocation and send the received new task to the robot cluster for execution in priority;
[0106] 5. When the robot cluster completes the entire task, the execution completion report is fed back to the decision system, the decision system summarizes and visualizes the execution completion report, and the summarized and visualized board is fed back to the boss.
[0107] The robot protocol adaptation unit 330 is built-in with private protocol analysis libraries of multiple manufacturers (KUKA, ABB, DJI, etc.), and is uniformly converted into the ROS2DDS standard protocol. The new robot terminal access period is ≤24 hours.
[0108] The business decision support layer 400 is used for full-data fusion, intelligent analysis, and decision suggestion generation. Specifically, the business decision support layer 400 includes a full-data fusion module 410, an intelligent analysis engine 420, and a decision suggestion generation module 430.
[0109] The full-data fusion module 410 is used to collect enterprise ERP, CRM, production system, and robot sensor data (daily processing data volume ≥1TB), and form a business data platform through knowledge graph association (entity matching accuracy ≥96%).
[0110] The intelligent analysis engine 420 is used to output key indicator analysis (such as “the core reason for the 3% decline in sales is regional logistics delay”) based on time series prediction (LSTM model) and causal inference (Do-Calculus algorithm), and the analysis accuracy is ≥95%.
[0111] The business decision causal inference algorithm used by the intelligent analysis engine 420 is:
[0112] Causal effect estimation model:
[0113]
[0114] Where:
[0115]
[0116] A=GNN(H) (causal graph adjacency matrix);
[0117] The dynamic resource allocation algorithm used by the intelligent analysis engine 420 is:
[0118] Quantum resource state:
[0119]
[0120] Task evolution operator:
[0121]
[0122] Optimal allocation:
[0123]
[0124] The decision suggestion generation module 430 is used to generate customized suggestions (such as conservative bosses focusing on risk warning and aggressive bosses focusing on opportunity mining) combined with the boss management style (learned through historical decision data), and the suggestion adoption rate is increased by more than 40%.
[0125] Referring to Figure 4 , a decision support logic flowchart is given, and the decision support specifically includes the following steps:
[0126] 1. Data input: Obtain enterprise ERP system (order / stock), CRM system (customer portrait), production sensor (device status) and robot log (execution feedback) data, and fuse these data;
[0127] 2. Intelligent analysis: trend analysis is performed based on time series prediction (LSTM model) to obtain trend analysis results, and root cause positioning analysis is performed based on causal inference (Do-Calculus algorithm) to obtain root cause positioning results, and then the trend analysis results and the root cause positioning results are associated with the knowledge graph;
[0128] 3. Decision suggestion generation: combined with the boss management style (learned through historical decision data), customized suggestions are generated, such as conservative bosses focusing on risk warning and aggressive bosses focusing on opportunity mining.
[0129] The following gives two specific use scenarios of the enterprise AI workstation system based on the private large model of the application:
[0130] Scenario 1: Whole-link management of manufacturing enterprises
[0131] Hardware deployment: heterogeneous computing cluster (10xH20 GPU) processes large model training and production data, and edge interface unit connects 20 AGVs and 5 welding robots;
[0132] Private large model training: fine-tune the basic model based on the production data (orders, equipment failures, quality inspection reports) in the past three years to generate a "special model for automobile parts manufacturing", and the accuracy rate of production parameter optimization suggestions is 94%;
[0133] Collaborative execution:
[0134] The boss sets the goal of "increasing the quarterly production capacity by 15%" → the decision support layer is decomposed into "optimizing production scheduling + improving equipment utilization";
[0135] AI digital employee layer: AI production scheduling and dispatching employee generates new production plan (reduces line change time by 20%), AI equipment administrator predicts failure (accuracy rate 96%);
[0136] Robot coordination layer: intelligent scheduling engine instructs AGV to transport materials according to new plan (path conflict rate 0.5%), welding robot uploads parameters to AI quality inspector in real time;
[0137] Decision support: system discovers "3 pm device energy consumption surge", analyzes reason as "cooling system efficiency decline", pushes "replace filter + adjust production period" suggestion to boss, energy consumption reduces by 8% after implementation.
[0138] After manufacturing scene verification, the system's innovative algorithm achieves the following core index improvements:
[0139] 1. Domain task accuracy Δ_acc = (92% - 60%) / (60%) = +53.3%
[0140] 2. Multi-robot conflict rate Δ_conflict = (1% - 20%) / (20%) = -95.0%
[0141] 3. Decision response delay
[0142] 4. Resource allocation efficiency η = (t_old - t_new) / t_old × 100% = (1000ms - 45ms) / 1000ms × 100% = 95.5%
[0143] Scenario 2: Chain retail business management
[0144] Hardware deployment: computing power cluster processes customer data and store monitoring, edge unit connects 10 store service robots;
[0145] Private large model training: fine-tune model based on member consumption data and promotion records, generate "retail exclusive model", customer churn early warning accuracy 93%;
[0146] Collaborative execution:
[0147] AI telemarketing agent screens high-potential customers (conversion rate increases by 45%), AI customer service follows up after-sales (satisfaction rate 96%);
[0148] Store service robots guide customers and count inventory, data is synchronized to AI warehouse manager in real time (replenishment response time is shortened to 2 hours);
[0149] Decision support: system analyzes "weekend sales decline", attributes to "new competitor promotion + insufficient staff in stores", suggests "targeted discount + dispatch 3 idle robots for support", weekend sales rise by 12% after implementation.
[0150] The above shows and describes the basic principles and main features of the present application and the advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above embodiments, and the above embodiments and descriptions in the specification are only to illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection of the present application is defined by the appended claims and their equivalents.
Claims
1. A private large model-based enterprise AI workstation system, characterized by, Comprise: a hardware base layer for providing computing power, storing data, and providing multiple hardware interfaces to interface with intelligent robot terminals of different manufacturers; an enterprise private large model layer for conducting exclusive model inspection, multi-modal interaction, and security audit under the support of the hardware base layer; an AI digital employee and robot collaboration layer for generating digital employees, intelligent collaboration scheduling, and adapting intelligent robot terminals under the support of the enterprise private large model layer; and an operating decision support layer for conducting full-volume data fusion, intelligent analysis, and generating decision recommendations. The hardware base layer comprises:
2. The private large model based enterprise AI workstation system of claim 1, wherein, a heterogeneous computing power cluster including several GPU servers, several CPU servers, and several FPGA acceleration cards; a distributed storage module that adopts cold and hot data layered storage and supports encrypted storage of enterprise operating data, large model parameters, and robot logs; and an edge interface unit deployed at production service sites, which includes multiple hardware interfaces for interfacing with intelligent robot terminals of different manufacturers. The GPU server adopts NVIDIA H20, the CPU server adopts Intel Xeon Platinum 8592, the heterogeneous computing power cluster provides at least 500 TFLOPS AI computing power and supports private large model training, the single model training period is not more than 72 hours, the real-time inference delay time is not more than 10 ms, the capacity of the distributed storage system is not less than 200 TB, and the hardware interfaces of the edge interface unit include EtherCAT interface, USB3.0 interface, and RS485 interface, with a data transmission rate of not less than 1 Gbps.
3. The private large model based enterprise AI workstation system of claim 2, wherein, The enterprise private large model layer comprises:
4. The private large model based enterprise AI workstation system of claim 1, wherein, an exclusive training engine for fine-tuning a basic large model based on enterprise historical data and generating an industry exclusive model; a multi-modal interaction module for supporting text, voice, and image input and output adapted to the post scenario; and a security audit unit for real-time monitoring of large model output and recording training data sources and model iteration logs in compliance with relevant regulations. The private large model fine-tuning algorithm of the exclusive training engine is a total loss function 5. The private large model based enterprise AI workstation system of claim 4, wherein, The AI digital employee and robot collaboration layer comprises: where the parameters are defined as: a = 0.7, β = 0.2, γ = 0.05, δ = 0.05; S = {4, 8, 12}: knowledge distillation layer indices; Sim(.): cosine similarity function.
6. The private large model based enterprise AI workstation system of claim 1, wherein, a digital employee generation and integration module for automatically generating new post digital employees based on private large models and post templates and accessing existing AI applications through standardized API; an intelligent collaboration scheduling engine for decomposing enterprise goals into digital employee tasks and robot tasks and dynamically allocating resources based on reinforcement learning, triggering task redistribution when robot power ≤ 20% or digital employee computing power is insufficient; and a robot protocol adaptation unit that internally stores private protocol analysis libraries of multiple manufacturers and uniformly converts them into ROS2DDS standard protocols. 7. The private large model based enterprise AI workstation system of claim 6, wherein, The multi-agent collaborative scheduling algorithm adopted by the intelligent collaborative scheduling engine is: Reinforcement learning strategy Real-time reward function where variable explanations: A CAE : generalized advantage estimation (γ = 0.99, λ = 0.95); path space of robot i; T prog : task progress value (0-1); C risk : collision risk coefficient (0-1).
8. The private large model based enterprise AI workstation system of claim 1, wherein, The operation decision support layer includes: A full-amount data fusion module, which is used to collect enterprise ERP, CRM, production system and robot sensor data, and form an operation data platform through knowledge graph association; An intelligent analysis engine, which is used to output key indicator analysis based on time series prediction and causal inference; and A decision suggestion generation module, which is used to generate customized suggestions in combination with the boss's management style.
9. The private large model based enterprise AI workstation system of claim 8, wherein, The operation decision causal inference algorithm adopted by the intelligent analysis engine is: Causal effect estimation model: Wherein: A=GNN(H) (causal graph adjacency matrix); The dynamic resource allocation algorithm adopted by the intelligent analysis engine is: Quantum resource state: Task evolution operator: Optimal allocation: