diff --git a/autogen/agentchat/contrib/reasoning_agent.py b/autogen/agentchat/contrib/reasoning_agent.py index b7ae8fc524..c20f84eaf8 100644 --- a/autogen/agentchat/contrib/reasoning_agent.py +++ b/autogen/agentchat/contrib/reasoning_agent.py @@ -41,7 +41,7 @@ """ -GRADER_message = "Rate the thinking trajectories for score 1 - 5 (1: worst, 5: best)." +GRADER_message = "Rate the response on a scale of 1 to 10 (1 being the worst and 10 being the best)." class ThinkNode: @@ -386,7 +386,7 @@ def rate_node(self, node: ThinkNode, ground_truth: str = None) -> float: if ground_truth: # override the system message self.grader.update_system_message( - f"Rate the trajectory or answer for score 1 - 5 (1: worst, 5: best). The Ground Truth is:\n{ground_truth}" + f"Rate the response on a scale of 1 to 10 (1 being the worst and 10 being the best). Use the following as the evaluation criteria: Ground Truth is:\n{ground_truth}" ) else: self.grader.update_system_message(GRADER_message) @@ -624,7 +624,7 @@ def generate_lats_response(self, messages, sender, config=None): # Helper function to determine if we should continue searching def should_continue(node, iteration): - if self.is_solved(): + if self._root.is_solved(): return False if iteration >= self.lats_max_iterations: return False @@ -654,8 +654,8 @@ def should_continue(node, iteration): request_reply=True, silent=not self.verbose, ) - # TODO: the candidate generation should be done by the assistant agent refer: https://ag2ai.github.io/ag2/docs/notebooks/lats_search/#candidate-generation, - # and im not sure how to do that, so for now we will just use the last message of the thinker + # TODO: the candidate generation should be done different, refer: https://ag2ai.github.io/ag2/docs/notebooks/lats_search/#candidate-generation, + # and im not sure how to approach, so for now we will just use the last message. candidates = re.findall( r"Option \d+:(.+?)(?=Option \d+:|$)", self.thinker.last_message()["content"].strip(), re.DOTALL ) diff --git a/notebook/agentchat_reasoning_agent.ipynb b/notebook/agentchat_reasoning_agent.ipynb index b527203b78..1bce80d029 100644 --- a/notebook/agentchat_reasoning_agent.ipynb +++ b/notebook/agentchat_reasoning_agent.ipynb @@ -75,7 +75,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -2762,7 +2762,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -2784,61 +2784,61 @@ "\u001b[33mtot_thinker\u001b[0m (to reasoning_agent):\n", "\n", "**Reflection** \n", - "The previous steps did not provide clear context on the specifics of the coffee roasting supply chain, such as constraints, objectives, or variables that should be included in the mixed integer linear program (MILP). While identifying key components of the supply chain may have been initiated, critical aspects such as cost factors, production capacities, and demand forecasts remain unaddressed. Clarifying these elements is essential for a well-structured MILP.\n", + "The previous steps in formulating a mixed integer linear program for a coffee roasting supply chain could be lacking specific details such as defining key variables, constraints, and objectives. However, it seems to have established a foundation to work from. Clarifying the scope—like whether to include sourcing, production, or distribution aspects—was not addressed. \n", "\n", "**Possible Options:** \n", - "Option 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints. \n", - "Option 2: Reiterate and clarify the user's objectives and requirements for the mixed integer linear program to ensure all necessary components are included. \n", - "Option 3: Develop an initial model by outlining a basic formulation for the MILP, incorporating variables such as roasting capacity, inventory levels, and delivery logistics. \n", - "Option 4: Gather data and resources related to coffee supply chains, such as supplier availability and pricing structures, to inform the MILP’s constraints and objective function.\n", + "Option 1: Define the key variables involved in the supply chain, such as amounts of coffee beans sourced, roasted, and sold. \n", + "Option 2: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts. \n", + "Option 3: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics. \n", + "Option 4: TERMINATE.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints.\n", + "Step 1: Define the key variables involved in the supply chain, such as amounts of coffee beans sourced, roasted, and sold.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 4\n", + "7\n", "\n", - "Reasoning: The step demonstrates a solid understanding of the fundamental components required for designing a mixed integer linear program. It outlines the necessity of identifying key parameters such as demand, capacity, cost, and time constraints, which are critical for formulating the problem. However, while it is a strong start, it lacks specific examples or details about how to quantify these parameters, which would enhance the clarity and applicability of the approach. A rating of 4 acknowledges the good reasoning while recognizing room for further development.\n", + "This response effectively introduces the task of designing a mixed integer linear program for a coffee roasting supply chain by suggesting the first step: defining key variables. However, it could be improved by providing more detail about what specific variables to consider, such as costs, capacities, and constraints, as well as a brief example of how these variables might be structured in a mathematical model.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Reiterate and clarify the user's objectives and requirements for the mixed integer linear program to ensure all necessary components are included.\n", + "Step 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 5\n", + "8\n", "\n", - "Reasoning: This step effectively prioritizes understanding the user's needs and objectives, which is crucial in designing a mixed integer linear program. By reiterating and clarifying the user’s goals, it ensures that all relevant components will be included in the formulation process. This user-centered approach indicates a thoughtful and comprehensive planning method, laying a strong foundation for subsequent steps in the project. The clarity and focus on requirements justify a rating of 5 for this reasoning trajectory.\n", + "This response is strong as it highlights the importance of identifying and outlining constraints, which is a crucial component in designing a mixed integer linear program (MILP). By focusing on production capacity, storage limits, and demand forecasts, it addresses relevant operational considerations effectively. However, it could be further improved by providing some examples of specific constraints or illustrating how these constraints interact within the supply chain, which would enhance clarity and applicability.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Develop an initial model by outlining a basic formulation for the MILP, incorporating variables such as roasting capacity, inventory levels, and delivery logistics.\n", + "Step 1: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 4\n", + "9\n", "\n", - "Reasoning: This step outlines a proactive approach to developing an initial model for the mixed integer linear program, highlighting the incorporation of essential variables like roasting capacity, inventory levels, and delivery logistics. By focusing on these critical elements, it demonstrates a clear pathway toward a structured mathematical formulation. However, it could benefit from more specificity regarding the relationships between these variables and how they impact the overall supply chain. Without detailing constraints or objective functions associated with the outlined variables, the reasoning is somewhat incomplete. Therefore, it merits a rating of 4, acknowledging its strengths while indicating room for improvement.\n", + "This response effectively outlines an essential step in designing a mixed integer linear program for a coffee roasting supply chain by emphasizing the need to formulate the objective function. By focusing on maximizing profit or minimizing costs, it directly addresses the fundamental goal of optimization in supply chain models. The response is clear and concise, although it could be even stronger if it included a brief example or explanation of how these profits or costs could be calculated based on variables within the supply chain. Overall, it's very effective and relevant to the question.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_thinker):\n", "\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Reiterate and clarify the user's objectives and requirements for the mixed integer linear program to ensure all necessary components are included.\n", + "Step 1: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics.\n", "---\n", "What are the possible next steps?\n", "\n", @@ -2846,64 +2846,68 @@ "\u001b[33mtot_thinker\u001b[0m (to reasoning_agent):\n", "\n", "**Reflection** \n", - "Reiterating and clarifying the user's objectives and requirements is a valuable step in refining the mixed integer linear program (MILP) design process. However, there is a need for more concrete actions following this clarity to formulate the model effectively. Gathering specific data regarding constraints, objectives, and operational details is vital for the successful development of a robust MILP.\n", + "The first step of formulating the objective function is a critical part of the mixed integer linear program (MILP). However, this step may lack clarity in specifying what variables and constraints will directly affect the objective. Understanding the structure of the coffee supply chain—including costs, revenues, and how these are affected by various factors—would enhance the accuracy of the objective function. Now, it's essential to build upon this foundation with a more structured approach.\n", "\n", "**Possible Options:** \n", - "Option 1: Identify specific parameters that need to be included in the MILP, such as the target roast levels, supply costs, and delivery schedules. \n", - "Option 2: Construct a list of potential variables, objective functions, and constraints that reflect the coffee roasting supply chain dynamics and ask the user for their input. \n", - "Option 3: Develop a preliminary MILP framework with hypothetical data to illustrate the structure and seek feedback from the user. \n", - "Option 4: Conduct research into best practices for coffee roasting supply chains to integrate industry standards and benchmarks into the MILP design.\n", + "Option 1: Identify the key variables that will be included in the objective function, such as coffee bean costs, roasting costs, and selling prices. \n", + "Option 2: Develop the constraint equations that reflect the limitations in the roasting capacity, storage, and demand fulfillment. \n", + "Option 3: Ensure to integrate fixed and variable costs into the objective function to have a comprehensive understanding of the profit landscape. \n", + "Option 4: TERMINATE.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Reiterate and clarify the user's objectives and requirements for the mixed integer linear program to ensure all necessary components are included.\n", - "Step 2: Identify specific parameters that need to be included in the MILP, such as the target roast levels, supply costs, and delivery schedules.\n", + "Step 1: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics.\n", + "Step 2: Identify the key variables that will be included in the objective function, such as coffee bean costs, roasting costs, and selling prices.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 5\n", + "8\n", "\n", - "Reasoning: This two-step approach demonstrates a comprehensive understanding of the process required to design a mixed integer linear program. The first step effectively emphasizes the importance of clarifying the user's objectives and requirements, ensuring all relevant factors are considered. The second step builds on this foundation by specifying concrete parameters that should be included in the model, such as target roast levels, supply costs, and delivery schedules, which are vital for accurate formulation. This structured and detailed approach ensures completeness in addressing the problem, justifying a rating of 5 for its clarity, thoroughness, and alignment with best practices for modeling supply chains.\n", + "This response effectively builds on the previous step by adding a second step that highlights the identification of key variables for the objective function. By specifying variables such as coffee bean costs, roasting costs, and selling prices, it provides clarity on what aspects influence the objective. However, it could be improved by mentioning how these variables might interact or contribute analytically to the overall objective function. Including a simple example of how they could be structured could provide additional depth and make the response more comprehensive. Overall, it's a solid answer that covers essential aspects of the task.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Reiterate and clarify the user's objectives and requirements for the mixed integer linear program to ensure all necessary components are included.\n", - "Step 2: Construct a list of potential variables, objective functions, and constraints that reflect the coffee roasting supply chain dynamics and ask the user for their input.\n", + "Step 1: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics.\n", + "Step 2: Develop the constraint equations that reflect the limitations in the roasting capacity, storage, and demand fulfillment.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 5\n", + "9\n", + "\n", + "This response effectively outlines a structured approach to designing a mixed integer linear program (MILP) for a coffee roasting supply chain. By formulating the objective function in Step 1 to maximize profit or minimize costs, it addresses one of the central elements of optimization. Step 2 successfully emphasizes the importance of developing constraint equations that reflect operational limitations, which are critical for practical implementation. \n", "\n", - "Reasoning: The proposed two-step approach is highly effective in establishing a comprehensive foundation for designing a mixed integer linear program. The first step emphasizes the importance of confirming the user's objectives and requirements, which is crucial for ensuring that the subsequent model is relevant and tailored to their needs. The second step advances the process by constructing a list of potential variables, objective functions, and constraints that pertain to the specific dynamics of the coffee roasting supply chain, while also actively seeking user input, promoting collaboration and ensuring that their insights are incorporated. This methodical and user-centered strategy demonstrates clarity, thoroughness, and a solid understanding of modeling practice, justifying a perfect rating of 5.\n", + "To further enhance this response, it could include examples of specific constraint equations or illustrate how the constraints might be formulated based on the variables related to roasting capacity, storage, and demand. Overall, it's a strong and coherent answer that covers key aspects of the task.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Reiterate and clarify the user's objectives and requirements for the mixed integer linear program to ensure all necessary components are included.\n", - "Step 2: Develop a preliminary MILP framework with hypothetical data to illustrate the structure and seek feedback from the user.\n", + "Step 1: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics.\n", + "Step 2: Ensure to integrate fixed and variable costs into the objective function to have a comprehensive understanding of the profit landscape.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 5\n", + "8\n", + "\n", + "This response effectively addresses the need to consider both fixed and variable costs in formulating the objective function, emphasizing a comprehensive understanding of the profit landscape. It reflects an important aspect of mixed integer linear programming (MILP), as both types of costs significantly impact profit calculations. \n", "\n", - "Reasoning: This approach outlines a thorough and effective strategy for developing a mixed integer linear program. The first step emphasizes the importance of reiterating and clarifying the user's objectives and requirements, ensuring that the model aligns with their goals. The second step builds on this foundation by proposing the development of a preliminary MILP framework with hypothetical data. This is an excellent practice, as it helps to illustrate the structure of the model and facilitates user understanding. Additionally, seeking feedback from the user at this stage promotes collaboration and enables adjustments based on their insights. This structured, user-focused method demonstrates clarity and practicality, justifying a rating of 5.\n", + "However, while it provides good insight, it could be improved by offering specific examples or defining what constitutes fixed versus variable costs in the context of a coffee roasting supply chain. Additionally, a brief overview of how these costs interact within the objective function or a formula would provide further clarity. Overall, it's a solid response that captures essential considerations in MILP formulation.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_thinker):\n", "\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints.\n", + "Step 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.\n", "---\n", "What are the possible next steps?\n", "\n", @@ -2911,274 +2915,260 @@ "\u001b[33mtot_thinker\u001b[0m (to reasoning_agent):\n", "\n", "**Reflection** \n", - "Identifying and defining key parameters for the coffee roasting supply chain is a crucial step in designing the mixed integer linear program (MILP). This foundational work sets the stage for constructing a well-informed model. However, without a clear progression to integrate these parameters into a cohesive framework, the process may stall. It's essential to translate these identified parameters into a structured model that captures the complexity of the supply chain.\n", + "Identifying and outlining the constraints related to production capacity, storage limits, and demand forecasts is a crucial step for formulating a mixed integer linear program (MILP). However, it is important to ensure these constraints are comprehensive and consider all aspects of the supply chain. There may be further refinement needed to quantify these constraints effectively and to ensure they are feasible in the context of the coffee roasting supply chain. Building on these identified constraints will enhance the program's robustness.\n", "\n", "**Possible Options:** \n", - "Option 1: Formulate the objective function of the MILP considering the identified key parameters and clarify what the model aims to optimize (e.g., minimizing costs, maximizing efficiency). \n", - "Option 2: Outline the constraints of the MILP based on the defined parameters, ensuring operational limits are accurately represented. \n", - "Option 3: Create a visual representation (such as a flowchart) of the coffee roasting supply chain incorporating the key parameters for easier understanding and communication. \n", - "Option 4: Gather empirical data to populate the identified parameters accurately, ensuring the model reflects real-world conditions and scenarios.\n", + "Option 1: Validate the constraints by testing them against real-world data to ensure they are realistic and achievable. \n", + "Option 2: Define the decision variables that will interact with these constraints, such as quantities of coffee roasted, costs incurred, and inventory levels. \n", + "Option 3: Formulate the non-negativity constraints to ensure that decision variables, such as inventory and production quantities, remain positive. \n", + "Option 4: TERMINATE.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints.\n", - "Step 2: Formulate the objective function of the MILP considering the identified key parameters and clarify what the model aims to optimize (e.g., minimizing costs, maximizing efficiency).\n", + "Step 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.\n", + "Step 2: Validate the constraints by testing them against real-world data to ensure they are realistic and achievable.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 5\n", + "9\n", + "\n", + "This response offers a clear and logical progression in designing a mixed integer linear program (MILP) for a coffee roasting supply chain. Step 1 effectively focuses on identifying and outlining constraints, which is vital for ensuring the program's feasibility. Step 2 enhances the approach by emphasizing the importance of validating these constraints against real-world data, promoting a practical application of the model.\n", "\n", - "Reasoning: This two-step approach is well-structured and effectively addresses the components needed to design a mixed integer linear program for a coffee roasting supply chain. The first step clearly establishes the need to identify and define key parameters, such as demand, capacity, cost, and time constraints, which are essential for the model's foundation. The second step logically follows by formulating the objective function, specifying the aims of the optimization process (e.g., minimizing costs, maximizing efficiency). This direct connection between the parameters and the objective function demonstrates a clear understanding of how to structure the MILP. The clarity and focus on essential aspects both support a comprehensive model and justify a perfect rating of 5.\n", + "However, to improve it further, the response could provide specifics on how to conduct this validation process or mention types of real-world data that could be useful. Including an example of how to assess the realism of a specific constraint would also add depth. Overall, it's a strong answer that captures critical aspects of designing a MILP while establishing a connection to real-world application.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints.\n", - "Step 2: Outline the constraints of the MILP based on the defined parameters, ensuring operational limits are accurately represented.\n", + "Step 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.\n", + "Step 2: Define the decision variables that will interact with these constraints, such as quantities of coffee roasted, costs incurred, and inventory levels.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 5\n", + "8\n", + "\n", + "This response provides a clear and logical approach to the task of designing a mixed integer linear program (MILP) for a coffee roasting supply chain. Step 1 focuses on identifying and outlining the relevant constraints, which is crucial for establishing the framework of the program. Step 2 effectively emphasizes the need to define decision variables that interact with these constraints, such as quantities of coffee roasted, costs incurred, and inventory levels, which is fundamental for optimization.\n", "\n", - "Reasoning: This two-step approach is effective in systematically addressing the design of a mixed integer linear program for a coffee roasting supply chain. The first step emphasizes the importance of identifying and defining key parameters, which is crucial for understanding the operational framework and ensuring that all relevant factors are included in the model. The second step builds upon this foundation by explicitly outlining the constraints of the MILP based on the defined parameters, which is essential for accurately representing operational limits and ensuring that the model is both realistic and applicable. This clear and logical progression demonstrates a strong grasp of modeling principles, thoroughness, and attention to detail, justifying a rating of 5.\n", + "To enhance this response, it could provide examples of specific decision variables and illustrate how they would be mathematically represented within the context of the MILP. Additionally, mentioning how these variables directly relate to the previously outlined constraints could strengthen the connection between the steps. Overall, it is a solid answer that covers key aspects of the task.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to tot_grader):\n", "\n", "Rate:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints.\n", - "Step 2: Create a visual representation (such as a flowchart) of the coffee roasting supply chain incorporating the key parameters for easier understanding and communication.\n", + "Step 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.\n", + "Step 2: Formulate the non-negativity constraints to ensure that decision variables, such as inventory and production quantities, remain positive.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mtot_grader\u001b[0m (to reasoning_agent):\n", "\n", - "Rating: 4\n", + "9\n", + "\n", + "This response presents a clear and logical framework for designing a mixed integer linear program (MILP) for a coffee roasting supply chain. Step 1 effectively establishes the foundation by identifying constraints related to production capacity, storage limits, and demand forecasts, which are critical elements in supply chain optimization. Step 2 highlights the essential aspect of formulating non-negativity constraints, ensuring that decision variables, like inventory levels and production quantities, are realistic by not allowing negative values.\n", "\n", - "Reasoning: This two-step approach is effective and demonstrates a solid understanding of the importance of both identifying key parameters and enhancing communication through visual representation. The first step adequately identifies essential components such as demand, capacity, cost, and time constraints, which are critical for modeling the coffee roasting supply chain. The second step introduces a valuable strategy by suggesting the creation of a visual representation, like a flowchart, to improve understanding and facilitate clearer communication of the supply chain dynamics. However, while this visual method is beneficial, the effectiveness of the flowchart depends on its execution and clarity in depicting the relationships among parameters. If the visual representation is poorly designed or lacks detail, it could diminish its intended benefit. Therefore, a rating of 4 reflects this potential, acknowledging the effectiveness of the approach while recognizing that successful implementation is key.\n", + "To enhance the response, it could include examples of how non-negativity constraints might be expressed mathematically or provide context on why adhering to these constraints is crucial in supply chain management. Nevertheless, the answer is solid and thoroughly addresses key components of the task.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to reasoning_agent):\n", "\n", "Answer the question Design a mixed integer linear program for a coffee roasting supply chain. Here is my thinking process:\n", "# Question: Design a mixed integer linear program for a coffee roasting supply chain\n", - "Step 1: Reiterate and clarify the user's objectives and requirements for the mixed integer linear program to ensure all necessary components are included.\n", - "Step 2: Identify specific parameters that need to be included in the MILP, such as the target roast levels, supply costs, and delivery schedules.\n", + "Step 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.\n", + "Step 2: Validate the constraints by testing them against real-world data to ensure they are realistic and achievable.\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to reasoning_agent):\n", "\n", - "To design a mixed integer linear program (MILP) for a coffee roasting supply chain, we need to clarify the objectives and requirements. Here’s the approach we'll take:\n", + "To design a mixed integer linear program (MILP) for a coffee roasting supply chain, we need to establish a model that incorporates the various components and constraints within the supply chain. Here’s how we can approach this:\n", "\n", - "### Step 1: Objectives and Requirements\n", - "- Determine key objectives: Cost minimization, maximizing quality, or meeting customer demand.\n", - "- Identify constraints: Capacity of roasters, delivery schedule, quality specifications, and storage limits.\n", - "- Specify decision variables: Amount of each coffee type to roast, scheduling of roasting times, etc.\n", + "### Step 1: Define the Components and Constraints\n", "\n", - "### Step 2: Define Parameters\n", "1. **Decision Variables**:\n", - " - Let \\( x_{ij} \\) be the amount of coffee type \\( i \\) roasted at facility \\( j \\).\n", - " - Let \\( y_j \\) be a binary variable representing whether facility \\( j \\) is operating (1) or not (0).\n", - "\n", - "2. **Parameters**:\n", - " - \\( C_{ij} \\): Cost of roasting coffee type \\( i \\) at facility \\( j \\).\n", - " - \\( D_i \\): Demand for coffee type \\( i \\).\n", - " - \\( K_j \\): Capacity of facility \\( j \\).\n", - " - \\( R_{ij} \\): Roast level for coffee type \\( i \\) at facility \\( j \\).\n", - "\n", - "3. **Objective Function**:\n", - " Minimize total cost:\n", - " \\[\n", - " \\text{Minimize} \\quad Z = \\sum_{i}\\sum_{j}C_{ij}x_{ij}\n", - " \\]\n", - "\n", - "4. **Constraints**:\n", - " - Meeting demand:\n", - " \\[\n", - " \\sum_{j} x_{ij} \\geq D_i \\quad \\forall i\n", - " \\]\n", - " - Capacity limits:\n", - " \\[\n", - " \\sum_{i} x_{ij} \\leq K_j \\cdot y_j \\quad \\forall j\n", - " \\]\n", - " - Binary constraint for facilities:\n", - " \\[\n", - " y_j \\in \\{0, 1\\} \\quad \\forall j\n", - " \\]\n", - "\n", - "### Step 3: Model Formulation\n", - "Combine the components into a coherent model. Here is a structured MILP formulation:\n", - "\n", - "\\[\n", - "\\begin{align*}\n", - "\\text{Minimize } & Z = \\sum_{i}\\sum_{j}C_{ij}x_{ij} \\\\\n", - "\\text{Subject to:} \\\\\n", - "& \\sum_{j} x_{ij} \\geq D_i \\quad \\forall i \\\\\n", - "& \\sum_{i} x_{ij} \\leq K_j \\cdot y_j \\quad \\forall j \\\\\n", - "& x_{ij} \\geq 0 \\quad \\forall i, j \\\\\n", - "& y_j \\in \\{0, 1\\} \\quad \\forall j \n", - "\\end{align*}\n", - "\\]\n", - "\n", - "### Step 4: Implementation in Python\n", - "To solve this MILP problem, we can use libraries such as `PuLP` or `Gurobi`. Here's a simple implementation using `PuLP`:\n", + " - Let \\( x_i \\) be the quantity of type \\( i \\) coffee produced.\n", + " - Let \\( y_j \\) be the binary variable indicating whether roasting facility \\( j \\) is open (1) or closed (0).\n", + " - Let \\( z_k \\) be the quantity of coffee stored in warehouse \\( k \\).\n", + "\n", + "2. **Objective Function**:\n", + " - The goal of the MILP could be to maximize profit or minimize costs. We can define the profit earned from coffee sales minus the costs of production and storage. This can be represented mathematically as:\n", + " \\[\n", + " \\text{Maximize } Z = \\sum_{i} (p_i \\cdot x_i) - \\sum_{j} (c_j \\cdot y_j) - \\sum_{k} (s_k \\cdot z_k)\n", + " \\]\n", + " where \\( p_i \\) is the price per unit of coffee type \\( i \\), \\( c_j \\) is the cost of operating facility \\( j \\), and \\( s_k \\) is the storage cost at warehouse \\( k \\).\n", + "\n", + "3. **Constraints**:\n", + " - **Production Capacity**:\n", + " \\[\n", + " x_i \\leq C_j \\cdot y_j \\quad \\forall i, j\n", + " \\]\n", + " This ensures that production does not exceed the capacity of open facilities.\n", + "\n", + " - **Demand Constraints**:\n", + " \\[\n", + " x_i \\geq D_i \\quad \\forall i\n", + " \\]\n", + " where \\( D_i \\) is the forecasted demand for coffee type \\( i \\).\n", + "\n", + " - **Storage Constraints**:\n", + " \\[\n", + " z_k \\leq S_k \\quad \\forall k\n", + " \\]\n", + " where \\( S_k \\) is the storage capacity of warehouse \\( k \\).\n", + "\n", + " - **Flow Conservation**:\n", + " \\[\n", + " \\sum_{i} x_i - \\sum_{k} z_k = 0\n", + " \\]\n", + " This ensures that the coffee produced is stored or used.\n", + "\n", + "### Step 2: Validate the Constraints\n", + "\n", + "To validate these constraints, we would typically:\n", + "- Collect data on actual production capacities, storage limits, and demand forecasts from the coffee roasting supply chain.\n", + "- Run simulations or historical analysis to ensure these constraints hold true, adjusting them as needed based on the real-world operation of the supply chain.\n", + "\n", + "If we were to implement this model, we would typically use a mathematical programming library (such as PuLP or Gurobi in Python) to solve it. This would involve plugging in actual data and using the solver to find the optimal production schedule, facility utilization, and storage allocation.\n", + "\n", + "### Example Formulation\n", + "\n", + "Below is an extracted example of how this MILP might be structured programmatically.\n", "\n", "```python\n", "# filename: coffee_roasting_milp.py\n", - "from pulp import LpProblem, LpMinimize, LpVariable, lpSum, LpBinary\n", + "from pulp import LpProblem, LpMaximize, LpVariable, lpSum, LpBinary\n", "\n", - "# Initialize the model\n", - "model = LpProblem(\"Coffee_Roasting_Supply_Chain\", LpMinimize)\n", + "# Create the model\n", + "model = LpProblem(\"Coffee_Roasting_Supply_Chain\", LpMaximize)\n", "\n", - "# Sample data (to be replaced with actual data)\n", - "coffee_types = ['A', 'B'] # Adjust as needed\n", - "facilities = ['F1', 'F2'] # Adjust as needed\n", - "C = {('A', 'F1'): 2, ('A', 'F2'): 3, ('B', 'F1'): 2.5, ('B', 'F2'): 3.5} # Costs\n", - "D = {'A': 100, 'B': 150} # Demand\n", - "K = {'F1': 120, 'F2': 180} # Capacity\n", + "# Decision Variables\n", + "x = LpVariable.dicts(\"Production\", coffee_types, lowBound=0)\n", + "y = LpVariable.dicts(\"Open_Facility\", facilities, cat=LpBinary)\n", + "z = LpVariable.dicts(\"Storage\", warehouses, lowBound=0)\n", "\n", - "# Decision variables\n", - "x = LpVariable.dicts(\"roast\", [(i, j) for i in coffee_types for j in facilities], lowBound=0)\n", - "y = LpVariable.dicts(\"facility\", facilities, cat=LpBinary)\n", + "# Objective Function\n", + "model += lpSum(profit[i] * x[i] for i in coffee_types) - lpSum(costs[j] * y[j] for j in facilities) - lpSum(storage_costs[k] * z[k] for k in warehouses)\n", "\n", - "# Objective function\n", - "model += lpSum(C[i,j] * x[i,j] for i in coffee_types for j in facilities)\n", + "# Constraints\n", + "for j in facilities:\n", + " model += lpSum(x[i] for i in coffee_types) <= capacity[j] * y[j]\n", "\n", - "# Demand constraints\n", "for i in coffee_types:\n", - " model += lpSum(x[i, j] for j in facilities) >= D[i]\n", + " model += x[i] >= demand[i]\n", "\n", - "# Capacity constraints\n", - "for j in facilities:\n", - " model += lpSum(x[i, j] for i in coffee_types) <= K[j] * y[j]\n", + "for k in warehouses:\n", + " model += z[k] <= capacity[k]\n", + "\n", + "model += lpSum(x[i] for i in coffee_types) - lpSum(z[k] for k in warehouses) == 0\n", "\n", "# Solve the model\n", "model.solve()\n", - "\n", - "# Output results\n", - "for i in coffee_types:\n", - " for j in facilities:\n", - " print(f\"Amount of coffee {i} roasted at {j}: {x[i,j].varValue}\")\n", - "for j in facilities:\n", - " print(f\"Facility {j} operating: {y[j].varValue}\")\n", + "print(\"Status:\", model.status)\n", + "print(\"Production quantities:\", {i: x[i].varValue for i in coffee_types})\n", + "print(\"Open facilities:\", {j: y[j].varValue for j in facilities})\n", + "print(\"Stored quantities:\", {k: z[k].varValue for k in warehouses})\n", "```\n", "\n", - "This code initializes a MILP model, defines decision variables, sets an objective function, adds constraints, solves the model, and prints the result.\n", - "\n", - "### Conclusion\n", - "You can run the above code to obtain the results of your coffee roasting supply chain optimization.\n", + "This code snippet is a starting point framework for designing a MILP for coffee roasting supply chains. \n", "\n", "TERMINATE\n", "\n", "--------------------------------------------------------------------------------\n", "\u001b[33mreasoning_agent\u001b[0m (to user):\n", "\n", - "To design a mixed integer linear program (MILP) for a coffee roasting supply chain, we need to clarify the objectives and requirements. Here’s the approach we'll take:\n", + "To design a mixed integer linear program (MILP) for a coffee roasting supply chain, we need to establish a model that incorporates the various components and constraints within the supply chain. Here’s how we can approach this:\n", "\n", - "### Step 1: Objectives and Requirements\n", - "- Determine key objectives: Cost minimization, maximizing quality, or meeting customer demand.\n", - "- Identify constraints: Capacity of roasters, delivery schedule, quality specifications, and storage limits.\n", - "- Specify decision variables: Amount of each coffee type to roast, scheduling of roasting times, etc.\n", + "### Step 1: Define the Components and Constraints\n", "\n", - "### Step 2: Define Parameters\n", "1. **Decision Variables**:\n", - " - Let \\( x_{ij} \\) be the amount of coffee type \\( i \\) roasted at facility \\( j \\).\n", - " - Let \\( y_j \\) be a binary variable representing whether facility \\( j \\) is operating (1) or not (0).\n", - "\n", - "2. **Parameters**:\n", - " - \\( C_{ij} \\): Cost of roasting coffee type \\( i \\) at facility \\( j \\).\n", - " - \\( D_i \\): Demand for coffee type \\( i \\).\n", - " - \\( K_j \\): Capacity of facility \\( j \\).\n", - " - \\( R_{ij} \\): Roast level for coffee type \\( i \\) at facility \\( j \\).\n", - "\n", - "3. **Objective Function**:\n", - " Minimize total cost:\n", - " \\[\n", - " \\text{Minimize} \\quad Z = \\sum_{i}\\sum_{j}C_{ij}x_{ij}\n", - " \\]\n", - "\n", - "4. **Constraints**:\n", - " - Meeting demand:\n", - " \\[\n", - " \\sum_{j} x_{ij} \\geq D_i \\quad \\forall i\n", - " \\]\n", - " - Capacity limits:\n", - " \\[\n", - " \\sum_{i} x_{ij} \\leq K_j \\cdot y_j \\quad \\forall j\n", - " \\]\n", - " - Binary constraint for facilities:\n", - " \\[\n", - " y_j \\in \\{0, 1\\} \\quad \\forall j\n", - " \\]\n", - "\n", - "### Step 3: Model Formulation\n", - "Combine the components into a coherent model. Here is a structured MILP formulation:\n", - "\n", - "\\[\n", - "\\begin{align*}\n", - "\\text{Minimize } & Z = \\sum_{i}\\sum_{j}C_{ij}x_{ij} \\\\\n", - "\\text{Subject to:} \\\\\n", - "& \\sum_{j} x_{ij} \\geq D_i \\quad \\forall i \\\\\n", - "& \\sum_{i} x_{ij} \\leq K_j \\cdot y_j \\quad \\forall j \\\\\n", - "& x_{ij} \\geq 0 \\quad \\forall i, j \\\\\n", - "& y_j \\in \\{0, 1\\} \\quad \\forall j \n", - "\\end{align*}\n", - "\\]\n", - "\n", - "### Step 4: Implementation in Python\n", - "To solve this MILP problem, we can use libraries such as `PuLP` or `Gurobi`. Here's a simple implementation using `PuLP`:\n", + " - Let \\( x_i \\) be the quantity of type \\( i \\) coffee produced.\n", + " - Let \\( y_j \\) be the binary variable indicating whether roasting facility \\( j \\) is open (1) or closed (0).\n", + " - Let \\( z_k \\) be the quantity of coffee stored in warehouse \\( k \\).\n", + "\n", + "2. **Objective Function**:\n", + " - The goal of the MILP could be to maximize profit or minimize costs. We can define the profit earned from coffee sales minus the costs of production and storage. This can be represented mathematically as:\n", + " \\[\n", + " \\text{Maximize } Z = \\sum_{i} (p_i \\cdot x_i) - \\sum_{j} (c_j \\cdot y_j) - \\sum_{k} (s_k \\cdot z_k)\n", + " \\]\n", + " where \\( p_i \\) is the price per unit of coffee type \\( i \\), \\( c_j \\) is the cost of operating facility \\( j \\), and \\( s_k \\) is the storage cost at warehouse \\( k \\).\n", + "\n", + "3. **Constraints**:\n", + " - **Production Capacity**:\n", + " \\[\n", + " x_i \\leq C_j \\cdot y_j \\quad \\forall i, j\n", + " \\]\n", + " This ensures that production does not exceed the capacity of open facilities.\n", + "\n", + " - **Demand Constraints**:\n", + " \\[\n", + " x_i \\geq D_i \\quad \\forall i\n", + " \\]\n", + " where \\( D_i \\) is the forecasted demand for coffee type \\( i \\).\n", + "\n", + " - **Storage Constraints**:\n", + " \\[\n", + " z_k \\leq S_k \\quad \\forall k\n", + " \\]\n", + " where \\( S_k \\) is the storage capacity of warehouse \\( k \\).\n", + "\n", + " - **Flow Conservation**:\n", + " \\[\n", + " \\sum_{i} x_i - \\sum_{k} z_k = 0\n", + " \\]\n", + " This ensures that the coffee produced is stored or used.\n", + "\n", + "### Step 2: Validate the Constraints\n", + "\n", + "To validate these constraints, we would typically:\n", + "- Collect data on actual production capacities, storage limits, and demand forecasts from the coffee roasting supply chain.\n", + "- Run simulations or historical analysis to ensure these constraints hold true, adjusting them as needed based on the real-world operation of the supply chain.\n", + "\n", + "If we were to implement this model, we would typically use a mathematical programming library (such as PuLP or Gurobi in Python) to solve it. This would involve plugging in actual data and using the solver to find the optimal production schedule, facility utilization, and storage allocation.\n", + "\n", + "### Example Formulation\n", + "\n", + "Below is an extracted example of how this MILP might be structured programmatically.\n", "\n", "```python\n", "# filename: coffee_roasting_milp.py\n", - "from pulp import LpProblem, LpMinimize, LpVariable, lpSum, LpBinary\n", + "from pulp import LpProblem, LpMaximize, LpVariable, lpSum, LpBinary\n", "\n", - "# Initialize the model\n", - "model = LpProblem(\"Coffee_Roasting_Supply_Chain\", LpMinimize)\n", + "# Create the model\n", + "model = LpProblem(\"Coffee_Roasting_Supply_Chain\", LpMaximize)\n", "\n", - "# Sample data (to be replaced with actual data)\n", - "coffee_types = ['A', 'B'] # Adjust as needed\n", - "facilities = ['F1', 'F2'] # Adjust as needed\n", - "C = {('A', 'F1'): 2, ('A', 'F2'): 3, ('B', 'F1'): 2.5, ('B', 'F2'): 3.5} # Costs\n", - "D = {'A': 100, 'B': 150} # Demand\n", - "K = {'F1': 120, 'F2': 180} # Capacity\n", + "# Decision Variables\n", + "x = LpVariable.dicts(\"Production\", coffee_types, lowBound=0)\n", + "y = LpVariable.dicts(\"Open_Facility\", facilities, cat=LpBinary)\n", + "z = LpVariable.dicts(\"Storage\", warehouses, lowBound=0)\n", "\n", - "# Decision variables\n", - "x = LpVariable.dicts(\"roast\", [(i, j) for i in coffee_types for j in facilities], lowBound=0)\n", - "y = LpVariable.dicts(\"facility\", facilities, cat=LpBinary)\n", + "# Objective Function\n", + "model += lpSum(profit[i] * x[i] for i in coffee_types) - lpSum(costs[j] * y[j] for j in facilities) - lpSum(storage_costs[k] * z[k] for k in warehouses)\n", "\n", - "# Objective function\n", - "model += lpSum(C[i,j] * x[i,j] for i in coffee_types for j in facilities)\n", + "# Constraints\n", + "for j in facilities:\n", + " model += lpSum(x[i] for i in coffee_types) <= capacity[j] * y[j]\n", "\n", - "# Demand constraints\n", "for i in coffee_types:\n", - " model += lpSum(x[i, j] for j in facilities) >= D[i]\n", + " model += x[i] >= demand[i]\n", "\n", - "# Capacity constraints\n", - "for j in facilities:\n", - " model += lpSum(x[i, j] for i in coffee_types) <= K[j] * y[j]\n", + "for k in warehouses:\n", + " model += z[k] <= capacity[k]\n", + "\n", + "model += lpSum(x[i] for i in coffee_types) - lpSum(z[k] for k in warehouses) == 0\n", "\n", "# Solve the model\n", "model.solve()\n", - "\n", - "# Output results\n", - "for i in coffee_types:\n", - " for j in facilities:\n", - " print(f\"Amount of coffee {i} roasted at {j}: {x[i,j].varValue}\")\n", - "for j in facilities:\n", - " print(f\"Facility {j} operating: {y[j].varValue}\")\n", + "print(\"Status:\", model.status)\n", + "print(\"Production quantities:\", {i: x[i].varValue for i in coffee_types})\n", + "print(\"Open facilities:\", {j: y[j].varValue for j in facilities})\n", + "print(\"Stored quantities:\", {k: z[k].varValue for k in warehouses})\n", "```\n", "\n", - "This code initializes a MILP model, defines decision variables, sets an objective function, adds constraints, solves the model, and prints the result.\n", - "\n", - "### Conclusion\n", - "You can run the above code to obtain the results of your coffee roasting supply chain optimization.\n", + "This code snippet is a starting point framework for designing a MILP for coffee roasting supply chains. \n", "\n", "TERMINATE\n", "\n", @@ -3216,40 +3206,155 @@ ")\n", "\n", "ans = user_proxy.initiate_chat(\n", - " reason_agent, message=\"Design a mixed integer linear program for a coffee roasting supply chain\"\n", + " reason_agent,\n", + " message=\"Design a mixed integer linear program for a coffee roasting supply chain\",\n", + " summary_method=last_meaningful_msg,\n", ")" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "To design a mixed integer linear program (MILP) for a coffee roasting supply chain, we need to establish a model that incorporates the various components and constraints within the supply chain. Here’s how we can approach this:\n", + "\n", + "### Step 1: Define the Components and Constraints\n", + "\n", + "1. **Decision Variables**:\n", + " - Let \\( x_i \\) be the quantity of type \\( i \\) coffee produced.\n", + " - Let \\( y_j \\) be the binary variable indicating whether roasting facility \\( j \\) is open (1) or closed (0).\n", + " - Let \\( z_k \\) be the quantity of coffee stored in warehouse \\( k \\).\n", + "\n", + "2. **Objective Function**:\n", + " - The goal of the MILP could be to maximize profit or minimize costs. We can define the profit earned from coffee sales minus the costs of production and storage. This can be represented mathematically as:\n", + " \\[\n", + " \\text{Maximize } Z = \\sum_{i} (p_i \\cdot x_i) - \\sum_{j} (c_j \\cdot y_j) - \\sum_{k} (s_k \\cdot z_k)\n", + " \\]\n", + " where \\( p_i \\) is the price per unit of coffee type \\( i \\), \\( c_j \\) is the cost of operating facility \\( j \\), and \\( s_k \\) is the storage cost at warehouse \\( k \\).\n", + "\n", + "3. **Constraints**:\n", + " - **Production Capacity**:\n", + " \\[\n", + " x_i \\leq C_j \\cdot y_j \\quad \\forall i, j\n", + " \\]\n", + " This ensures that production does not exceed the capacity of open facilities.\n", + "\n", + " - **Demand Constraints**:\n", + " \\[\n", + " x_i \\geq D_i \\quad \\forall i\n", + " \\]\n", + " where \\( D_i \\) is the forecasted demand for coffee type \\( i \\).\n", + "\n", + " - **Storage Constraints**:\n", + " \\[\n", + " z_k \\leq S_k \\quad \\forall k\n", + " \\]\n", + " where \\( S_k \\) is the storage capacity of warehouse \\( k \\).\n", + "\n", + " - **Flow Conservation**:\n", + " \\[\n", + " \\sum_{i} x_i - \\sum_{k} z_k = 0\n", + " \\]\n", + " This ensures that the coffee produced is stored or used.\n", + "\n", + "### Step 2: Validate the Constraints\n", + "\n", + "To validate these constraints, we would typically:\n", + "- Collect data on actual production capacities, storage limits, and demand forecasts from the coffee roasting supply chain.\n", + "- Run simulations or historical analysis to ensure these constraints hold true, adjusting them as needed based on the real-world operation of the supply chain.\n", + "\n", + "If we were to implement this model, we would typically use a mathematical programming library (such as PuLP or Gurobi in Python) to solve it. This would involve plugging in actual data and using the solver to find the optimal production schedule, facility utilization, and storage allocation.\n", + "\n", + "### Example Formulation\n", + "\n", + "Below is an extracted example of how this MILP might be structured programmatically.\n", + "\n", + "```python\n", + "# filename: coffee_roasting_milp.py\n", + "from pulp import LpProblem, LpMaximize, LpVariable, lpSum, LpBinary\n", + "\n", + "# Create the model\n", + "model = LpProblem(\"Coffee_Roasting_Supply_Chain\", LpMaximize)\n", + "\n", + "# Decision Variables\n", + "x = LpVariable.dicts(\"Production\", coffee_types, lowBound=0)\n", + "y = LpVariable.dicts(\"Open_Facility\", facilities, cat=LpBinary)\n", + "z = LpVariable.dicts(\"Storage\", warehouses, lowBound=0)\n", + "\n", + "# Objective Function\n", + "model += lpSum(profit[i] * x[i] for i in coffee_types) - lpSum(costs[j] * y[j] for j in facilities) - lpSum(storage_costs[k] * z[k] for k in warehouses)\n", + "\n", + "# Constraints\n", + "for j in facilities:\n", + " model += lpSum(x[i] for i in coffee_types) <= capacity[j] * y[j]\n", + "\n", + "for i in coffee_types:\n", + " model += x[i] >= demand[i]\n", + "\n", + "for k in warehouses:\n", + " model += z[k] <= capacity[k]\n", + "\n", + "model += lpSum(x[i] for i in coffee_types) - lpSum(z[k] for k in warehouses) == 0\n", + "\n", + "# Solve the model\n", + "model.solve()\n", + "print(\"Status:\", model.status)\n", + "print(\"Production quantities:\", {i: x[i].varValue for i in coffee_types})\n", + "print(\"Open facilities:\", {j: y[j].varValue for j in facilities})\n", + "print(\"Stored quantities:\", {k: z[k].varValue for k in warehouses})\n", + "```\n", + "\n", + "This code snippet is a starting point framework for designing a MILP for coffee roasting supply chains. \n", + "\n", + "\n" + ] + } + ], + "source": [ + "print(ans.summary)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "5\n" + "3\n" ] }, { "data": { "text/plain": [ "[{'instruction': '# Question: Design a mixed integer linear program for a coffee roasting supply chain',\n", - " 'preferred_response': 'Step 1: Develop an initial model by outlining a basic formulation for the MILP, incorporating variables such as roasting capacity, inventory levels, and delivery logistics.',\n", - " 'dispreferred_response': 'Step 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints.'},\n", + " 'preferred_response': 'Step 1: Define the key variables involved in the supply chain, such as amounts of coffee beans sourced, roasted, and sold.',\n", + " 'dispreferred_response': 'Step 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.'},\n", " {'instruction': '# Question: Design a mixed integer linear program for a coffee roasting supply chain',\n", - " 'preferred_response': 'Step 1: Develop an initial model by outlining a basic formulation for the MILP, incorporating variables such as roasting capacity, inventory levels, and delivery logistics.',\n", - " 'dispreferred_response': \"Step 1: Reiterate and clarify the user's objectives and requirements for the mixed integer linear program to ensure all necessary components are included.\"},\n", - " {'instruction': '# Question: Design a mixed integer linear program for a coffee roasting supply chain\\nStep 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints.',\n", - " 'preferred_response': 'Step 2: Formulate the objective function of the MILP considering the identified key parameters and clarify what the model aims to optimize (e.g., minimizing costs, maximizing efficiency).',\n", - " 'dispreferred_response': 'Step 2: Create a visual representation (such as a flowchart) of the coffee roasting supply chain incorporating the key parameters for easier understanding and communication.'},\n", - " {'instruction': '# Question: Design a mixed integer linear program for a coffee roasting supply chain\\nStep 1: Identify and define key parameters for the coffee roasting supply chain, including demand, capacity, cost, and time constraints.',\n", - " 'preferred_response': 'Step 2: Outline the constraints of the MILP based on the defined parameters, ensuring operational limits are accurately represented.',\n", - " 'dispreferred_response': 'Step 2: Create a visual representation (such as a flowchart) of the coffee roasting supply chain incorporating the key parameters for easier understanding and communication.'}]" + " 'preferred_response': 'Step 1: Define the key variables involved in the supply chain, such as amounts of coffee beans sourced, roasted, and sold.',\n", + " 'dispreferred_response': 'Step 1: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics.'},\n", + " {'instruction': '# Question: Design a mixed integer linear program for a coffee roasting supply chain\\nStep 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.',\n", + " 'preferred_response': 'Step 2: Validate the constraints by testing them against real-world data to ensure they are realistic and achievable.',\n", + " 'dispreferred_response': 'Step 2: Define the decision variables that will interact with these constraints, such as quantities of coffee roasted, costs incurred, and inventory levels.'},\n", + " {'instruction': '# Question: Design a mixed integer linear program for a coffee roasting supply chain\\nStep 1: Identify and outline the constraints related to production capacity, storage limits, and demand forecasts.',\n", + " 'preferred_response': 'Step 2: Formulate the non-negativity constraints to ensure that decision variables, such as inventory and production quantities, remain positive.',\n", + " 'dispreferred_response': 'Step 2: Define the decision variables that will interact with these constraints, such as quantities of coffee roasted, costs incurred, and inventory levels.'},\n", + " {'instruction': '# Question: Design a mixed integer linear program for a coffee roasting supply chain\\nStep 1: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics.',\n", + " 'preferred_response': 'Step 2: Develop the constraint equations that reflect the limitations in the roasting capacity, storage, and demand fulfillment.',\n", + " 'dispreferred_response': 'Step 2: Identify the key variables that will be included in the objective function, such as coffee bean costs, roasting costs, and selling prices.'},\n", + " {'instruction': '# Question: Design a mixed integer linear program for a coffee roasting supply chain\\nStep 1: Formulate the objective function that maximizes profit or minimizes costs based on the supply chain dynamics.',\n", + " 'preferred_response': 'Step 2: Develop the constraint equations that reflect the limitations in the roasting capacity, storage, and demand fulfillment.',\n", + " 'dispreferred_response': 'Step 2: Ensure to integrate fixed and variable costs into the objective function to have a comprehensive understanding of the profit landscape.'}]" ] }, - "execution_count": 11, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } diff --git a/website/blog/2024-12-18-Reasoning-and-MCTS/index.mdx b/website/blog/2024-12-18-Reasoning-and-MCTS/index.mdx index 819062fe8f..fdaa31048a 100644 --- a/website/blog/2024-12-18-Reasoning-and-MCTS/index.mdx +++ b/website/blog/2024-12-18-Reasoning-and-MCTS/index.mdx @@ -46,7 +46,7 @@ The MCTS implementation in ReasoningAgent follows four key steps: ```python choices_weights = [ # exploitation term - (child.value / (child.visits + EPSILON)) + + (child.value / (child.visits + EPSILON)) + # exploration term self.exploration_constant * math.sqrt((2 * math.log(node.visits + EPSILON) / (child.visits + EPSILON))) for child in node.children @@ -87,8 +87,8 @@ ReasoningAgent now supports ground truth evaluation by allowing users to include prompt = """What is the expected maximum dice value if you can roll a 6-sided dice three times? GROUND_TRUTH: -We define X as the highest outcome among the three rolls. -The probability that X is at least m is 1 - \left(\frac{m-1}{6}\right)^3 for each m from 1 to 6. +We define X as the highest outcome among the three rolls. +The probability that X is at least m is 1 - \left(\frac{m-1}{6}\right)^3 for each m from 1 to 6. Summing these probabilities gives the expectation E(X) = \sum_{m=1}^{6} [1 - (\frac{m-1}{6})^3]. Calculating this sum results in E(X) = 6 - \frac{225}{216} = \frac{119}{24}, which approximates to 4.9583. Therefore, the expected maximum value when rolling a six-sided die three times is \frac{119}{24} or approximately 4.9583."""