index stringlengths 3 8 | instruction stringclasses 1
value | input stringlengths 526 19.8k | output stringlengths 1.19k 35.5k | answer float64 -9,800,000 100B | ori stringclasses 2
values |
|---|---|---|---|---|---|
0_1 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A travel agency provides customized travel packages with four distinct activity options: sightseeing tours (A), outdoor adventures (B), cultural activities (C), and culinary excursions (D). Each activity type has specific costs and satisfaction ratings, detailed as follows: A costs 100 units with 70 satisfact... | <think>
We are given four activity types: A, B, C, D.
We need to decide the quantity of each activity type to include (nonnegative integers).
Additionally, we must include at least three different activity types.
Strategy:
We will use binary variables to indicate whether an activity type is included (i.e., if q... | 560 | IndOR |
1_1 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A company specializing in travel planning offers four categories of activities: sightseeing (A) at 100 units cost and 70 satisfaction, outdoor (B) at 200 units cost and 90 satisfaction, cultural (C) at 300 units cost and 120 satisfaction, and food-based (D) at 400 units cost and 150 satisfaction. The objectiv... | <think>
We are given four activity types: A, B, C, D.
We have:
- Costs: [100, 200, 300, 400] for A, B, C, D respectively.
- Satisfactions: [70, 90, 120, 150] for A, B, C, D respectively.
Budget: 800 units.
Constraint: At least three distinct activity types must be selected.
Modeling Strategy: Binary Selectio... | 560 | IndOR |
3_0 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
An airline seeks to enhance its loyalty program by boosting member engagement through mileage rewards. The program categorizes members into Gold and Silver tiers, requiring minimum annual flights of 5000 miles for Gold Card holders and 3000 miles for Silver Card holders. To manage expenses, the airline caps t... | <think>
We are given:
- Two tiers: Gold and Silver.
- Gold: min flights = 5000 miles, max rewards = 10000 miles.
- Silver: min flights = 3000 miles, max rewards = 6000 miles.
- Gold earns 2 points per mile flown -> so 2 * (miles flown by Gold) is the reward for Gold.
- Silver earns 1 point per mile flown -> s... | 16,000 | IndOR |
5_1 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
An airline aims to refine its loyalty program by incentivizing flights through mileage rewards. Gold Card members are required to fly 5000 miles yearly, while Silver Card members need 3000 miles. The program restricts annual rewards to a maximum of 10000 miles for Gold and 6000 miles for Silver members. Gold ... | <think>
We are dealing with a bilevel optimization problem. However, note that the problem description does not explicitly state a typical bilevel structure (like a leader-follower between two agents). Instead, it seems to be a linear programming problem with two types of members and constraints.
But the strategy says... | 16,000 | IndOR |
9_1 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A healthcare analytics firm aims to optimize a chronic disease management program by balancing cost efficiency and patient health improvements. The program offers three interventions: medication (x1) at 100 yuan per instance, behavioral therapy (x2) at 50 yuan, and health education (x3) at 30 yuan. These inte... | <think>
We are going to use Goal Programming. According to the strategy, we will treat one objective as a hard constraint and optimize the other.
In this problem, we have two objectives:
1. Minimize total cost.
2. Maximize total health index (which is equivalent to minimizing the negative of the health index).
... | 18,010 | IndOR |
10_0 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A medical data company is designing a cost-effective chronic disease solution with three treatment options: medication (x1, 100 yuan, 80 health points), behavioral sessions (x2, 50 yuan, 70 health points), and educational programs (x3, 30 yuan, 60 health points). The optimization must satisfy: no more than 50... | <think>
We are given a problem with three treatment options: medication (x1), behavioral sessions (x2), and educational programs (x3).
The goal is to minimize cost (or maximize health?) but the problem does not specify. However, the problem says "cost-effective", and we have a budget constraint and a health goal.
Sin... | 18,010 | IndOR |
10_1 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A medical data company is designing a cost-effective chronic disease solution with three treatment options: medication (x1, 100 yuan, 80 health points), behavioral sessions (x2, 50 yuan, 70 health points), and educational programs (x3, 30 yuan, 60 health points). The optimization must satisfy: no more than 50... | <think>
We are going to use the Relaxation and Rounding strategy.
Steps:
1. First, we solve the problem as a linear program (LP) by relaxing the integer requirements (allowing continuous variables).
2. Then, we round the LP solution to integers. However, we must ensure that the rounded solution still satisfies the c... | 18,010 | IndOR |
10_2 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A medical data company is designing a cost-effective chronic disease solution with three treatment options: medication (x1, 100 yuan, 80 health points), behavioral sessions (x2, 50 yuan, 70 health points), and educational programs (x3, 30 yuan, 60 health points). The optimization must satisfy: no more than 50... | <think>
We are given a problem with three treatment types: medication (x1), behavioral (x2), and educational (x3).
Since the strategy is to decompose by treatment type, we note that the problem naturally has three separate decision variables.
However, the problem is small and separable only in the sense that the cons... | 18,010 | IndOR |
15_0 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A company distributing emergency supplies must assign rescue materials to three disaster zones: A, B, and C. Each zone has varying disaster severity, leading to different material requirements. The objective is to minimize the total delivery time, with time weights of 50 hours for A, 100 hours for B, and 200 ... | <think>
We are given:
Three zones: A, B, C.
Objective: minimize total delivery time = 50*A + 100*B + 200*C, where A, B, C are the material units allocated to each zone.
Constraints:
1. A + B <= 500
2. B + C >= 300
3. C <= 600
4. A >= 50
Additionally, the demand ranges (with integer units) are:
A: b... | 32,500 | IndOR |
16_0 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
An emergency response firm needs to distribute relief supplies to three affected areas: A, B, and C, each with distinct disaster levels influencing material needs. The aim is to reduce total distribution time, weighted at 50 hours per unit for A, 100 for B, and 200 for C. Allocation rules are: A and B’s total... | <think>
We are given a problem to distribute relief supplies to three areas: A, B, and C.
The goal is to minimize the total weighted distribution time, with weights per unit: 50 for A, 100 for B, and 200 for C.
Constraints:
1. A and B’s total materials ≤ 500 units.
2. B and C’s total ≥ 300 units.
3. C’s maximu... | 32,500 | IndOR |
16_1 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
An emergency response firm needs to distribute relief supplies to three affected areas: A, B, and C, each with distinct disaster levels influencing material needs. The aim is to reduce total distribution time, weighted at 50 hours per unit for A, 100 for B, and 200 for C. Allocation rules are: A and B’s total... | <think>
We are given a problem that we will model using a hierarchical optimization approach as per the strategy.
However, note: the strategy description says to decompose into two stages: first optimize allocation between high and low priority areas (A+B vs. C) and then refine within subgroups.
But the problem does ... | 32,500 | IndOR |
17_0 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A relief organization must allocate emergency supplies to three disaster areas—A, B, and C—with differing needs due to disaster intensity. The goal is to minimize total delivery time, factoring in weights of 50 hours (A), 100 hours (B), and 200 hours (C). Constraints: A + B ≤ 500 units, B + C ≥ 300 units, C ≤... | <think>
We are given a problem to allocate emergency supplies to three disaster areas A, B, and C.
The goal is to minimize the total delivery time, which is calculated as:
Total delivery time = (amount allocated to A) * 50 + (amount allocated to B) * 100 + (amount allocated to C) * 200
Constraints:
1. A + B ≤ ... | 32,500 | IndOR |
17_1 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A relief organization must allocate emergency supplies to three disaster areas—A, B, and C—with differing needs due to disaster intensity. The goal is to minimize total delivery time, factoring in weights of 50 hours (A), 100 hours (B), and 200 hours (C). Constraints: A + B ≤ 500 units, B + C ≥ 300 units, C ≤... | <think>
We are given a problem to allocate emergency supplies to three disaster areas: A, B, and C.
The goal is to minimize the total delivery time, which is calculated as:
Total delivery time = (units to A) * 50 + (units to B) * 100 + (units to C) * 200
Constraints:
1. A + B <= 500
2. B + C >= 300
3. C ... | 32,500 | IndOR |
17_2 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A relief organization must allocate emergency supplies to three disaster areas—A, B, and C—with differing needs due to disaster intensity. The goal is to minimize total delivery time, factoring in weights of 50 hours (A), 100 hours (B), and 200 hours (C). Constraints: A + B ≤ 500 units, B + C ≥ 300 units, C ≤... | <think>
We are given a problem with three disaster areas: A, B, and C.
The goal is to minimize the total delivery time, which is defined as the sum of the products of the allocated units and the time weights per unit for each area.
Weights: A: 50 hours per unit, B: 100 hours per unit, C: 200 hours per unit.
Constra... | 32,500 | IndOR |
24_0 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A sports facility's management team seeks to optimize their operations by maximizing profits across four key projects: basketball (B), football (F), music concerts (M), and exhibitions (E). Each project has specific revenue and cost figures per event (in 10,000 yuan): B (500/200), F (800/300), M (700/250), E ... | <think>
We are given a problem to maximize profits for a sports facility with four projects: basketball (B), football (F), music concerts (M), and exhibitions (E).
Step-by-step modeling reasoning:
1. **Define Sets:**
- We have a set of projects: `projects = ['B', 'F', 'M', 'E']`.
2. **Parameters:**
- Revenue p... | 84,500 | IndOR |
24_1 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
A sports facility's management team seeks to optimize their operations by maximizing profits across four key projects: basketball (B), football (F), music concerts (M), and exhibitions (E). Each project has specific revenue and cost figures per event (in 10,000 yuan): B (500/200), F (800/300), M (700/250), E ... | <think>
We are given:
Projects: basketball (B), football (F), music concerts (M), exhibitions (E)
Revenue and cost per event (in 10,000 yuan):
B: revenue 500, cost 200 -> profit = 500 - 200 = 300
F: revenue 800, cost 300 -> profit = 500
M: revenue 700, cost 250 -> profit = 450
E: revenue 600... | 84,500 | IndOR |
25_0 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
The sports facility aims to maximize annual profits by strategically scheduling four types of events: basketball (B), football (F), music concerts (M), and exhibitions (E). Financials per event (in 10,000 yuan) are: B earns 500 with 200 cost, F earns 800 with 300 cost, M earns 700 with 250 cost, and E earns 6... | <think>
We are given:
- Four event types: B (basketball), F (football), M (music concerts), E (exhibitions)
- For each event type, we have:
Revenue and cost (so profit per event = revenue - cost)
B: profit = 500 - 200 = 300 (in 10,000 yuan)
F: profit = 800 - 300 = 500
M: profit = 700... | 84,500 | IndOR |
26_0 | You are an expert in mathematical optimization and operations research.
Your task is to generate a high-quality mathematical model for a given optimization problem.
1. You should write a detailed **step-by-step modeling reasoning** about how to define sets, parameters, variables, objective function and constraints.
2. ... | #Question
Optimizing profit for a sports facility involves planning four event types: basketball (B: 500/200 yuan per event), football (F: 800/300), music concerts (M: 700/250), and exhibitions (E: 600/150). Annual limits include: ≤200 total events, with B≤50, F≤40, M≤45, E≤65. Two operational constraints apply: (1) th... | <think>
We are given a problem to maximize profit for a sports facility with four event types: basketball (B), football (F), music concerts (M), and exhibitions (E).
Sets:
- Event types: I = {'B', 'F', 'M', 'E'}
Parameters for each event type i in I:
- Profit per event (revenue minus cost):
B: 500 - 200 =... | 84,500 | IndOR |
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