gurobi output explanation

GAMS/Gurobi supports sensitivity analysis (post-optimality analysis) for linear programs which allows one to find out more about an optimal solution for a problem. Python Implementation Gurobi Output and Analysis Problem Description A mining company needs to create a five-year operating plan for a certain area with four mines in it. H. Paul Williams, Model Building in Mathematical Programming, fifth edition (Page 255-256, 354-356). \end{equation} The full model can be stated as \begin{equation} \max \sum_{t \in T} \sum_{p \in P} k_p * u_{t,p} r * s_{t,p} \end{equation} \begin{equation} s_{t-1,p} + b_{t,p} = u_{t,p}+ s_{t,p} \quad \forall t \in T \setminus t_0, \ \forall p \in P \end{equation} \begin{equation} b_{t_0,p} = u_{t_0,p} + s_{t_0,p} \quad \forall p \in P. \end{equation} \begin{equation} s_{t_e,p} = z \quad \forall p \in P. \end{equation} \begin{equation} s_{t,p} \leq z \quad \forall p \in P, \forall t \in T. \end{equation} \begin{equation} \sum_{p \in P} f_{pm}*b_{t,p} + g*d_{tm} \leq g*q_{tm} \quad \forall t \in T, \quad \forall m \in M. \end{equation} \begin{equation} \sum_{t \in T} d_{tm} = (q_{m}-k_{m}) \quad \forall t \in T, \quad \forall m \in M. \end{equation} \begin{equation} b_{t,o},u_{t,o},s_{t,o} \geq 0 \quad \forall t \in T, \ \forall p \in P \end{equation} \begin{equation} 0 \leq d_{t,m} \leq k_{m}, d_{t,m} \in \mathbb{Z} \quad \forall t \in T, \ \forall m \in M \end{equation}. You can either use pulp.GUROBI or pulp.GUROBI_CDM. For each time period $t \in T$ and each skill level $s \in S$ we have given the required manpower $g_{t,s}$, For each skill level $s \in S$ we have given the current manpower $h_{s}$, the percentage of workers who leave in the first year $i_s$, the percentage of workers who leave in the other years $j_s$, the maximal amount of workers, who can get recruited $k_s$, the retraining cost $l_s$ to the next level, the cost to layoff and employee $m_s$, the part-time worker cost $n_s$ and the overmanning cost $o_s$. rev2022.11.3.43003. Please find attached an example model. In this example, we will solve a few optimization problems with increasing complexity. 29 #! $u_{t,p}$ describes how much we sell of product p in the month $t$. is equivalent to setting Gurobi Output and Analysis Problem Description A factory makes seven products (Prod 1 to Prod 7) using a range of machines including: Four grinders Two vertical drills Three horizontal drills One borer One planer Each product has a defined profit contribution per unit sold (defined as the sales price per unit minus the cost of raw materials). For added clarity: none of this output is coming from JuMP or Julia. It consists of the profit for each product minus cost for storing the unsold products. to Gurobi Optimization Hello - I am using "results = opt.solve (m, tee=True)" and I know that tee=True will show the solver output but I thought Tobias is asking for a logfile wherein details. If their objective was to minimize costs, how much could they further reduce costs? remove slap brush texture. See the Gurobi documentation for details. Thank you! Hope this helps Seba! Click here to agree with the cookies statement, 500 PROD 1 1000 PROD 2 300 PROD 3 300 PROD 4 800 PROD 5 200 PROD 6 100 PROD 7, 600 PROD 1 500 PROD 2 200 PROD 3 400 PROD 5 300 PROD 6 150 PROD 7, 400 PROD 1 700 PROD 2 100 PROD 3 100 PROD 4 600 PROD 5 400 PROD 6 200 PROD 7, 300 PROD 1 600 PROD 2 500 PROD 5 400 PROD 6 100 PROD 7, 100 PROD 1 100 PROD 2 100 PROD 3 100 PROD 4 100 PROD 5 100 PROD 7, 100 PROD 2 100 PROD 3 100 PROD 4 100 PROD 5 100 PROD 7, 100 PROD 2 500 PROD 3 100 PROD 4 1000 PROD 5 300 PROD 6, 550 PROD 1 550 PROD 2 150 PROD 3 350 PROD 4 1150 PROD 5 550 PROD 6 110 PROD 7, 500 PROD 1 500 PROD 2 100 PROD 3 300 PROD 4 1100 PROD 5 500 PROD 6 60 PROD 7. The raw oils needed can be divided into two categories: In each month there is an upper limit on the amount of each product that can be sold. We have three type of workers with different skills levels. I have several different variables. gurobi_options . The variables can be formulated as: \begin{equation} a_{t,s},b_{t,s},c_{t,s},d_{t,s},e_{t,s} \geq 0 \quad \forall t \in T, \ \forall s \in S \end{equation} \begin{equation} f_{t,s_1,s_2} \geq 0 \quad \forall t \in T, \ \forall s_1,s_2 \in S \end{equation} The continuity constraints ensure that per skill level and per year the current needed workers (LaborForce), the number of workers laid off and the workers who gets retrained to the current level, minus the people who gets retrained from the current level to a different skill level, equals the LaborForce of the last year (or the CurrentStrength in the first year) plus the recruited workers. The process is to call gurobi_cl for a batch script and pass in the LP file for solving. These policies cost USD 498 677 over the three years and result in a total layoffs of 1424 workers. This is the reference manual for the Gurobi TM Optimizer. Next, we create a model and the variables. The Maintenance constraints ensure that the specified number and types of machines are down due maintaince in some month. Again, alternative solutions should be considered if necessary to ensure that these layoffs are the minimum possible for this (min-imum) level of cost. For each product (seven kinds of products) and each time period (month) we will create variables for the amount of which products will get manufactured, held and sold. Update: works as intended. Which month a machine is down is down is now part of the optimization. Thanks for contributing an answer to Stack Overflow! At most 50 units of each product can be stored in each month. Connect and share knowledge within a single location that is structured and easy to search. Let $ T $ be a set of time periods, where $ t_0 \in T $ is the first period and $ t_e \in T $ the last period. What plan should they adopt in order to do this? \begin{equation} f_{t,s_2,s_3} \leq 200 \quad \forall t \in T \end{equation} \begin{equation} f_{t,s_1,s_3} = 0 \quad \forall t \in T \end{equation} The RetrainingSemiSkilled states that the retraining of semiskilled workers to skilled workers is limited no more than one quarter of the skilled labor force at this time. The capacity constraints ensure that for each month the time all products need on a certain kind of machine is lower or equal than the available hours for that machine in that month multiplied by the number of available machines in that month. A mathematical optimization model has five components, namely: Sets and indices. Fully Compatible You set parameters to control the solution pool; the multiple solutions are returned in the Solution Pool named components. Saving for retirement starting at 68 years old. Why do missiles typically have cylindrical fuselage and not a fuselage that generates more lift? :). The exception to the above are the grinding machines where only two of them need to be down during the six months. However, by the end of June there should be 50 units of each product in inventory. Horror story: only people who smoke could see some monsters. Next, we insert the constraints. By proceeding, you agree to the use of cookies. The overmanning constraints ensure that the total overmanning over all skill levels in one year is no more than 150. Is there a topology on the reals such that the continuous functions of that topology are precisely the differentiable functions? Also, for the purposes of this model, there are no production sequencing issues that need to be taken into account. answered May 24, 2018 at 0:33. mmghu. Does the Fog Cloud spell work in conjunction with the Blind Fighting fighting style the way I think it does? Gurobi Python sensitivity analysis log file, Get intermediate results of Gurobi optimization, Gurobi resume optimization after model modification, How to solve optimization problem using Gurobi, Interpret the LP optimization result from Gurobi. I am using Gurobi to solve a MIP problem, and I want to see how its MIPGap changes with respect to the Runtime. The website uses cookies to ensure you get the best experience. Yeah, but I guess JuMP as of today is the nicest way to use the Gurobi solver :-), Julia - Understanding JuMP Gurobi outputs, https://www.gurobi.com/documentation/9.1/refman/mip_logging.html, Making location easier for developers with new data primitives, Stop requiring only one assertion per unit test: Multiple assertions are fine, Mobile app infrastructure being decommissioned, 2022 Moderator Election Q&A Question Collection. $a_{t,s}$ describes how many workers of skill level $s $ get recruited in the time period $t$. Gurobi.jl is a wrapper for the Gurobi Optimizer. I still get an optimal solution printout after this happens with a gap of 11.1% corresponding to the Heuristics solution. Let $P$ be a set of products and $M$ be a set of machines. Through the purchase of new machinery, it is expected that there will be less need for unskilled labor and more need for skilled and semi-skilled labor. I am wondering why it is necessary to, Gurobi Optimization Result Writing into Csv file, Making location easier for developers with new data primitives, Stop requiring only one assertion per unit test: Multiple assertions are fine, Mobile app infrastructure being decommissioned, 2022 Moderator Election Q&A Question Collection. Thank you! \begin{equation} s_{t_e,p} = z \quad \forall p \in P. \end{equation} The store capacity constraints restrict the amount of each product which can be stored in each month. The callback code does not provide MIPGap, and I don't know how to retrieve this attribute before the model terminates (get optimal solution). There can be $z$ products of each type stored in each month and storage cost $r$ per product per month occur. Gurobi.jl is a wrapper for the Gurobi Optimizer. It is possible to recruit new people, train workers to improve/decrease their skills or put them into part-time (short-time). Replacing outdoor electrical box at end of conduit. keep cutting without branching in MIP solver (Gurobi), Multi dimensional array in Gurobi/Jump/Julia, Gurobi mixed-integer linear programming problem gap information, Computing Irreducible Inconsistent Subsystem (IIS) using Julia JuMP (Gurobi), Julia - Gurobi Callbacks on array of JuMP variables, Retrieve constraints matrix from Gurobi or MOI or JuMP in Julia, How to use callback functions of Gurobi in Drake. See the Gurobi documentation for details. The aim is to create an optimal multi-period operation plan to minimize the total number of layoffs over the whole horizon. The multiple optimal solutions are called the alternate basic solution.Alternate or multiple optimal solutions occurs in LLP problem when the objective function line is. I firstly would like to thank all the members who have been working hard to solve problems of GUROBI users. In staffing planning problems, choices must be made regarding the recruitment, training, layoffs (redundancy) and scheduling of staff. When the migration is complete, you will access your Teams at stackoverflowteams.com, and they will no longer appear in the left sidebar on stackoverflow.com. and Instead of pre-defining a maintenance schedule for the machines, as was done in Factory Planning I, in this version of the model we will also optimize for the maintenance schedule. $e_{t,s}$ describes how many workers of skill level $s $ are overmanned in the time period $t$. . Gurobi added the R API for the solution pool in version 8.0. Best way to get consistent results when baking a purposely underbaked mud cake. Are cheap electric helicopters feasible to produce? Find centralized, trusted content and collaborate around the technologies you use most. Layoffs Each laid-off worker is entitled to a separation payment at the rate of USD 200 per unskilled worker and USD 500 per semi-skilled or skilled worker. Also there cannot be people trained in one year from Unskilled to Skilled. For example var.varName = 'A' var.x =2 var.varName = 'B' var.x =3 The excel file is written as below: Well, I am checking for feasibility; the problem is feasible and yielding an answer. You all are really expertise in your domain and provide accurate solution to what is being asked as it happened many time in my case. Hello All, I get the following output from my model solve: What does the current node "cutoff" objective mean? The information has been submitted successfully. our different APIs, refer to our Link to the OutputFlag documentation here . This training costs the company USD 400 per worker. Not the answer you're looking for? However, this number can not exceed 25% of the current skilled labor force and this training costs USD 500 per worker. These limits are shown below: Up to 100 units of each product may be stored in inventory at a cost of $0.50 per unit per month. In staffing planning problems, choices must be made regarding the recruitment, training, layoffs (redundancy) and scheduling of staff. Gurobi interactive shell Start the IS: open the terminal, enter exec gurobi.sh Read a model from a file and return a Model object gurobi > m = read('model path') Invoke the optimize method on the Model object gurobi > m.optimize() Reset the optimization and start from the begining m.reset() Click here to agree with the cookies statement. In this example well model and solve a manpower planning problem. More information can be found in our Privacy Policy. Does it make sense to say that if someone was hired for an academic position, that means they were the "best"? Stack Overflow for Teams is moving to its own domain! For each product $p \in P$ and each type of machine $m \in M$ we are given the time $f_{pm}$ (in hours) the product $p$ needs to be manufactured on the machine $m$. The first column shows the average number of simplex iterations performed per node in the branch-and-cut tree. Setting OutputFlag to 0 will suppress solver output. This is due to capacity limitations. The Gurobi Optimizer solves such models using state-of-the-art mathematics and computer science. Each machine can work $g$ hours a month. $s_{t,p}$ describes how much we store of product p in the month $t$. This reflects a gain of $15 140 over the course of six months vs. the Factory Planning I example as a result of seeking an optimal maintenance schedule instead of the one imposed in that example. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. In addition, it is possible train semi-skilled workers to make them into skilled workers. Asking for help, clarification, or responding to other answers. The balance constraints ensure that the amount of product that is in the storage in the prior month and the amount that gets manufactured equals the amount that is sold and held for each product in the current month. Link to other Gurobi flags here. Setting OutputFlag to 0 The Gurobi Solver really shines on modern multi-core PCs. This constraint describes the change in the total amount of employed workers. Non-anthropic, universal units of time for active SETI, Leading a two people project, I feel like the other person isn't pulling their weight or is actively silently quitting or obstructing it. Making statements based on opinion; back them up with references or personal experience. How do I simplify/combine these two methods? First, I am assuming Gurobi is able to be run on multiple nodes, so correct me if this is not possible.. This makes sure that all products in the model are manufactured in some month. I do not need their corresponding value which can only be "1" since they are binary variables. It has two components: a thin wrapper around the complete C API an interface to MathOptInterface The C API can be accessed via Gurobi.GRBxx functions, where the names and arguments are identical to the C API. There can be multiple machines per machine type. When this gap is smaller than the MIPGap parameter, optimization terminates. The multiple optimal solutions arise in a linear programming problem with more than one set of basic solutions that can minimize or maximize the required objective function. I am using Gurobi 7 to solve my MIP. Thank you! The contribution and manufacturing time value are shown below. The factory produces product six days a week using two eight-hour shifts per day. The endstore constraints force that at the end of the last month the storage contains the specified amount of each product. \begin{equation} \min \sum_{t \in T} l_s f_{t,s_1,s_2} + l_s f_{t,s_2,s_3} + \sum_{s \in S} m_s b_{t,s} + n_s d_{t,s} + o_s e_{t,s} \end{equation}, The full model (with the first objective) can be stated as: \begin{equation} \min \sum_{t \in T} \sum_{s \in S} d_{t,s} \end{equation} \begin{equation} c_{t,s} = g_{t,s} + e_{t,s} + 0.5 * b_{t,s} \quad \forall t \in T \end{equation} \begin{equation} \sum_{s \in S} e_{t,s} \leq 150 \quad \forall t \in T \end{equation} \begin{equation} f_{t,s_2,s_3} \leq 0.25 c_{t,s} \quad \forall t \in T \end{equation} \begin{equation} f_{t,s_2,s_3} \leq 200 \quad \forall t \in T \end{equation} \begin{equation} f_{t,s_1,s_3} = 0 \quad \forall t \in T \end{equation} \begin{equation} c_{t,s} + d_{t,s} i_s a_{t,s} + \sum_{z \in S : z < s} (- j_sf_{t,z,s} + f_{t,s,z}) + \sum_{z \in S : z > s} (f_{t,s,z} pf_{t,z,s})= j_s c_{t-1,s} \forall t \in T \setminus t_0, \ \forall s \in S \end{equation} \begin{equation} c_{t_0,s} + d_{t_0,s} i_s a_{t_0,s} + \sum_{z \in S : z < s} (- j_sf_{t_0,z,s} + f_{t_0,s,z}) + \sum_{z \in S : z > s} (f_{t_0,s,z} pf_{t_0,z,s})= j_s h_{s} \ \forall s \in S \end{equation} \begin{equation} a_{t,s},b_{t,s},c_{t,s},d_{t,s},e_{t,s} \geq 0 \quad \forall t \in T, \ \forall s \in S \end{equation} \begin{equation} f_{t,s_1,s_2} \geq 0 \quad \forall t \in T, \ \forall s_1,s_2 \in S \end{equation}, The full model (with the second objective) can be stated as: \begin{equation} \min \sum_{t \in T} l_s f_{t,s_1,s_2} + l_s f_{t,s_2,s_3} + \sum_{s \in S} m_s b_{t,s} + n_s d_{t,s} + o_s e_{t,s} \end{equation} \begin{equation} c_{t,s} = g_{t,s} + e_{t,s} + 0.5 * b_{t,s} \quad \forall t \in T \end{equation} \begin{equation} \sum_{s \in S} e_{t,s} \leq 150 \quad \forall t \in T \end{equation} \begin{equation} f_{t,s_2,s_3} \leq 0.25 c_{t,s} \quad \forall t \in T \end{equation} \begin{equation} f_{t,s_2,s_3} \leq 200 \quad \forall t \in T \end{equation} \begin{equation} f_{t,s_1,s_3} = 0 \quad \forall t \in T \end{equation} \begin{equation} c_{t,s} + d_{t,s} i_s a_{t,s} + \sum_{z \in S : z < s} (- j_sf_{t,z,s} + f_{t,s,z}) + \sum_{z \in S : z > s} (f_{t,s,z} pf_{t,z,s})= j_s c_{t-1,s} \forall t \in T \setminus t_0, \ \forall s \in S \end{equation} \begin{equation} c_{t_0,s} + d_{t_0,s} i_s a_{t_0,s} + \sum_{z \in S : z < s} (- j_sf_{t_0,z,s} + f_{t_0,s,z}) + \sum_{z \in S : z > s} (f_{t_0,s,z} pf_{t_0,z,s})= j_s h_{s} \ \forall s \in S \end{equation} \begin{equation} a_{t,s},b_{t,s},c_{t,s},d_{t,s},e_{t,s} \geq 0 \quad \forall t \in T, \ \forall s \in S \end{equation} \begin{equation} f_{t,s_1,s_2} \geq 0 \quad \forall t \in T, \ \forall s_1,s_2 \in S \end{equation}. An example implementation is: This plan results in a total profit of $108 855. For each month $t \in T$ and each product $p \in P$ we introduce continuous non-negative variables $b_{t,p}$, $u_{t,p}$, $s_{t,p}$. What should the production and maintenance plans look like? In addition, the manufacturing of each product requires a certain amount of time on each machine (in hours). Asking for help, clarification, or responding to other answers. Set the OutputFlag or LogToConsole parameter to 0 before the Gurobi environment is started. The event included presentations from our customers and partners about how mathematical optimization is transforming their businesses, as well as product updates and technical training. Let $T$ be a set of time periods (months), where $t_0 \in T$ is the first month and $t_e \in T$ the last month.
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