the assignment problem constraint x41

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How can I solve this constrained assignment problem?

The assignment problem is defined as follows:

There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one task to each agent in such a way that the total cost of the assignment is minimized.

The number of tasks is larger than the number of agents.

My problem statement though imposes an additional constraint on the above.

Each task belongs to exactly one 'category'. Each 'category' has an associated maximum number of tasks that can be assigned. Enforce this constraint on the earlier definition.

For a layman's example, consider this -

A restaurant serves n customers (agents), and has on it's menu m possible dishes (tasks), with m > n. Each customer gives his preference for each of the m dishes, which is the cost for this particular assignment problem. Find a solution which minimizes cost i.e. which gives each customer a dish that is as high on their preference as possible. Additionally, each dish belong to a certain cuisine (category). The restaurant can only make a certain number of dishes per cuisine. Enforce this constraint on the problem above.

I understand that this is a very specific problem, but any help would be appreciated.

I am currently solving the first part of the problem using the Hungarian Algorithm for assignment.

• optimization
• combinatorics
• assignment-problem

• 2 $\begingroup$ You should be able to reformulate this as a Maximum-Flow Problem $\endgroup$ –  Francesco Gramano Commented Jan 15, 2015 at 18:45

3 Answers 3

Introduce dummy variables with zero cost so that it becomes a balanced assignment, which can be solved with Hungarian Algorithm .

• $\begingroup$ Does not work for the additional constraint. $\endgroup$ –  Rohan Sood Commented Jul 5, 2015 at 11:51

This can be formulated as an instance of minimum-cost flow problem . Have a graph with one vertex per agent, one vertex per task, and one vertex per category. Now add edges:

Add an edge from the source to each agent, with capacity 1 and cost 0.

Add an edge from each agent to each task, with capacity 1 and cost according to the cost of that assignment.

Add an edge from each task to the category it is part of, with capacity 1 and cost 0.

Add an edge from each category to the sink, with capacity given by the maximum number of tasks assignable in that category and cost 0.

Now find the minimum-cost flow of size $t$, where $t$ is the number of tasks. There are polynomial-time algorithms for that.

I know it is a bit late for an answer to that post. Maybe you should have closed it within a year of no relevant answer. The problem is not that easy, just with one additional constraint, there is a lot of work dealing with the problem. You can use branch and bound algorithm. In the branch and bound, there are different ways to proceed.

• 1 $\begingroup$ Could you please describe the branch and bound algorithm in detail? $\endgroup$ –  xskxzr Commented Sep 1, 2020 at 1:12
• $\begingroup$ it is tree like method, based on : 1) solving a relaxation of your problem,, a good relaxation (without some complicating constraints). 2) setting up a branching criteria (a way how you construct the subproblems). You have to manage with bounds, upper and lowers bounds. There are ways to fathom (cut it out) a vertex or branch of the tree according to the bounds. if it is a min problem, then a lower bound is determined by the value obtained by solving the relaxed problem, and an upper bound is the value of any feasible solution (that satisfies all the constraints of the initial problem). $\endgroup$ –  Rima Awhid Commented Sep 2, 2020 at 23:15

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OR: Assignment problem constraint

Not what you're looking for?

The assignment problem constraint x31 + x32 + x33 + x34 <= 2 means

a. agent 2 can be assigned to at most 3 tasks.

b. agent 3 can be assigned to at most 2 tasks.

c. a mixture of agents 1, 2, 3, and 4 will be assigned to 2 or less tasks.

d. there is no feasible solution.

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Solution summary.

The solution is about interpretation of assignment constraint

Solution Preview

Assignment problem in stricter sense does not allow this constraint as an agent can be assigned to one and only one task ...

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5 Corrected Constraint Logic Programming Exercises

Constraint logic programming.

This page presents detailed corrected exercises of the problem of logic programming by constraints, which is a natural mix of logic programming and constraint programming .

Consider the following puzzle:

Each region of the grid must be filled with a number between 0 and 9 so that

• the numbers in two adjacent regions (vertically or horizontally) are different
• whenever there are four regions that meet at a point (indicated by a small circle), the sum of their numbers is equal to 20.

Solve this problem by constraint logic programming.

Let's name from top left to bottom right (by line) the empty squares by a letter. Each domain has a value between 0 and 9. Thereafter, the two constraints must be filled in manually.

For each square, its score must be different from its neighbours.

For each circle, the sum must be equal to 20.

We therefore have the following constraint logic programming:

Consider the game Bokkusu. The object of the game is to mark certain squares of the given grid in black.

Each box has two values: an A value and a B value. The numbers on the right denote the A values of the boxes in each corresponding row and the numbers at the bottom denote the B values of the boxes in each corresponding column (These values always range from 1 to the size of the grid by increasing by 1 from left to right or from top to bottom).

The values on the left indicate the sum of the B values of the black boxes for each row and the values on the top indicate the sum of the A values of the black boxes for each column. An example of a grid and its solution is given in the figure. In the solution of this example we have for example 7 = 1 + 2 + 4 (the boxes with B value of 1, 2 and 4 are marked black) and 6 = 2 + 4 (the boxes with A values of 2 and 4 are marked).

Let's name each square in the grid in a matrix fashion. For the constraints, the sum of the binary variables (white=0 or black=1) multiplied by the coefficients on the left or on the top must be equal to the value opposite.

We consider the problem of generating a timetable. There are 7 classes and 4 slots. A slot can accommodate a maximum of 2 lessons. There are the following constraints:

– Course 4 must be before course 6. – Course 5 must be before course 7. – Course 6 must be before course 2. – Course 1 cannot be in parallel with courses 2, 3, 4 and 7. – Course 2 cannot be in parallel with courses 3 and 6. – Course 3 cannot be in parallel with courses 4, 5 and 6. – Course 4 cannot be in parallel with courses 5 and 6. – Course 5 cannot be in parallel with course 7.

We will consider that the courses are domains, and that they can take a value from 1 to 4 corresponding to the niche that will be chosen. Constraint logic programming is as follows:

Inshi no heya is a Japanese logic game. It is played on a rectangular grid of cells which are separated into rectangles. One dimension of each rectangle is 1 while the other dimension varies.

Each rectangle is placed horizontally or vertically and contains a number. The goal is to fill all cells with numbers from 1 to 9 so that:

– If we multiply all the digits of each rectangle we obtain the number indicated in the rectangle – No number appears more than once in a column. – No number appears more than once in a line.

An example of an original grid and a solution are given below:

Each box of the matrix is considered as a domain, each box can take a value from 1 to 5. The constraints are simple since the sum of the boxes of a certain perimeter must be equal to a given number.

Skyscrapers are built on an NxN grid. Each skyscraper has a number of floors corresponding to its size (from 1 to N). In each column and each row each size appears exactly once. The numbers on the edges of the grid indicate how many skyscrapers can be seen when looking from that point towards the corresponding row or column. A skyscraper is visible if all the skyscrapers in front of it are smaller. Here is an example of a grid and its solution:

For example, in the second line from the bottom looking from the left we can see 2 skyscrapers: the one of height 3 and the one of height 4. Here is a second problem of a grid (5×5) to solve:

You can use the predefined predicate fd_cardinality(+List, ?Count) where List is a list of constraints and Count is the number of List constraints satisfied.

A three-dimensional bin packing problem with item fragmentation and its application in the storage location assignment problem

• Research Paper
• Published: 04 September 2024

Cite this article

• Hamid Salamati-Hormozi   ORCID: orcid.org/0000-0001-6500-3403 1 ,
• Ali Husseinzadeh Kashan   ORCID: orcid.org/0000-0002-6004-6882 1 &
• Bakhtiar Ostadi   ORCID: orcid.org/0000-0001-8472-6244 1  

This paper introduces the three-dimensional bin packing problem with item fragmentation (3D-BPPIF) and explores its application in the storage location assignment problem (SLAP) to efficiently allocate warehouse spaces to product groups. Based on real-world constraints, the aim is to find an effective 3D-packing of the product groups into warehouse storage spaces to minimize the total distance. Given the internal limitations present in many warehouses, the storage spaces are not homogeneous, making the allocation to product groups a challenging task that can reduce space utilization efficiency. Accordingly, to effectively utilize warehouse storage spaces, we developed a MILP formulation incorporating the concepts of shape changeability and item fragmentation, significantly enhancing the flexibility of the arrangements. Due to the NP-hard nature of the problem, we proposed a simulated annealing-based meta-heuristic to solve large-scale real-world problems. Numerous computational experiments prove the validity of the proposed model and illustrate that the proposed algorithm can provide appropriate 3D assignments.

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Bortfeldt A, Wäscher G (2013) Constraints in container loading–a state-of-the-art review. Eur J Oper Res 229(1):1–20

Article   Google Scholar  

Caserta M, Voß S, Sniedovich M (2011) Applying the corridor method to a blocks relocation problem. Or Spectrum 33(4):915–929

Chen C, Lee S-M, Shen Q (1995) An analytical model for the container loading problem. Eur J Oper Res 80(1):68–76

Crainic TG, Perboli G, Tadei R (2008) Extreme point-based heuristics for three-dimensional bin packing. INFORMS J Comput 20(3):368–384

Crainic TG, Perboli G, Tadei R (2009) TS2PACK: a two-level tabu search for the three-dimensional bin packing problem. Eur J Oper Res 195(3):744–760

De Koster R, Le-Duc T, Roodbergen KJ (2007) Design and control of warehouse order picking: a literature review. Eur J Oper Res 182(2):481–501

Den Boef E, Korst J, Martello S, Pisinger D, Vigo D (2005) Erratum to “the three-dimensional bin packing problem”: robot-packable and orthogonal variants of packing problems. Oper Res 53(4):735–736

Derhami S, Smith JS, Gue KR (2017) Optimising space utilisation in block stacking warehouses. Int J Prod Res 55(21):6436–6452

Derhami S, Smith JS, Gue KR (2019) Space-efficient layouts for block stacking warehouses. IISE Trans 51(9):957–971

Derhami S, Smith JS, Gue KR (2020) A simulation-based optimization approach to design optimal layouts for block stacking warehouses. Int J Prod Econ 223:107525

Dijkstra AS, Roodbergen KJ (2017) Exact route-length formulas and a storage location assignment heuristic for picker-to-parts warehouses. Transp Res Part e Logist Transp Rev 102:38–59

Duan J, Tong X, Ni F, He Z, Chen L, Yuan M (2022) A data-driven column generation algorithm for bin packing problem in manufacturing industry. https://arxiv.org/abs/2202.12466

Elhedhli S, Gzara F, Yildiz B (2019) Three-dimensional bin packing and mixed-case palletization. INFORMS J Optim 1(4):323–352

Ene S, Öztürk N (2012) Storage location assignment and order picking optimization in the automotive industry. Int J Adv Manuf Technol 60(5):787–797

Erbayrak S, Özkır V, Yıldırım UM (2021) Multi-objective 3D bin packing problem with load balance and product family concerns. Comput Ind Eng 159:107518

Farhadi Sartangi M, Husseinzadeh Kashan A, Haleh H, Kazemi A (2022) A mixed integer linear formulation and a grouping league championship algorithm for a multiperiod-multitrip order picking system with product replenishment to minimize total tardiness. Complexity 2022

Frazelle EH (1989) Stock location assignment and order picking productivity. Georgia Institute of Technology

Google Scholar  

Gonçalves JF, Resende MG (2013) A biased random key genetic algorithm for 2D and 3D bin packing problems. Int J Prod Econ 145(2):500–510

Gu J, Goetschalckx M, McGinnis LF (2007) Research on warehouse operation: a comprehensive review. Eur J Oper Res 177(1):1–21

Gu J, Goetschalckx M, McGinnis LF (2010) Research on warehouse design and performance evaluation: a comprehensive review. Eur J Oper Res 203(3):539–549

Harrath Y (2022) A three-stage layer-based heuristic to solve the 3D bin-packing problem under balancing constraint. J King Saud Univ-Comput Inf Sci 34(8):6425–6431

Hausman WH, Schwarz LB, Graves SC (1976) Optimal storage assignment in automatic warehousing systems. Manage Sci 22(6):629–638

He K, Tole K, Ni F, Yuan Y, Liao L (2020) Adaptive large neighborhood search for circle bin packing problem. https://arxiv.org/abs/2001.07709

Jang D-W, Kim SW, Kim KH (2013) The optimization of mixed block stacking requiring relocations. Int J Prod Econ 143(2):256–262

Junqueira L, Morabito R, Yamashita DS (2012) Three-dimensional container loading models with cargo stability and load bearing constraints. Comput Oper Res 39(1):74–85

Kashan AH, Akbari AA, Ostadi B (2015) Grouping evolution strategies: an effective approach for grouping problems. Appl Math Model 39(9):2703–2720

Kashan AH, Kashan MH, Karimiyan S (2013) A particle swarm optimizer for grouping problems. Inf Sci 252:81–95

Kofler M, Beham A, Wagner S, Affenzeller M (2014) Affinity based slotting in warehouses with dynamic order patterns. In: Advanced methods and applications in computational intelligence. Springer, pp 123–143

Kovács G (2020) Special optimization process for warehouse layout design. Vehicle and Automotive Engineering

Mahvash B, Awasthi A, Chauhan S (2013) Column generation based heuristic for the three dimensional vehicle loading problem. In: International conference on computational logistics

Mahvash B, Awasthi A, Chauhan S (2017) A column generation-based heuristic for the three-dimensional bin packing problem with rotation. J Oper Res Soc:1–13

Maniezzo V, Boschetti MA, Gutjahr WJ (2021) Stochastic premarshalling of block stacking warehouses. Omega 102:102336

Martello S, Pisinger D, Vigo D (2000) The three-dimensional bin packing problem. Oper Res 48(2):256–267

Martello S, Pisinger D, Vigo D, Boef ED, Korst J (2007) Algorithm 864: general and robot-packable variants of the three-dimensional bin packing problem. ACM Trans Math Softw (TOMS) 33(1):7-es

Muppani VR, Adil GK (2008) Efficient formation of storage classes for warehouse storage location assignment: a simulated annealing approach. Omega 36(4):609–618

Narciso M (2010) Revisiting the pallet loading problem using a discrete event system approach to minimize logistic costs

Paquay C (2017) The three-dimensional rectangular multiple bin size bin packing problem with transportation constraints: a case study in the field of air transportation. Springer

Book   Google Scholar  

Paquay C, Limbourg S, Schyns M (2018) A tailored two-phase constructive heuristic for the three-dimensional Multiple Bin Size Bin Packing Problem with transportation constraints. Eur J Oper Res 267(1):52–64

Paquay C, Schyns M, Limbourg S (2016) A mixed integer programming formulation for the three-dimensional bin packing problem deriving from an air cargo application. Int Trans Oper Res 23(1–2):187–213

Petersen CG, Aase GR, Heiser DR (2004) Improving order‐picking performance through the implementation of class‐based storage. Int J Phys Distrib Logist Manag

Petersen CG, Siu C, Heiser DR (2005) Improving order picking performance utilizing slotting and golden zone storage. Int J Oper Prod Manag

Prasad SA, Krishnakumar P (2021) Higher order block heuristics for 2D pallet loading problems with multiple box inputs. Mater Today Proc 46:4625–4633

Riccardo A, Giulia B, Riccardo M (2017) Design and manage deep lane storage system layout: an iterative decision-support model. Int J Adv Manuf Technol 92(1–4):57–67

Roodbergen KJ, Vis IF, Taylor GD Jr (2015) Simultaneous determination of warehouse layout and control policies. Int J Prod Res 53(11):3306–3326

Silva A, Coelho LC, Darvish M, Renaud J (2020) Integrating storage location and order picking problems in warehouse planning. Transp Res Part e Logist Transp Rev 140:102003

Tappia E, Roy D, Melacini M, De Koster R (2019) Integrated storage-order picking systems: technology, performance models, and design insights. Eur J Oper Res 274(3):947–965

Tole K, Moqa R, Zheng J, He K (2023) A simulated annealing approach for the circle bin packing problem with rectangular items. Comput Ind Eng 176:109004

Trivella A, Pisinger D (2016) The load-balanced multi-dimensional bin-packing problem. Comput Oper Res 74:152–164

Venkitasubramony R, Adil GK (2019) An integrated design approach for class-based block stacked warehouse. Facilities

Yuan Y, Tole K, Ni F, He K, Xiong Z, Liu J (2022) Adaptive simulated annealing with greedy search for the circle bin packing problem. Comput Oper Res 144:105826

Zhang G, Nishi T, Turner SD, Oga K, Li X (2017) An integrated strategy for a production planning and warehouse layout problem: Modeling and solution approaches. Omega 68:85–94

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Suppose a problem involving the packing of 3 items into a bin with dimensions \(4 \times 4 \times 2\) (see Fig. 

The available space of a bin with dimensions \(4 \times 4 \times 2\)

16 ). Table

10 represents the specifications of the items. The fixed item, with volume 4, is represented by a black box in the bin and serves as an obstacle. The order of packing the items is predetermined based on the ascending order of COI. The packing phase is as follows:

Warehouse door coordinates (I/O): \(\left( {O^{x} ,O^{y} ,O^{z} } \right) = \left( {0,0,0} \right)\) .

List of sorted items ( S) : \(S = \left\{ {1 \to 2 \to 3} \right\}\) .

1.1 Iteration #1

Update the available space: the best candidate points (nearest points to the I/O) to assign the first item are A, B, and C (Fig. 

The available space in iteration #1

Call the first item from the list \(S\) : \(v_{1} = 6.\)

Regarding the objective function (minimizing the total distance to the I/O point), the model tries to find the best location and dimensions for the item. Various arrangement options are shown in Fig. 

Different arrangements of the first item in iteration #1

18 . As shown, the best arrangement for \(v_{1} = 6\) is the place with the minimum value of objective function which it is \(z = 12.2\) .

Fix the location and dimensions of the item:

1.2 Iteration #2

Update the available space: point A is occupied by the first item. The available spaces closest to the I/O point (points B and C) are shown in Fig. 

The available space in iteration #2

Call the second item from the list \(S\) : \(v_{2} = 7.\)

There is no feasible way to arrange the second item as a single piece within the available space. Therefore, the model divides it into two parts. Some arrangement options are shown in Fig. 

Different arrangements of the second item in iteration #2

20 . The best arrangement for \(v_{2} = 7\) results in a minimum objective function value of \(z = 30.7\) .

1.3 Iteration #3

Update the available space: points B and C are occupied by the second item. The available spaces closest to the I/O point (D, E, F, and G) are shown in Fig. 

The available space in iteration #3

Call the third item from the list S: \(v_{3} = 10.\)

There is no way to arrange the third item with a single box in the available space. As a result, the model divides it into two parts. Different arrangement modes are shown in Fig. 

Different arrangements of the third item in iteration #3

22 . The best arrangement for \(v_{3} = 10\) is obtained. The points F and G are occupied by the third item.

Fix location and dimensions of item:

Arrangements of classes 7–27 of large-size items

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Salamati-Hormozi, H., Husseinzadeh Kashan, A. & Ostadi, B. A three-dimensional bin packing problem with item fragmentation and its application in the storage location assignment problem. 4OR-Q J Oper Res (2024). https://doi.org/10.1007/s10288-024-00576-6

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Received : 05 December 2023

Revised : 27 June 2024

Accepted : 14 August 2024

Published : 04 September 2024

DOI : https://doi.org/10.1007/s10288-024-00576-6

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• Three-dimensional bin packing problem
• Storage location assignment problem
• Item fragmentation
• Shape changeability
• Simulated annealing

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