Improved layout structure with complexity measures for the Manufacturer’s Pallet Loading Problem (MPLP] using a Block approach

Purpose: The purpose of this paper is to study the Manufacturers pallet-loading problem (MPLP), by loading identical small boxes onto a rectangle pallet to maximise the pallet utilization percentage while reducing the Complexity of loading.Design/methodology/approach: In this research a Block approach is proposed using a Mixed integer linear programming (MILP) model that generates layouts of an improved structure, which is very effective due to its properties in grouping boxes in a certain orientation along the X and Y axis. Also, a novel complexity index is introduced to compare the complexity for different pallet loading, which have the same pallet size but different box arrangements.Findings: The proposed algorithm has been tested against available data-sets in literature and the complexity measure and graphical layout results clearly demonstrate the superiority of the proposed approach compared with literature Manufacturers pallet-loading problem layouts.Originality/value: This study aids real life manufactures operations when less complex operations are essential to reduce the complexity of pallet loading.

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Polyhedral Results and Branch-and-Cut for the Resource Loading Problem

INFORMS Journal on Computing ◽

10.1287/ijoc.2020.0957 ◽

2020 ◽

Author(s):

Guopeng Song ◽

Tamás Kis ◽

Roel Leus

Keyword(s):

Resource Use ◽

Capacity Planning ◽

Mixed Integer Linear Programming ◽

Branch And Cut ◽

Mixed Integer ◽

The Novel ◽

Due Dates ◽

Capacity Limits ◽

Resource Loading ◽

Loading Problem

We study the resource loading problem, which arises in tactical capacity planning. In this problem, one has to plan the intensity of execution of a set of orders to minimize a cost function that penalizes the resource use above given capacity limits and the completion of the orders after their due dates. Our main contributions include a novel mixed-integer linear-programming (MIP)‐based formulation, the investigation of the polyhedra associated with the feasible intensity assignments of individual orders, and a comparison of our branch-and-cut algorithm based on the novel formulation and the related polyhedral results with other MIP formulations. The computational results demonstrate the superiority of our approach. In our formulation and in one of the proofs, we use fundamental results of Egon Balas on disjunctive programming.

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A Comparison of Two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting

INFORMS Journal on Computing ◽

10.1287/ijoc.2021.1114 ◽

2021 ◽

Author(s):

John Alasdair Warwicker ◽

Steffen Rebennack

Keyword(s):

Linear Programming ◽

Linear Function ◽

Integer Linear Programming ◽

Mixed Integer Linear Programming ◽

Piecewise Linear ◽

Piecewise Linear Function ◽

Mixed Integer ◽

Data Sets ◽

Binary Variables ◽

Function Fitting

The problem of fitting continuous piecewise linear (PWL) functions to discrete data has applications in pattern recognition and engineering, amongst many other fields. To find an optimal PWL function, the positioning of the breakpoints connecting adjacent linear segments must not be constrained and should be allowed to be placed freely. Although the univariate PWL fitting problem has often been approached from a global optimisation perspective, recently, two mixed-integer linear programming approaches have been presented that solve for optimal PWL functions. In this paper, we compare the two approaches: the first was presented by Rebennack and Krasko [Rebennack S, Krasko V (2020) Piecewise linear function fitting via mixed-integer linear programming. INFORMS J. Comput. 32(2):507–530] and the second by Kong and Maravelias [Kong L, Maravelias CT (2020) On the derivation of continuous piecewise linear approximating functions. INFORMS J. Comput. 32(3):531–546]. Both formulations are similar in that they use binary variables and logical implications modelled by big-[Formula: see text] constructs to ensure the continuity of the PWL function, yet the former model uses fewer binary variables. We present experimental results comparing the time taken to find optimal PWL functions with differing numbers of breakpoints across 10 data sets for three different objective functions. Although neither of the two formulations is superior on all data sets, the presented computational results suggest that the formulation presented by Rebennack and Krasko is faster. This might be explained by the fact that it contains fewer complicating binary variables and sparser constraints. Summary of Contribution: This paper presents a comparison of the mixed-integer linear programming models presented in two recent studies published in the INFORMS Journal on Computing. Because of the similarity of the formulations of the two models, it is not clear which one is preferable. We present a detailed comparison of the two formulations, including a series of comparative experimental results across 10 data sets that appeared across both papers. We hope that our results will allow readers to take an objective view as to which implementation they should use.

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Mixed Integer Linear Programming Models to Solve a Real-Life Vehicle Routing Problem with Pickup and Delivery

Applied Sciences ◽

10.3390/app11209551 ◽

2021 ◽

Vol 11 (20) ◽

pp. 9551

Author(s):

Ali Louati ◽

Rahma Lahyani ◽

Abdulaziz Aldaej ◽

Racem Mellouli ◽

Muneer Nusir

Keyword(s):

Linear Programming ◽

Vehicle Routing ◽

Integer Linear Programming ◽

Vehicle Routing Problem ◽

Mixed Integer Linear Programming ◽

Real Life ◽

Mixed Integer ◽

Pickup And Delivery ◽

Routing Problem

This paper presents multiple readings to solve a vehicle routing problem with pickup and delivery (VRPPD) based on a real-life case study. Compared to theoretical problems, real-life ones are more difficult to address due to their richness and complexity. To handle multiple points of view in modeling our problem, we developed three different Mixed Integer Linear Programming (MILP) models, where each model covers particular constraints. The suggested models are designed for a mega poultry company in Tunisia, called CHAHIA. Our mission was to develop a prototype for CHAHIA that helps decision-makers find the best path for simultaneously delivering the company’s products and collecting the empty boxes. Based on data provided by CHAHIA, we conducted computational experiments, which have shown interesting and promising results.

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Solving a Real-Life Distributor’s Pallet Loading Problem

Mathematical and Computational Applications ◽

10.3390/mca26030053 ◽

2021 ◽

Vol 26 (3) ◽

pp. 53

Author(s):

Mauro Dell’Amico ◽

Matteo Magnani

Keyword(s):

Bin Packing ◽

Real Life ◽

Second Phase ◽

Pallet Loading ◽

Minimum Number ◽

Loading Problem ◽

The Difference ◽

Two Phases ◽

The Stability ◽

Selection Of

We consider the distributor’s pallet loading problem where a set of different boxes are packed on the smallest number of pallets by satisfying a given set of constraints. In particular, we refer to a real-life environment where each pallet is loaded with a set of layers made of boxes, and both a stability constraint and a compression constraint must be respected. The stability requirement imposes the following: (a) to load at level k+1 a layer with total area (i.e., the sum of the bottom faces’ area of the boxes present in the layer) not exceeding α times the area of the layer of level k (where α≥1), and (b) to limit with a given threshold the difference between the highest and the lowest box of a layer. The compression constraint defines the maximum weight that each layer k can sustain; hence, the total weight of the layers loaded over k must not exceed that value. Some stability and compression constraints are considered in other works, but to our knowledge, none are defined as faced in a real-life problem. We present a matheuristic approach which works in two phases. In the first, a number of layers are defined using classical 2D bin packing algorithms, applied to a smart selection of boxes. In the second phase, the layers are packed on the minimum number of pallets by means of a specialized MILP model solved with Gurobi. Computational experiments on real-life instances are used to assess the effectiveness of the algorithm.

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A Bender’s Algorithm of Decomposition Used for the Parallel Machine Problem of Robotic Cell

Mathematics ◽

10.3390/math9151730 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1730

Author(s):

Mohammad Reza Komari Alaei ◽

Mehmet Soysal ◽

Atabak Elmi ◽

Audrius Banaitis ◽

Nerija Banaitiene ◽

...

Keyword(s):

Linear Programming ◽

Integer Linear Programming ◽

Mixed Integer Linear Programming ◽

Real Life ◽

Parallel Machine ◽

Mixed Integer ◽

Robotic Cell ◽

Cell Scheduling ◽

Parallel Machine Problem ◽

Machine Problem

The present research addresses the single transportation robot used to alleviate problems of robotic cell scheduling of the machines. For the purpose of minimizing the make-span, a model of mixed-integer linear programming (MILP) has been suggested. Since the inefficiency exists in NP-hard, a decomposition algorithm posed by Bender was utilized to alleviate the problem in real life situations. The proposed algorithm can be regarded as an efficient attempt to apply optimality Bender’s cuts regarding the problem of parallel machine robotic cell scheduling in order to reach precise resolutions for medium and big sized examples. The numerical analyses have demonstrated the efficiency of the proposed solving approach.

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