This paper presents a new mixed integer programming model for the Proportional Lot-Sizing Problem (plsp) with identical parallel machines and set-up times overlapping two periods. The proposed model assumes constant period length and explicitly calculates the distribution of set-up operations among periods. The presented results of computational experiments with standard mip methods prove that ...

In this paper, we introduce a new spatially constrained clustering problem called the max-p-regions problem. It involves the clustering of a set of geographic areas into the maximum number of homogeneous regions such that the value of a spatially extensive regional attribute is above a predefined threshold value. We formulate the max-p-regions problem as a mixed integer programming (MIP) proble...

A simulation-based scheduling mechanism for photoreconnaissance satellite is presented in this paper. The satellite scheduling problem belongs to a class of singlemachine scheduling problems with time window constraint. It is NP-hard in computational complexity. Based on simulation platform, a mixed integer programming model is used to formulate the problem and an advanced tabu algorithm is ado...

Collision-tolerant trajectory planning is the consideration that collisions, if they are planned appropriately, enable more effective path planning for robots capable of handling them. A mixed integer programming (MIP) optimization formulation demonstrates the computational practicality of optimizing trajectories that comprise planned collisions. A damage quantification function is proposed, an...

1 Summary: This paper deals with lot sizing and scheduling for a single-stage production system where setup costs and times are sequence dependent. A large bucket mixed integer programming (MIP) model is formulated which considers only eecient sequences. A tailor-made enumeration method of the branch-and-bound type solves problem instances optimally and eeciently. Furthermore, it will become cl...

Split cuts form a well-known class of valid inequalities for mixed-integer programming problems (MIP). Cook et al. (1990) showed that the split closure of a rational polyhedron P is again a polyhedron. In this paper, we extend this result from a single rational polyhedron to the union of a finite number of rational polyhedra. We also show how this result can be used to prove that some generaliz...

In this thesis, we review and synthesize a number of algorithmic approaches for optimizing the job-shop scheduling problem (JSSP). The complexity of the JSSP leads to large and difficult combinatorial optimization models. In Chapter 1, we review first an analytical method based on Mixed Integer Programming (MIP). Second, we review an assumption-based heuristic method. In Chapter 2, the JSSP is ...

this paper uses the weighted l$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. when all variables are integer it finds the whole set of efficient solutions. in each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...

Machine learning (ML) has been recently introduced to solving optimization problems, especially for combinatorial (CO) tasks. In this paper, we survey the trend of leveraging ML solve mixed-integer programming problem (MIP). Theoretically, MIP is an NP-hard problem, and most CO problems can be formulated as MIP. Like other human-designed heuristic algorithms rely on good initial solutions cost ...