Recent Improvements Using Constraint Integer Programming for Resource Allocation and Scheduling

Constraint integer programming (CIP) is a novel paradigm which integrates constraint programming (CP), mixed integer programming (MIP), and satisfiability (SAT) modeling and solving techniques. In this paper we discuss the software framework and solver SCIP (Solving Constraint Integer Programs), which is free for academic and non-commercial use and can be downloaded in source code. This paper gives an overview of the main design concepts of SCIP and how it can be used to solve constraint integer programs. To illustrate the performance and flexibility of SCIP, we apply it to two different problem classes. First, we consider mixed integer programming and show by computational experiments that SCIP is almost competitive to specialized commercial MIP solvers, even though SCIP supports the more general constraint integer programming paradigm. We develop new ingredients that improve current MIP solving technology. As a second application, we employ SCIP to solve chip design verification problems as they arise in the logic design of integrated circuits. This application goes far beyond traditional MIP solving, as it includes several highly non-linear constraints, which can be handled nicely within the constraint integer programming framework. We show anecdotally how the different solving techniques from MIP, CP, and SAT work together inside SCIP to deal with such constraint classes. Finally, experimental results show that our approach outperforms current state-of-the-art techniques for proving the validity of properties on circuits containing arithmetic.

Integer programming models for the q-mode problem

A cutting plane algorithm for the site layout planning problem with travel barriers

The paper presents a modeling framework to analyze some important issues associated with operation planning of a power system. Major activities involved in operations planning of large integrated power systems are considered simultaneously to ensure optimal utilization of generation and transmission capacity. The model also examines optimal transmission expansion plans vis‐à‐vis fuel supply issues. A mixed integer programming model is developed for this purpose and the Indian power system considered. Specific emphasis is on spatial transmission expansion plan for the existing Indian inter‐state transmission grid and new transmission links, coordinated operation of the isolated regional grids and system benefits accruing from transmission expansion, enhanced fuel production and supply rescheduling to ensure efficient operation of various generating stations.

Dynamic hoist scheduling problem with multi-capacity reentrant machines: A mixed integer programming approach

In apparel manufacturing, cut pieces produced by the cutting process are a key input work-in-process (WIP) to the bottleneck sewing process. However, an excessive inventory of cut pieces not only requires extra storage space but also creates difficulties with shop floor control. This study determines the ideal cutting times of fabric lays by minimising the cut piece inventory under the constraint that sufficient cut pieces are produced in time to satisfy the bottleneck usage. This study proposes a mixed integer programming (MIP) model and a heuristic method to solve the problem. The solutions for most test instances of the problem that are calculated by the heuristic method are not as good as those by the MIP solver; however, the heuristic method computation times are negligible. The experiments show that the MIP model’s efficiency significantly improves by starting from an initial solution provided by the proposed heuristic method.

We solve the flexible job shop scheduling problems (F-JSSPs) to minimize makespan. First, we compare the constraint programming (CP) model with the mixed-integer programming (MIP) model for F-JSSPs. Second, we exploit the decomposable structure within the models and develop an efficient CP–logic-based Benders decomposition (CP-LBBD) technique that combines the complementary strengths of MIP and CP models. Using 193 instances from the literature, we demonstrate that MIP, CP, and CP-LBBD achieve average optimality gaps of 25.50%, 13.46%, and 0.37% and find optima in 49, 112, and 156 instances of the problem, respectively. We also compare the performance of the CP-LBBD with an efficient Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, which has been appraised for finding 125 optima on 178 instances. CP-LBBD finds 143 optima on the same set of instances. We further examine the performance of the algorithms on 96 newly (and much larger) generated instances and demonstrate that the average optimality gap of the CP increases to 47.26%, whereas the average optimality of CP-LBBD remains around 1.44%. Finally, we conduct analytics on the performance of our models and algorithms and counterintuitively find out that as flexibility increases in data sets the performance CP-LBBD ameliorates, whereas that of the CP and MIP significantly deteriorates.

In this paper, we deal with the least distance problem (LDP) in Data Envelopment Analysis (DEA), which is to find a closest efficient target over the whole efficient frontier. To this end, we define the efficient frontier by a linear complementarity system and propose a mixed integer programming (MIP) approach to solve the LDP. Our proposed MIP approach: (1) can solve the LDP based on [Formula: see text]-norm ([Formula: see text]) by using a state-of-the-art solver and obtain the closest efficient target over the whole efficient frontier instead of a subset of it; (2) can be applied for computing the least distance DEA models satisfying the monotonicity; (3) is more user-friendly, because it allows a decision maker to improve the efficiency of a decision making unit (DMU) by setting the affordable input/output level under his/her circumstance. Thus, the efficient target provided by our approach may be more appropriate from the perspective of the decision makers of DMUs.

Testable implications of general equilibrium models: An integer programming approach

Traditional vehicle routing problems implicitly assume that only one crew operates a vehicle for the entirety of its journey. However, this assumption is violated in many applications arising in humanitarian and military logistics. This paper considers a joint vehicle and crew routing and scheduling problem in which crews are able to interchange vehicles, resulting in space and time interdependencies between vehicle routes and crew routes. The problem is formulated as a mixed integer programming (MIP) model and a constraint programming (CP) model that overlay crew routing constraints over a standard vehicle routing problem. The constraint program uses a novel optimization constraint to detect infeasibility and to bound crew objectives. This paper also explores methods using large neighborhood search over the MIP and CP models. Experimental results indicate that modeling the vehicle and crew routing problems jointly and supporting vehicle interchanges for crews may bring significant benefits in cost reduction compared with a method that sequentializes these decisions.

In this paper, we propose a mixed integer programming (MIP) model to solve the experimental courses scheduling problem. And we use the experimental courses historical data in our information systems to solve the MIP model. The results of the numerical example demonstrate that the proposed model can reach an optimal solution in a short period of time. The MIP model can provide the decision-making support for the experimental courses arrangement.

An inexact multi-objective mixed-integer nonlinear programming approach for water-soil-fertilizer management under uncertainty considering “footprint family-planetary boundary” assessment

Automated vacuum waste collection (AVWC) uses air suction on a closed network of underground pipes to transport waste from the drop off points scattered throughout the city to a central collection point, reducing greenhouse gas emissions and the inconveniences of conventional methods (odors, noise). Since a significant part of the cost of operating AVWC systems is energy consumption, we have started a project, together with a company that builds and installs such systems, with the aim of applying constraint programming technology to schedule the daily emptying sequences of the drop off points in such a way that energy consumption is minimized. In this paper we describe how the problem of deciding the drop off points that should be emptied at a given time can be modeled as a constraint integer programming (CIP) problem. Moreover, we report on experiments using real data from AVWC systems installed in different cities that provide empirical evidence that CIP offers a suitable technology for reducing energy consumption in AVWC.

A special ordered set approach for optimizing a discontinuous separable piecewise linear function

The aim of this paper is to point out that the mixed nonlinear integer programming model proposed by Toksari and Guner (Int J Adv Manuf Technol 38:801–808, 2008) is incorrect. We present a mixed nonlinear 0–1 programming model for the same scheduling problem based on their model.