In this paper, we consider the problem of scheduling on two-machine permutation flowshop with minimal time lags between consecutive operations of each job. The aim is to find a feasible schedule that minimizes the total tardiness. This problem is known to be NP-hard in the strong sense. We propose two mixed-integer linear programming (MILP) models and two types of valid inequalities which aim t...

in this paper, we consider a flow shop scheduling problem with availability constraints (fsspac) for the objective of minimizing the makespan. in such a problem, machines are not continuously available for processing jobs due to preventive maintenance activities. we proposed a mixed-integer linear programming (milp) model for this problem which can generate non-permutation schedules. furthermor...

Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic,...

The problem of laying out a survivable IP network over a WDM network is considered. The links of the IP network are realized by unprotected lightpaths of the WDM network, and the lightpaths must be routed so that the IP network remains connected after any fault. Crochat and Le Boudec [2] introduced the problem for the case of single fiber-link failures, and Modiano and Narula-Tam [5] provided a...

First-order programming (FOP) is a new representation language that combines the strengths of mixed-integer linear programming (MILP) and first-order logic (FOL). In this paper we describe a novel feasibility proving system for FOP formulas that combines MILP solving with instance-based methods from theorem proving. This prover allows us to perform lifted inference by repeatedly refining a prop...

This paper addresses the solution of a nonlinear boolean quadratic programming problem using three different approaches. The first uses a classic linearization technique to transform the original problem into a Mixed Integer Linear Programming (MILP) problem for which multiple formulations are studied. The second uses the capabilities of current MILP solvers to deal with Mixed Integer Quadratic...

This paper presents an intellectual property (IP)-based system-on-chip (SoC) synthesis framework focusing on how to select IPs from different sources and how to integrate the selected IPs using on-chip buses. In order to synthesize an on-chip bus-based SoC architecture using IPs with imprecise design costs, we propose a possibilistic mixed integer linear programming (PMILP) model, which is conv...

We study an assignment type resource-constrained project scheduling problem with resources being multi-skilled personnel to minimize the total staffing costs. We develop a hybrid Benders decomposition (HBD) algorithm that combines the complimentary strengths of both mixed-integer linear programming (MILP) and constraint programming (CP) to solve this NP-hard optimization problem. An effective c...

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations. First-order logic (FOL), on the other hand, excels at reasoning about classes of objects, but lacks a rich representation of uncertainty. While representing propo...

The problem of selecting processes and capacity expansion policies for a chemical complex consisting of continuous chemical processes can be formulated as a multiperiod mixed integer linear programming problem. Based on a variable disaggregation technique that exploits lot sizing substructures, we propose two reformulations of the conventional MILP model. The first one is an NLP reformulation t...