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...

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...

Over the past few decades, neuroscience experiments have become increasingly complex and naturalistic. Experimental design has in turn more challenging, as must conform to an ever-increasing diversity of constraints. In this article, we demonstrate how process can be greatly assisted using optimization tool known mixed-integer linear programming (MILP). MILP provides a rich framework for incorp...

We study the performance of Empirical Revenue Maximizing (ERM) mechanism in a single-item, single-seller, single-buyer setting. assume buyer’s valuation is drawn from regular distribution F and that seller has access to two independently samples F. By solving family mixed-integer linear programs (MILPs), ERM proven guarantee at least .5914 times optimal revenue expectation. Using solutions thes...

A conic integer program is an integer programming problem with conic constraints.Manyproblems infinance, engineering, statistical learning, andprobabilistic optimization aremodeled using conic constraints. Herewe studymixed-integer sets definedby second-order conic constraints.We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second...

Here, we consider single vendor-buyer model with multi-product and multi-customer and multi-facility location-production-distribution problem. It is assumed that the players of the supply chain are coordinated by sharing information. Vendor manufactures produce different products at different plants with limited capacities and then distribute the products to the consumers according to determini...