This paper presents a novel three-phase heuristic/algorithmic approach for the multi-depot routing problem with time windows and heterogeneous vehicles. It has been derived from embedding a heuristic-based clustering algorithm within a VRPTW optimization framework. To this purpose, a rigorous MILP mathematical model for the VRPTW problem is first introduced. Likewise other optimization approach...

In wireless sensor networks, the sensor nodes collect data, which are routed to a sink node. Most of the existing proposals address the routing problem to maximize network lifetime in the case of a single sink node. In this paper, we extend this problem into the case of multiple sink nodes. To maximize network lifetime, we consider the two problems: (i) how to position multiple sink nodes in th...

Symmetry in mathematical optimisation is of broad and current interest. In problem classes such as mixed-integer linear programming (MILP), equivalent solutions created by symmetric variables and constraints may combinatorially increase the search space. Identifying problem symmetries is an important step towards expediting tree-based algorithms such as branch-and-cut because computationally cl...

Tactical planning MILP models for fast moving consumer goods companies are often intractable for realistic applications containing thousands of Stock-Keeping Units (SKUs). Decomposition methods can be applied to these MILP models to allow realistic cases to be optimized. In this paper we present a Multi-SKU decomposition algorithm based on decomposing the full scale MILP model into submodels co...

Abstract We consider the problem of scheduling under demand uncertainty a multiproduct batch plant represented through the State Task Network. Given a scheduling horizon consisting of several time-periods in which product demands are placed, the objective is to select a schedule that maximizes the expected profit. We present a multistage stochastic Mixed Integer Linear Programming (MILP) model,...

In this paper we make a comparative study of several mixed integer linear programming (MILP) formulations for resource-constrained project scheduling problems (RCPSPs). First, we present three discrete and continuous time MILP formulations issued from the literature. Second, instead of relying on the traditional discretization of the time horizon, we propose MILP formulations for the RCPSP base...

In many real-world hybrid (mixed discrete continuous) planning problems such as Reservoir Control, Heating, Ventilation and Air Conditioning (HVAC), and Navigation, it is difficult to obtain a model of the complex nonlinear dynamics that govern state evolution. However, the ubiquity of modern sensors allow us to collect large quantities of data from each of these complex systems and build accur...

In this paper we present a mixed integer linear programming (MILP) resource allocation model with hard and soft resource constraints for projects. By definition, a hard resource constraint is not resolvable within the given planning horizon, but a soft resource conflict may be managed by a flexible "hiring-firing" strategy. A "well-balanced" optimal schedule for the soft resources is characteri...

the aim of this study is to propose a new mixed integer linear programming (milp) model to find the minimum required number of yard cranes, rubber tyred gantry cranes (rtgcs), for completion the total amount of works at the end of planning horizon. in other word, we find the optimal number of yard cranes in a container terminal which completes the total amount of works. the paper supports the p...

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...