# Morteza DavariSKEMA Business School

Morteza Davari

PhD

Assistant Professor of Operations Research @ SKEMA Business School

## About

27

Publications

7,743

Reads

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188

Citations

Introduction

I am an Assistant Professor at SKEMA Business School, Lille, France.

Additional affiliations

August 2020 - present

December 2017 - August 2020

January 2017 - November 2017

## Publications

Publications (27)

We consider the simultaneous scheduling of multiple sport leagues, with
inter-dependencies arising from teams in different leagues belonging to the same club.
The problem is to assign teams to Home-Away patterns while minimizing the total
capacity violation over all clubs during the season. We show that this Multi-league
Scheduling Problem can be s...

We consider a single-machine scheduling problem with release dates and inventory constraints. Each job has a deterministic processing time and has an impact (either positive or negative) on the central inventory level. We aim to find a sequence of jobs such that the makespan is minimized while all release dates and inventory constraints are met. We...

This paper studies the complexity of single-machine scheduling with an external resource, which is rented for a non-interrupted period. Jobs that need this external resource are executed only when the external resource is available. There is a cost associated with the scheduling of jobs and a cost associated with the duration of the renting period...

This paper considers the problem of maximizing the expected net present value of a project under uncertain cash flows, which are described by a supporting set of discrete scenarios. While cash flows are often considered more or less stable in countries with a stable economy, they can be quite uncertain in countries with financial and/or political c...

We study the scheduling of jobs on a single parallel-batching machine with non-identical job sizes and incompatible job families. Jobs from the same family have the same processing time and can be loaded into a batch, as long as the batch size respects the machine capacity. The objective is to minimize the total weighted completion time; this commo...

As the COVID pandemic shows, infection spreads widely across regions, impacting economic activity in unforeseen ways. We represent here how the geographic spread of the pandemic, by reducing the workers’ participation to economic life, undermines the ability of firms and as a result the entire supply networks to satisfy customers’ demands. We model...

We study the scheduling of jobs on a single parallel-batching machine with non-identical job sizes and incompatible job families. Jobs from the same family have the same processing time and can be loaded into a batch, as long as the batch size respects the machine capacity. The objective is to minimize the total weighted completion time. The proble...

In this work, we study a project scheduling problem with the aim of maximizing the net present value. We assume that there are sufficient internal resources to complete the activities, but we should rent an expensive external resource (e.g. crane, bulldozer, concrete mixer, etc) to complete some activities. First, this problem is modeled by two dif...

Uncertainty has become an inevitable aspect of project scheduling. We study the resource-constrained project scheduling problem (RCPSP) with stochastic durations. One of the most studied approaches to deal with stochastic durations is that of proactive and reactive scheduling. Previous researches often studied proactive and reactive scheduling rath...

The proactive and reactive resource-constrained project scheduling problem (PR-RCPSP), that has been introduced recently (Davari and Demeulemeester, 2017), deals with activity duration uncertainty in a very unique way. The optimal solution to an instance of the PR-RCPSP is a proactive and reactive policy (PR-policy) that is a combination of a basel...

The resource-constrained project scheduling problem (RCPSP) has been widely studied during the last few decades. In real-world projects, however, not all information is known in advance and uncertainty is an inevitable part of these projects. The chance-constrained resource-constrained project scheduling problem (CC-RCPSP) has been recently introdu...

There has been a lot of recent work on sport tournament scheduling. However, much of the literature has focused on scheduling a single tournament (league). In this work, we consider scheduling multiple leagues, with inter-dependencies arising from teams in different leagues belonging to the same club. This is a common setting for instance in youth...

We consider a single-machine scheduling problem with release dates and inventory constraints. Each job has a deterministic processing time and has an impact (either positive or negative) on the central inventory level. We aim to find a sequence of jobs such that the makespan is minimized while all release dates and inventory constraints are met. We...

We study a single-machine scheduling problem that is a generalization of a number of problems for which computational procedures have already been published. Each job has a processing time, a release date, a due date, a deadline and a weight representing the penalty per unit-time delay beyond the due date. The goal is to schedule all jobs such that...

In the realm of scheduling problems, different sources of uncertainty such as probabilistic durations of jobs or stochastic breakdowns of machines can arise. Given this, one highly desirable characteristic of an intelligent schedule is to bring better punctuality with less efficiency-loss because a dominant factor in customer appreciation is punctu...

A fundamental challenge associated with research or new product development projects is identifying that innovative activity that will deliver success. In such projects, it is typically the case that innovative breakthroughs can be achieved by any of several possible alternative technologies, some of which may fail due to the technological risks in...

We study a single-machine scheduling problem that is a generalization of a number of problems for which computational procedures have already been published. Each job has a processing time, a release date, a due date, a deadline and a weight representing the penalty per unit-time delay beyond the due date. The goal is to schedule all jobs such that...

This thesis studies order acceptance and scheduling problems in a single-machine environment where the set of jobs contains firm-planned jobs and optional jobs. Each job has a processing time, a release date, a due date, a deadline, a revenue and a weight representing the penalty per unit-time delay when it is completed after its due date but befor...

Uncertainty is an inevitable element in many practical production planning and scheduling environments. When a due date is predetermined for performing a set of jobs for a customer, production managers are often concerned with establishing a schedule with the highest possible confidence of meeting the due date. In this paper, we study the problem o...

## Questions

Questions (5)

I am wondering whether you have any idea about the complexity of the following graph coloring problem:

Simple case:

We are given the following 5-regular bipartite graph: G(V,E) where V = A U B. By definition they are five edges incident to each vertex in A and five to each vertex in B. Since the problem is k-regular and bipartite, there is an edge-coloring with 5 colors and that can be found in polynomial time. This is straightforward but unfortunately my problem is more complex.

My case:

Consider graph G and the following five colors: c1, c2, c3, c4 and c5 where each color has two neighbors:

c1 is a neighbor of c5 and c2,

c2 is a neighbor of c1 and c3,

c3 is a neighbor of c2 and c4,

c4 is a neighbor of c3 and c5,

c5 is a neighbor of c4 and c1.

Let D be a set of non-overlapping pairs of edges (e1,e2) that must only admit neighboring colors. Thus, if e1 (respectively e2) admits c1, then e2 (respectively e1) must admit either c2 or c5.

Is it possible to color G with colors c1, c2, c3, c4 and c5 such that all pairs in D admit neighboring colors? Can this coloring be done in polynomial time?

Side information:

Example of overlapping pairs: (e1,e2) and (e2,e3) are overlapping pairs since both include e2.

I have any 2k-regular (multi) graph. I know that there exists a 2-factorization. The question is not the existence but the complexity. Can I find such a 2-factorization in polynomial time?

I have a matrix of form:

1 0 0 0 | 1 0 0 0 | 0 0 0 0

0 1 0 0 | 0 1 0 0 | 0 0 0 0

0 0 1 0 | 0 0 1 0 | 0 0 0 0

0 0 0 1 | 0 0 0 1 | 0 0 0 0

-----------------------------------------------

1 1 0 0 | 0 0 0 0 | 0 0 0 0

0 0 1 1 | 0 0 0 0 | 0 0 0 0

0 0 0 0 | 1 1 0 0 | 0 0 0 0

0 0 0 0 | 0 0 1 1 | 0 0 0 0

-----------------------------------------------

-1 0 -1 0 | 0 0 0 0 | 1 0 0 0

0 -1 0 -1 | 0 0 0 0 | 0 1 0 0

0 0 0 0 |-1 0 -1 0 | 0 0 1 0

0 0 0 0 | 0 -1 0 -1 | 0 0 0 1

Most columns have three non-zero values!

However, I tested with MATLAB and it is totally uni-modular. How can I prove that it is TUM?

My question is about the classic resource constrained project scheduling problem. In my approach, I need to compute a lower bound which is both very tight and very fast. The linear relaxation of which MILP formulation for RCPSP gives the best lower bound? I expect that one of the time-indexed versions provides the best lower bound but I am not sure which one.

Does anyone know of any other fast (linear/polynomial) and tight lower bounding approach?

In my research, I developed a model (for a stochastic scheduling problem) which works with stochastic variables. These stochastic variables assumed to follow phase type distribution in the model. One of the databases in the literature, however, contains beta distributed data, which theoretically cannot be solved using our model.

We think it might be possible to approximate these beta distributed data by a phase type distribution. I have a limitation on the number of moments (should be less than 5).

What is the easiest and/or best way of doing that?

Thanks,

## Projects

Project (1)