Oded Berman

University of Toronto | U of T · Rotman School of Management

New product and service introductions require careful joint planning of production and marketing campaigns. Consequently, they typically utilize multiple information channels to stimulate customer awareness and resultant word‐of‐mouth (WOM), availing of standard budget allocation tools. By contrast, when enacting strategic allocation decisions – wh...

This paper focuses on designing a facility network, taking into account that the system may be congested. The objective is to minimize the overall fixed and service capacity costs, subject to the constraints that for any demand the disutility from travel and waiting times (measured as the weighted sum of the travel time from a demand to the facilit...

We consider conditional facility location problems with unreliable facilities that can fail with known probabilities. The demand is uniformly distributed over a convex polygon in the rectilinear plane where a number of facilities are already present, and it is required to optimally locate another facility. We analyze properties of the exponential f...

We study two p‐center models on a network with probabilistic demand weights. In the first, which is called the maximum probability p‐center problem, the objective is to maximize the probability that the maximum demand‐weighted distance between the demand and the open facilities does not exceed a given threshold value. In the second, referred to as...

We consider a proposed system that would place sensors in a number of wastewater manholes in a community in order to detect genetic remnants of SARS-Cov-2 found in the excreted stool of infected persons. These sensors would continually monitor the manhole’s wastewater, and whenever virus remnants are detected, transmit an alert signal. In a recent...

Problem definition: Autonomous vehicles (AVs) are predicted to enter the consumer market in less than a decade. There is currently no consensus on whether their presence will have a positive impact on users and society. The skeptics of automation foresee increased congestion, whereas the advocates envision smoother traffic with shorter travel times...

About 50% of individuals infected with the novel Coronavirus (SARS-CoV-2) suffer from intestinal infection as well as respiratory infection. They shed virus in their stool. Municipal sewage systems carry the virus and its genetic remnants. These viral traces can be detected in the sewage entering a wastewater treatment plant (WTP). Such virus signa...

In this article, we address two network design problems for a responsive supply chain that consists of make‐to‐order (make‐to‐assemble) facilities facing stochastic demand and service time. The response time to customer orders, critical to the success of the supply chain, is the sum of the flow time in the facility and the delivery time to the cust...

In this paper, we examine whether it is optimal to use electric vehicles (EVs) in the car sharing market and investigate the environmental impact of pulling the EVs from the market. We develop a model consisting of a profit‐maximizing car sharing company (CSC) and a population of utility‐maximizing customers. The CSC sets the number of EVs, the num...

In this paper we develop a generalized framework and a novel methodology to simultaneously optimize locations and design decisions for a set of facilities that are facing competition from pre-existing facilities. The framework encompasses multi-attribute design decisions, an elastic customer demand mechanism that can capture both expansion and cann...

About 50% of individuals infected with the novel Coronavirus (SARS-CoV-2) suffer from intestinal infection as well as respiratory infection. They shed virus in their stool. Municipal sewage systems carry the virus and its genetic remnants. These viral traces can be detected in the sewage entering a wastewater treatment plant (WTP). Such virus signa...

We consider a two-echelon production inventory system with a manufacturer having limited production capacity and a distribution center (DC). There is a positive transportation time between the manufacturer and the DC. Customers gain a value by receiving the product and incur a waiting cost when facing a delay. We assume that customers' waiting cost...

This paper studies a Markovian two-station tandem queueing network with impatient customers. Queueing networks with abandonment are common in many industries, e.g., call centers and healthcare. Therefore, their management has received much attention. The resulting model is a level-dependent quasi-birth-and-death (LDQBD) process. Such models are con...

The main goal of this paper is to present a simple and tractable methodology for incorporating data uncertainty into optimization models in the presence of binary variables. We introduce the Almost Robust Discrete Optimization (ARDO). ARDO extends the Integrated Chance-Constrained approach, developed for linear programs, to include binary integer v...

Preferences for different ages of perishable products exist in many applications, including grocery items and blood products. In this paper, we study a multi‐period stochastic perishable inventory system with multiple priority classes that require products of different ages. The firm orders the product with a positive leadtime and sells it to multi...

In this chapter we describe facility location models where consumers generate streams of stochastic demands for service, and service times are stochastic. This combination leads to congestion, where some of the arriving demands cannot be served immediately and must either wait in queue or be lost to the system. These models have applications that r...

We consider the problem of service network design: choosing the optimal number, locations, and service capacities of facilities, taking into account that facilities may have a finite or an infinite waiting room. Accordingly, our service measure is either the percentage of blocked customers or the percentage of customers who need to wait in line. Th...

This paper studies a stochastic congested location problem in the network of a service system that consists of facilities to be established in a finite number of candidate locations. Population zones allocated to each open service facility together creates a stream of demand that follows a Poisson process and may cause congestion at the facility. T...

This paper shows that operational flexibility interacting with informational uncertainty may lead to truthful information exchange in equilibrium even when the communication is nonbinding and unverifiable, i.e., “cheap talk.” We consider a model consisting of a manufacturer releasing a new product with uncertain release date and demand, and a retai...

Covering location models assume that a demand point is either fully covered or not covered at all. Gradual cover models consider the possibility of partial cover. In this paper, we investigate the issue of joint partial coverage by several facilities in a multiple facilities location model. We establish theoretical foundations for the properties of...

In a recent paper Lopez-de-los-Mozos et al. (2013), an algorithmic approach was presented for the robust (minmax regret) absolute deviation single-facility location problem on networks with node weights which are linear functions of an uncertain or dynamically changing parameter. The problem combines the mean absolute deviation criterion, which is...

Under current regulations, red blood cell (RBC) units can be transfused to patients up to 42 days after donation. However, recent studies suggest an association between the age of transfused RBCs and adverse clinical outcomes for their recipients. Therefore, there is an interest in inventory management policies that could reduce the age of transfus...

In the last two decades, terrorism has become a major issue around the world. We analyze a continuous conflict between a terrorist (Terrorist) and a passive defender (Defender). Defender is passive because her actions can influence only the costs (damages) when Terrorist attacks. We focus on high-trajectory fire attacks and passive responses to the...

We consider a continuous review ( s, S ) model of perishable items with lost sales. Once items are perished the entire inventory drops instantaneously to zero. The total cost includes the cost of: ordering, unsatisfied demand, units destroyed, holding, and fixed cost of perishability. Both the time to perishability and the lead times are assumed to...

We study networks of facilities that must provide coverage under conditions of uncertainty with respect to travel times and customer demand. We model this uncertainty through a set of scenarios. Since opening new facilities and/or closing existing ones is often quite expensive, we focus on optimal re-configuration of the network, that is finding a...

We consider a two-echelon production-inventory system with a single manufacturer operating from a warehouse and a distribution center (DC) using the continuous review inventory policy where transportation times between the two echelons are generally distributed. We first derive the optimal reorder point at the DC, and then, propose a heuristic to a...

This paper, motivated by a collaboration with a healthcare service provider, focuses on stochastic open-shop service networks with two objectives: more traditional macrolevel measures (such as minimizing total system time or minimizing total number of tardy customers) and the atypical microlevel measure of reducing the incidents of excessively long...

We analyze two different mechanisms for assigning customers to locations in inventory location models: Direct Assignment (DA), where customers are assigned by the system operator to optimize overall system performance; and, Customer Choice (CC), where customers self-assign to the most convenient (generally closest) open facility. DA is natural for...

In this paper we study the effect of a decision maker's risk attitude on the median and center problems, two well-known location problems, with uncertain demand in the mean-variance framework. We provide a mathematical programming formulation for both problems in the form of quadratic programming and develop solution procedures. In particular, we c...

Background: Although recent randomized controlled trials have not found increased risk of morbidity/mortality with older red blood cells (RBCs), several large trials will be completed soon providing power to detect smaller risks if indeed they exist. Hence, there may still be a need for inventory management policies that could reduce the age of tr...

This paper focuses on designing facility networks in the public sector so as to maximize the number of people benefiting from their services. We develop an analytical framework for the maximal accessibility network design problem that involves determining the optimal number, locations, and capacities of a network of public sector facilities. We ass...

We consider facility location problems where the demand is continuously and uniformly distributed over a convex polygon with m vertices in the rectilinear plane, n facilities are already present, and the goal is to find an optimal location for an additional facility. Based on an analysis of structural properties of incremental Voronoi diagrams, we...

This paper considers two covering location problems on a network where the demand is distributed along the edges. The first is the classical maximal covering location problem. The second problem is the obnoxious version where the coverage should be minimized subject to some distance constraints between the facilities. It is first shown that the fin...

Mismatch between supply and demand when the uncertainty of the demand is high and the supply lead time is relatively long, such as seasonal good markets, can result in high overstocking and understocking costs. In this paper we propose transshipment as a powerful mechanism to mitigate the mismatch between the supply and demand. We consider a finite...

In this chapter we describe facility location models where consumers generate streams of stochastic demands for service, and service times are stochastic. This combination leads to congestion, where some of the arriving demands cannot be served immediately and must either wait in queue or be lost to the system. These models have applications that r...

Mismatch between supply and demand when the uncertainty of the demand is high and the supply lead time is relatively long such as seasonal good markets can result in high overstocking and understocking costs. In this paper we propose proactive transshipment as a powerful mechanism to mitigate the mismatch between the supply and demand. We consider...

We consider a two-echelon inventory system with a capacitated centralized production facility and several distribution centers (DCs). Both production and transportation times are stochastic with general distributions. Demand arrives at each DC according to an independent Poisson process and is backlogged if the DC is out of stock. We allow differen...

Introduction of a new, innovative product or service is a fundamental problem that managers face regularly. The temporal sales pattern of such a product is often dynamically influenced by word of mouth as well as by marketing and distribution support. Appropriate marketing support strategies must be specified to induce the best sales pattern; howev...

In this article, we consider the cooperative maximum covering location problem on a network. In this model, it is assumed that each facility emits a certain “signal” whose strength decays over distance according to some “signal strength function.” A demand point is covered if the total signal transmitted from all the facilities exceeds a predefined...

Spatial planners often make "comprehensive" decisions on the location of public service facilities by using the concept of urban hierarchy: population centers at the upper level of the hierarchy (typically large cities) get the highest level facilities, such as specialized hospitals and universities, while the centers at the lower levels of hierarc...

We consider the problem of locating facilities of two types at nodesof a tree network. Customers may need just one type of service, or bothtypes; in the latter case, to minimize transportation costs, the customers visit facilities of both types in a single trip. Each facility incurs a fixed cost that depends on the type of the facility and the node...

The most common measure of waiting time is the overall expected waiting time for service. However, in service networks the perception of waiting may also depend on how it is distributed among different stations. Therefore, reducing the probability of a long wait at any station may be important in improving customers’ perception of service quality....

We consider a two-echelon supply chain problem, where the demand of a set of retailers is satisfied from a set of suppliers and shipped through a set of capacitated cross-docks that are to be established. The objective is to determine the number and location of cross-docks and the assignment of retailers to suppliers via cross-docking so that the t...

In the last two decades, terrorism has become a major issue around the world. We analyze a conflict between a terrorist (Terrorist) and a passive defender (Defender) using a simple game theoretical model. Defender is passive as her actions can only influence the costs (damages) when Terrorist attacks. We consider single and multi period games. In e...

A cooperative covering location problem anywhere on the networks is analysed. Each facility emits a signal that decays by the distance along the arcs of the network and each node observes the total signal emitted by all facilities. A node is covered if its cumulative signal exceeds a given threshold. The cooperative approach differs from traditiona...

In this paper we study a class of locations models where facilities are not perfectly reliable and failures may be correlated. We analyze problems with Median and Center objectives under complete and incomplete customer information regarding the state of facilities. The goal is to understand how failure probabilities, correlations, availability of...

Bid price, also referred to as shadow price, is a fundamental economic concept to measure the marginal value of a resource. It is one of the key drivers to determine pricing or capacity allocation decisions in revenue management (RM). Our paper provides a probabilistic characterization of the optimal policies in RM from the perspective of bid-price...

► We considered a potential bioterror attack on an airport with subsequent resource allocation. ► The problem of minimizing the expected number of deaths and its min–max counterpart is addressed. ► Marginal analysis algorithms can solve the problem given estimates of the total number of initially infected passengers. ► It is presented a c...

In this article, we study how the operational decisions of a firm manager depend on her own incentives, the capital structure, and financial decisions in the context of the newsvendor framework. We establish a relationship between the firm’s cost of raising funds and the riskiness of the inventory decisions of the manager. We consider four types of...

In this paper we develop a service network design model that explicitly takes into account the elasticity of customer demand with respect to travel distance and congestion delays. The model incorporates a feedback loop between customer demand and congestion at the facilities. The problem is to determine the number of facilities, their locations, th...

In contrast with sick people who need urgent medical attention, the clientele of preventive healthcare have a choice in whether to participate in the programs offered in their region. In order to maximize the total participation to a preventive care program, it is important to incorporate how potential clients choose the facilities to patronize. We...

We consider a coordinated location-inventory model where distribution centers (DCs) follow a periodic-review (R,S) inventory policy and system coordination is achieved by choosing review intervals at the DCs from a menu of permissible choices. We introduce two types of coordination: partial coordination where each DC may choose its own review inter...

Both public and private facilities often have to provide adequate service under a variety of conditions. In particular travel times, that determine customer access, change due to changing traffic patterns throughout the day, as well as a result of special events ranging from traffic accidents to natural disasters. We study the maximum covering loca...

We address a stochastic facility location and vehicle assignment problem in which customers are served by full return trips. The problem consists of simultaneously locating a set of facilities, determining the vehicle fleet size at each facility, and allocating customers to facilities and vehicles in the presence of random travel times. Such travel...

We consider a two-echelon inventory system with a manufacturer operating from a warehouse supplying multiple distribution centers (DCs) that satisfy the demand originating from multiple sources. The manufacturer has a finite production capacity and production times are stochastic. Demand from each source follows an independent Poisson process. We a...

We consider the following basic search path problem: a customer residing at a node of a network needs to obtain service from one of the facilities; facility locations are known and fixed. Facilities may become inoperational with certain probability; the state of the facility only becomes known when the facility is visited. Customer travel stops whe...

We study the gradual covering location problem on a network with uncertain demand. A single facility is to be located on the network. Two coverage radii are defined for each node. The demand originating from a node is considered fully covered if the shortest distance from the node to the facility does not exceed the smaller radius, and not covered...

A family of discrete cooperative covering problems is analysed in this paper. Each facility emits a signal that decays by the distance and each demand point observes the total signal emitted by all facilities. A demand point is covered if its cumulative signal exceeds a given threshold. We wish to maximize coverage by selecting locations for p faci...

In this paper, we consider the problem of making simultaneous decisions on the location, service rate (capacity) and the price of providing service for facilities on a network. We assume that the demand for service from each node of the network follows a Poisson process. The demand is assumed to depend on both price and distance. All facilities are...

T wo factors that their influence on the demand has been investigated in many papers are (i) the shelf space allocated to a product and to its complement or supplement products and (ii) the instantaneous inventory level seen by customers. Here we analyze the joint shelf space allocation and inventory decisions for multiple items with demand that de...

In this article, we propose a global optimization technique (Big Segment Small Segment) for solving single facility location problems on a network when the location of the facility can either at nodes or along the links of the network. Some multiple facility location problems can be solved by recursively solving single facility problems. The techni...

We study the problem of locating n facilities subject to failure on a unit line segment. The objective is to minimize the expected travel distance assuming that customers have information about the status of each facility ahead of time and thus travel directly to the closest operating facility (if one exists). The problem was previously studied onl...

The gradual covering location problem seeks to establish facilities on a network so as to maximize the total demand covered, allowing partial coverage. We focus on the gradual covering location problem when the demand weights associated with nodes of the network are random variables whose probability distributions are unknown. Using only informatio...

Modern Location Theory includes a large and growing field studying the impact of various types of uncertainty in location models. This field of Stochastic Location Models can be traced back to the pioneering work of Frank, whose 1966 paper “Optimum Locations on a Graph with Probabilistic Demands” represents the first formal analysis of stochastic i...

The goal of the paper is to provide an overview of the following classes of models:Gradual cover models: These models seek to relax the “all or nothing” assumption by replacing it with a general coverage function which represents the proportion of demand covered at a certain distance from the facility.The cooperative cover model: This recently deve...

This paper is an in-depth treatment of an inventory control problem with perishable items. We focus on two prototypes of perishability for items that have a common shelflife and that arrive in batches with zero lead time: (i) sudden deaths due to disasters (e.g., spoilage because of extreme weather conditions or a malfunction of the storage place)...

We study the problem of locating p facilities to serve clients residing at the nodes of a network with discrete probabilistic demand weights. The objective is to maximize the probability that the total weighted distance from a client to the closest facility does not exceed a given threshold value. The problem is formulated as an integer program but...

A major problem addressed during the preparation of spatial development plans relates to the accessibility to facilities where services of general interest such as education, health care, public safety, and justice are offered to the population. In this context, planners typically aim at redefining the level of hierarchy to assign to the urban cent...

A cooperative-covering family of location problems is proposed in this paper. Each facility emits a (possibly non-physical) “signal” which decays over the distance and each demand point observes the aggregate signal emitted by all facilities. It is assumed that a demand point is covered if its aggregate signal exceeds a given threshold; thus facili...

Five common options for workforce flexibility and their robustness under uncertain demand are investigated. In the first stage, a firm makes optimal staffing decisions according to estimated demand and a given workforce flexibility policy. In the second stage, it reallocates its workforce to react to demand shocks. Numerical results are presented t...

We analyze the benefits of inventory pooling in a multi-location newsvendor framework. Using a number of common demand distributions, as well as the distribution-free approximation, we compare the centralized (pooled) system with the decentralized (non-pooled) system. We investigate the sensitivity of the absolute and relative reduction in costs to...

In this paper we develop a network location model that combines the characteristics of ordered median and gradual cover models resulting in the Ordered Gradual Covering Location Problem (OGCLP). The Gradual Cover Location Problem (GCLP) was specifically designed to extend the basic cover objective to capture sensitivity with respect to absolute tra...

ABSTRACT In this article, we analyze a location model where facilities may be subject to disruptions. Customers do not have advance information about whether a given facility is operational or not, and thus may have to visit several facilities before finding an operational one. The objective is to locate a set of facilities to minimize the total ex...

Preventive healthcare aims at reducing the likelihood and severity of potentially life-threatening illnesses by protection and early detection. The level of participation to preventive healthcare programs is a crucial factor in terms of their effectiveness and efficiency. This paper provides a methodology for designing a network of preventive healt...

Substantial literature has been devoted to supply chain coordination. The majority of this literature ignores competition between supply chains. Moreover, a significant part of this literature focuses on coordination that induce the supply chain members to follow strategies that produce the equilibria chosen by a vertically integrated supply chain....

In this paper we propose a covering problem where the covering radius of a facility is controlled by the decision-maker; the cost of achieving a certain covering distance is assumed to be a monotonically increasing function of the distance (i.e., it costs more to establish a facility with a greater covering radius). The problem is to cover all dema...

Spatial development plans often aim at defining the level of hierarchy to assign to the urban centers of a region, each level being characterized by a class of facilities. The services provided at the facilities typically include education, health care, public safety, and justice. In this paper we present a multiperiod, multilevel location model fo...

A location problem with stochastic demand and congestion where mobile servers respond to service calls originating from nodes is considered. The problem is of the set-covering type: only servers within the coverage radius of the demand-generating node may respond to a call. The service level constraint requires that at least one server must be avai...

In this paper, we introduce the multiple server center location problem. p servers are to be located at nodes of a network. Demand for services of these servers is located at each node, and a subset of nodes are to be chosen to locate one or more servers in each. Each customer selects the closest server. The objective is to minimize the maximum tim...

The problem considered in this paper is to find p locations for p facilities such that the weights attracted to each facility will be as close as possible to one another. We model this problem as minimizing the maximum among all the total weights attracted to the various facilities. We propose solution procedures for the problem on a network, and f...

Preventive healthcare aims at reducing the likelihood and severity of potentially life-threatening illnesses by protection and early detection. The level of participation in preventive healthcare programs is a critical determinant in terms of their effectiveness and efficiency. This article presents a methodology for designing a network of preventi...

In this paper, we present efficient solution approaches for discrete multi-facility competitive interaction model. Applying the concept of “Tangent Line Approximation” presented by the authors in their previous work, we develop efficient computational approaches—both exact and approximate (with controllable error bound α). Computational experiments...

This article presents the maximal covering problem on a network when some of the weights can be negative. Integer programming formulations are proposed and tested with ILOG CPLEX. Heuristic algorithms, an ascent algorithm, and simulated annealing are proposed and tested. The simulated annealing approach provides the best results for a data set comp...

We study a single server retrial queue with Bernoulli vacations and a priority queue. A customer who finds the server busy upon arrival, either joins the priority queue with probability α, or leaves the service area and enters a retrial group (orbit) with probability α-bar (= 1 − α). Using the supplementary variable technique, we find the joint pro...

Consider a situation where p facilities need to be located by a leader, on the nodes of a network, to provide maximum coverage of demand generated at nodes of the network. At some point in the future it is expected that one of the links of the network will become unusable either due to a terrorist attack or a natural disaster (by the follower). The...