Dynamic facility location problems aim at placing one or more valuable resources over a planning horizon to meet customer demand. Existing literature commonly assumes that customer demand quantities are defined independently for each time period. In many planning contexts, however, unmet demand carries over to future time periods. Unmet demand at some time periods may therefore affect decisions of subsequent time periods. This work studies a novel location problem, where the decision maker places facilities over time to capture cumulative customer demand. We propose two mixed-integer programming formulations for this problem, and show that one of them has a tighter continuous relaxation and allows the representation of more general customer demand behaviour. We characterize the computational complexity for this problem, and analyze which problem characteristics result in NP-hardness. We then propose an exact branch-and-Benders-cut method, and show that this method is approximately five times faster, on average, than solving the tighter formulation directly in our computational experiments. Our results also quantify the benefit of accounting for cumulative customer demand within the optimization framework, since the corresponding planning solutions perform much better than those obtained by ignoring cumulative demand or employing myopic heuristics. We also draw managerial insights on the quality of service perceived by customers when the provider places facilities under cumulative customer demand.
Facility location decisions significantly impact customer behavior and consequently the resulting demand in a wide range of businesses. Furthermore, sequentially realized uncertain demand enforces strategically determining locations under partial information. To address these issues, we study a facility location problem where the distribution of customer demand is dependent on location decisions. We represent moment information of stochastic demand as a piecewise linear function of facility-location decisions. Then, we propose a decision-dependent distributionally robust optimization model, an…
We consider the robust single-source capacitated facility location problem with uncertainty in customer demands. A cardinality-constrained uncertainty set is assumed for the robust problem. To solve it efficiently, we propose an allocation-based formulation derived by Dantzig-Wolfe decomposition and a branch-and-price algorithm. The computational experiments show that our branch-and-price algorithm outperforms CPLEX in many cases, which solves the ordinary robust reformulation. We also examine the trade-off relationship between the empirical probability of infeasibility and the additional cost…
This paper considers the two-stage capacitated facility location problem (TSCFLP) in which products manufactured in plants are delivered to customers via storage depots. Customer demands are satisfied subject to limited plant production and limited depot storage capacity. The objective is to determine the locations of plants and depots in order to minimize the total cost including the fixed cost and transportation cost. A hybrid evolutionary algorithm (HEA) with genetic operations and local search is proposed. To avoid the expensive calculation of fitness of population in terms of computationa…
Indian e-commerce industry has evolved over the last decade and is expected to grow over the next few years. The focus has now shifted to turnaround time (TAT) due to the emergence of many third-party logistics providers and higher customer expectations. The key consideration for delivery providers is to balance their overall operating costs while meeting the promised TAT to their customers. E-commerce delivery partners operate through a network of facilities whose strategic locations help to run the operations efficiently. In this work, we identify the locations of hubs throughout the country…
We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation and exploit the problem structures to derive two valid inequalities, based on submodularity and concave overestimation, respectively. We use the two valid inequalities in a branch-and-cut algorithm to find globa…
The growth of e-commerce has created increasing complexity in logistics services. To remain competitive, logistics and e-commerce companies are exploring new modes as supplements to traditional home delivery, one of which is the self-service parcel locker. This paper studies a parcel locker location problem where a company plans to introduce the locker service by locating locker facilities to attract customers. The objective is to maximize the profit, accounting for the revenue and the cost of facilities. To estimate the revenue, we use the threshold Luce model (TLM) to predict customers' like…
We study a variant of the competitive facility location problem, in which a company is to locate new facilities in a market where competitor's facilities already exist. We consider the scenario where only a limited number of possible attractiveness levels is available, and the company has to select exactly one level for each open facility. The goal is to decide the facilities' locations and attractiveness levels that maximize the profit. We apply the gravity-based rule to model the behavior of the customers and formulate a multi-ratio linear fractional 0-1 program. Our main contributions are t…
The P-median facility location problem with user preferences (PUP) studies an operator that locates P facilities to serve customers/users in a cost-efficient manner, upon anticipating customer preferences and choices. The problem can be visualized as a leader-follower game in which the operator is the leader that opens facilities, whereas the customer is the follower who observes the operator's location decision at first and then seeks services from the most preferred facility. Such a modeling perspective is of practical importance as we have witnessed its applications to various problems, suc…
We consider the problem of scheduling appointments for a finite customer population to a service facility with customer no-shows, to minimize the sum of customer waiting time and server overtime costs. Since appointments need to be scheduled ahead of time we refer to this problem as an optimization problem rather than a dynamic control one. We study this optimization problem in fluid and diffusion scales and identify asymptotically optimal schedules in both scales. In fluid scale, we show that it is optimal to schedule appointments so that the system is in critical load; thus heavy-traffic con…
We study a general class of quadratic capacitated $p$-location problems facility location problems with single assignment where a non-separable, non-convex, quadratic term is introduced in the objective function to account for the interaction cost between facilities and customer assignments. This problem has many applications in the field of transportation and logistics where its most well-known special case is the single-allocation hub location problem and its many variants. The non-convex, binary quadratic program is linearized by applying a reformulation-linearization technique and the resu…
The $p$-center problem (pCP) is a fundamental problem in location science, where we are given customer demand points and possible facility locations, and we want to choose $p$ of these locations to open a facility such that the maximum distance of any customer demand point to its closest open facility is minimized. State-of-the-art solution approaches of pCP use its connection to the set cover problem to solve pCP in an iterative fashion by repeatedly solving set cover problems. The classical textbook integer programming (IP) formulation of pCP is usually dismissed due to its size and bad line…
The assortment planning problem is a central piece in the revenue management strategy of any company in the retail industry. In this paper, we study a robust assortment optimization problem for substitutable products under a sequential ranking-based choice model. Our modeling approach incorporates the cumulative effect of finding multiple unavailable products on the customers' purchase decisions. To model the highly uncertain order in which a customer explores the products to buy, we present a bi-level optimization approach to maximize the expected revenue under the worst-case order of product…
In this paper, the problem of optimal dynamic pricing for retail electricity with an unknown demand model is considered. Under the day-ahead dynamic pricing (a.k.a. real time pricing) mechanism, a retailer obtains electricity in a twosettlement wholesale market and serves its customers in real time. Without knowledge on the aggregated demand function of its customers, the retailer aims to maximize its retail surplus by sequentially adjusting its price based on the behavior of its customers in the past. An online learning algorithm, referred to as piecewise linear stochastic approximation (PWLS…
Stanford University（斯坦福大学）；Imperial College Business School（帝国理工学院商学院）
In this paper, we consider an online resource allocation problem where a decision maker accepts or rejects incoming customer requests irrevocably in order to maximize expected reward given limited resources. At each time, a new order/customer/bid is revealed with a request of some resource(s) and a reward. We consider a stochastic setting where all the orders are i.i.d. sampled from an unknown distribution. Such formulation arises from many classic applications such as the canonical (quantity-based) network revenue management problem and the Adwords problem. While the literature on the topic m…
We consider a queueing facility where customers decide when to arrive. All customers have the same desired arrival time (w.l.o.g.\ time zero). There is one server, and the service times are independent and exponentially distributed. The total number of customers that demand service is random, and follows the Poisson distribution. Each customer wishes to minimize the sum of three costs: earliness, tardiness and waiting. We assume that all three costs are linear with time and are defined as follows. Earliness is the time between arrival and time zero, if there is any. Tardiness is simply the tim…
The Vehicle Fleet Sizing, Positioning and Routing Problem with Stochastic Customers (VFSPRP-SC) consists on pairing strategic decisions of depot positioning and fleet sizing with operational vehicle routing decisions while taking into account the inherent uncertainty of demand. We successfully solve the VFSPRP-SC with a methodology comprised of two main blocks: i) a scenario generation phase and ii) a two-stage stochastic program. For the first block, a set of scenarios is selected with a simulation-based approach that captures the behavior of the demand and allows us to come up with different…
This paper studies the design of a service system in the presence of economies-of-scale. The goal is to make decision on the number, location, service capacities of facilities as well as on the allocation of customers to the opened facilities in order to minimize the cost of whole system. The total cost includes opening and serving costs of facilities aggregated to the transportation and waiting costs of customers. To reflect the economies-of-scale in the modeling, a general opening cost function is supposed for each service facility with the characteristic of being concave and non-decreasing …
This article presents a matheuristic algorithm for the single-source capacitated facility location problem (SSCFLP) and its variants: SSCFLP with K facilities (SSCKFLP), SSCFLP with contiguous service areas (CFLSAP), and SSCFLP with K facilities and contiguous service areas (CKFLSAP). The algorithm starts from an initial solution, and iteratively improves the solution by exactly solving large neighborhood-based sub-problems. The performance of the algorithm is tested on 5 sets of SSCFLP benchmark instances. Among the 272 instances, 191 optimal solutions are found, and 35 best-known solutions a…
Facility and covering location models are key elements in many decision aid tools in logistics, supply chain design, telecommunications, public infrastructure planning, and many other industrial and public sectors. In many applications, it is likely that customers are not dichotomously covered by facilities, but gradually covered according to, e.g., the distance to the open facilities. Moreover, customers are not served by a single facility, but by a collection of them, which jointly serve them. In this paper we study the recently introduced multiple gradual cover location problem (MGCLP). The…
A Heuristic Framework of Variable Neighborhood Descent Methods for the Large-Scale Multi-Level Facility Location Problem in Supply Chain Networks
A. R. Sanchez, Jr. School of Business, Texas A&M International University（德克萨斯农工大学国际学院A.R.桑切斯商学院）；School of Business Administration, The University of Mississippi（密西西比大学工商管理学院）
This paper proposes a mathematical model for the design of a two-echelon supply chain where a set of suppliers serve a set of terminal facilities that receive uncertain customer demands. This model integrates a number of system decisions in both the planning and operational stages, including facility location, multi-level service assignments, multi-modal transportation configuration, and inventory management. In particular, we consider probabilistic supplier disruptions that may halt product supply from certain suppliers from time to time. To mitigate the impact from supplier disruptions, a te…
The operation of the power grid is becoming more stressed, due to the addition of new large loads represented by Electric Vehicles (EVs) and a more intermittent supply due to the incorporation of renewable sources. As a consequence, the coordination and control of projected EV demand in a network of fast charging stations becomes a critical and challenging problem. In this paper, we introduce a game theoretic based decentralized control mechanism to alleviate negative impacts from the EV demand. The proposed mechanism takes into consideration the non-uniform spatial distribution of EVs that in…
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. The service time at each facility is stochastic and depends on the service capacity and follows a general distribution that can differ for each facility. The service capacity is selected from a given (bounded or unbounded) interval. The objective of o…
In this paper, we introduce a new variant of the $p$-median facility location problem in which it is assumed that the exact location of the potential facilities is unknown. Instead, each of the facilities must be located in a region around their initially assigned location (the neighborhood). In this problem, two main decisions have to be made simultaneously: the determination of the potential facilities that must be open to serve the demands of the customers and the location of the open facilities in their neighborhoods, at global minimum cost. We present several mixed integer non-linear prog…
We study the maximum capture problem in facility location under random utility models, i.e., the problem of seeking to locate new facilities in a competitive market such that the captured user demand is maximized, assuming that each customer chooses among all available facilities according to a random utility maximization model. We employ the generalized extreme value (GEV) family of discrete choice models and show that the objective function in this context is monotonic and submodular. This finding implies that a simple greed heuristic can always guarantee an (1-1/e) approximation solution. W…
Supply chain network is critical to serving customers, so the most common practices are to determine the number, location, and capacity of facilities. But at the same time, uncertainties and risks must be taken into account in order to control delays. In this context, many optimisation models have been developed to use the results in transportation network and therefore improve the supply chain performance. Models were developed in both routing and zoning/districting problems, and different cases have been discussed in the literature, such as facility location problems, urban problems, and tra…
Metaheuristic algorithms for the induced P-median problem with upgrades
Universidad Rey Juan Carlos（雷乌斯·琼卡洛斯大学）；ITA-UNIFESP Graduate Program in Operations Research（ITA-UNIFESP运筹学研究生项目）；Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)（离散数学与理论计算机科学中心）
