Navneet Vidyarthi

Response time reduction in make-to-order and assemble-to-order supply chain design

Make-to-order and assemble-to-order systems are successful business strategies in managing responsive supply chains, characterized by high product variety, highly variable customer demand and short product life cycles. These systems usually spell long customer response times due to congestion. Motivated by the strategic importance of response time reduction, this paper presents models for designing make-to-order and assemble-to-order supply chains under Poisson customer demand arrivals and general service time distributions. The make-to-order supply chain design model seeks to simultaneously determine the location and the capacity of distribution centers (DCs) and allocate stochastic customer demand to DCs by minimizing response time in addition to the fixed cost of opening DCs and equipping them with sufficient assembly capacity and the variable cost of serving customers. The problem is setup as a network of spatially distributed M/G/1 queues, modeled as a non-linear mixed-integer program, and linearized using a simple transformation and a piecewise linear approximation. An exact solution approach is presented that is based on the cutting plane method. Then, the problem of designing a two-echelon assemble-to-order supply chain comprising of plants and DCs serving a set of customers is considered. A Lagrangean heuristic is proposed that exploits the echelon structure of the problem and uses the solution methodology for the make-to-order problem. Computational results and managerial insights are provided. It is empirically shown that substantial reduction in response times can be achieved with minimal increase in total costs in the design of responsive supply chains. Furthermore, a supply chain configuration that considers congestion is proposed and its effect on the response time can be very different from the traditional configuration that ignores congestion.

The impact of hub failure in hub-and-spoke networks

Hub facilities are subject to unpredictable disruptions caused by severe weather condition, natural disasters, labor dispute, and vandalism to cite a few. Disruptions at hubs result in excessive transportation costs and economic losses as customers (demand) initially served by these facilities must now be served by other hubs. In this study, we first present a novel mathematical model that builds hub-and-spoke systems under the risk of hub disruption. In developing the model, we assume that once a hub stops normal operations, the entire demand initially served by this hub is handled by a backup facility. The objective function of the model minimizes the weighted sum of transportation cost in regular situation and the expected transportation cost following a hub failure. We adopted a linearization for the model and present an efficient evolutionary approach with specifically designed operators. We solved a number of small problem instances from the literature using CPLEX for our enhanced mathematical model. The obtained results are also used as a platform for assessing the performance of our proposed meta-heuristic which is then tested on large instances with promising results. We further study and provide results for the relaxed problem in which demand points affected by disruption are allowed to be reallocated to any of the operational hubs in the network.

Cost Framework for Evaluation of Information Technology Alternatives in Supply Chain

Organizations are often facing the problem of determining the degree of investment in building information links with their suppliers and buyers to reduce costs, lead times, and quality problems, improve timely customized delivery, increase asset utilization, and improve corporate profitability. One of the critical enablers for an efficient and effective supply chain is timely planning and information processing across the entire value-added chain. This paper presents an analytical model for selecting the right mix of analytical software and hardware alternatives at various planning and execution levels of an organization to remain competitive in a supply chain. Factors such as quality, reliability, flexibility, timeliness and organizational compatibility have been quantified into cost components that form the weighted cost function. The weights of the various cost components of software and hardware are derived from pair-wise comparison. These weights account for the relative importance of alternative supply chain strategies for an organization. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.

Exact and heuristic approaches for the cycle hub location problem

In this paper, we present solution algorithms for the cycle hub location problem (CHLP), which seeks to locate p hub facilities that are connected by means of a cycle, and to assign non-hub nodes to hubs so as to minimize the total cost of routing flows through the network. This problem is useful in modeling applications in transportation and telecommunications systems, where large setup costs on the links and reliability requirements make cycle topologies a prominent network architecture. We present a branch-and-cut algorithm that uses a flow-based formulation and two families of mixed-dicut inequalities as a lower bounding procedure at nodes of the enumeration tree. We also introduce a metaheuristic based on greedy randomized adaptive search procedure to obtain initial upper bounds for the exact algorithm and to obtain feasible solutions for large-scale instances of the CHLP. Numerical results on a set of benchmark instances with up to 100 nodes and 8 hubs confirm the efficiency of the proposed solution algorithms.

The impact of directed choice on the design of preventive healthcare facility network under congestion

Preventive healthcare (PH) programs and services aim at reducing the likelihood and severity of potentially life-threatening illness by early detection and prevention. The effectiveness of these programs depends on the participation level and the accessibility of the users to the facilities providing the services. Factors that impact the accessibility include the number, type, and location of the facilities as well as the assignment of the clients to these facilities. In this paper, we study the impact of system-optimal (i.e., directed) choice on the design of the preventive healthcare facility network under congestion. We present a model that simultaneously determines the location and the size of the facilities as well as the allocation of clients to these facilities so as to minimize the weighted sum of the total travel time and the congestion associated with waiting and service delay at the facilities. The problem is set up as a network of spatially distributed M/G/1 queues and formulated as a nonlinear mixed integer program. Using simple transformation of the nonlinear objective function and piecewise linear approximation, we reformulate the problem as a linear model. We present a cutting plane algorithm based exact (𝜖-optimal) solution approach. We analyze the tradeoff between travel time and queuing time and its impact on the location and capacity of the facilities as well as the allocation of clients to these facilities under a directed choice policy. We present a case study that deals with locating mammography clinics in Montreal, Canada. The results show that incorporating congestion in the PH facility network design substantially reduces the total time spent by clients. The proposed model allows policy makers to direct clients to facilities in an equitable manner resulting in better accessibility.

An exact algorithm for the modular hub location problem with single assignments

We study a hub location problem with flow-dependent transportation costs.We propose a branch-and-bound algorithm that uses Lagrangean dual bounds.Numerical results are reported for benchmark instances with up to 75 nodes. A key feature of hub-and-spoke networks is the consolidation of flows at hub facilities. The bundling of flows allows reduction in the transportation costs, which is frequently modeled using a constant discount factor that is applied to the flow cost associated with all interhub links. In this paper, we study the modular hub location problem, which explicitly models the flow-dependent transportation costs using modular arc costs. It neither assumes a full interconnection between hub nodes nor a particular topological structure, instead it considers link activation decisions as part of the design. We propose a branch-and-bound algorithm that uses a Lagrangean relaxation to obtain lower and upper bounds at the nodes of the enumeration tree. Numerical results are reported for benchmark instances with up to 75 nodes.

Modelling and analysis of hub-and-spoke networks under stochastic demand and congestion

Motivated by the strategic importance of congestion management, in this paper we present a model to design hub-and-spoke networks under stochastic demand and congestion. The proposed model determines the location and capacity of the hub nodes and allocate non-hub nodes to these hubs while minimizing the sum of the fixed cost, transportation cost and the congestion cost. In our approach, hubs are modelled as spatially distributed M/G/1 queues and congestion is captured using the expected queue lengths at hub facilities. A simple transformation and a piecewise linear approximation technique are used to linearize the resulting nonlinear model. We present two solution approaches: an exact method that uses a cutting plane approach and a novel genetic algorithm based heuristic. The numerical experiments are conducted using CAB and TR datasets. Analysing the results obtained from a number of problem instances, we illustrate the impact of congestion cost on the network topology and show that substantial reduction in congestion can be achieved with a small increase in total cost if congestion at hub facilities is considered at the design stage. The computational results further confirm the stability and efficiency of both exact and heuristic approaches.

Bandwidth packing problem with queueing delays: modelling and exact solution approach

We present a more generalized model for the bandwidth packing problem with queuing delays under congestion than available in the extant literature. The problem, under Poison call arrivals and general service times, is set up as a network of spatially distributed independent M/G/1 queues. We further present two exact solution approaches to solve the resulting nonlinear integer programming model. The first method, called finite linearization method, is a conventional Big-M based linearization, resulting in a finite number of constraints, and hence can be solved using an off-the-shelve MIP solver. The second method, called constraint generation method, is based on approximating the non-linear delay terms using supporting hyperplanes, which are generated as needed. Based on our computational study, the constraint generation method outperforms the finite linearization method. Further comparisons of results of our proposed constraint generation method with the Lagrangean relaxation based solution method reported in the literature for the special case of exponential service times clearly demonstrate that our approach outperforms the latter, both in terms of the quality of solution and computation times.

Facility location under service level constraints for heterogeneous customers

We study the problem of locating service facilities to serve heterogeneous customers. Customers requiring service are classified as either high priority or low priority, where high priority customers are always served on a priority basis. The problem is to optimally locate service facilities and allocate their service zones to satisfy the following coverage and service level constraints: (1) each demand zone is served by a service facility within a given coverage radius; (2) at least