Service System Design with Immobile Servers, Stochastic Demand and Economies of Scale

The service system design problem seeks to locate facilities, determine their capacity, and assign customers to them in order to improve the service quality and the customers' experience while minimizing the capacity acquisition cost, the customer access cost, and the average waiting cost. While the centralization of facilities will lead to economies of scale, decentralizing them will lead to faster response times. Traditionally, the capacity acquisition costs were assumed linear with a xed setup cost. In this work, we explicitly account for economies of scale by modeling the cost as a concave function of capacity. In this thesis, we model and provide solution methodologies for the service system design problem with immobile servers, stochastic demand and economies of scale. We start by reformulating the problem, and then provide solution approaches based on piece-wise linearization, Second Order Cone Programming (SOCP), and Lagrangian Relaxation.Extensive numerical testing on a standard data set is provided and the results analyzed

Response Time Reduction and Service Level Differentiation in Supply Chain Design: Models and Solution Approaches

Make-to-order (MTO) and assemble-to-order (ATO) systems are emerging business strategies in managing responsive supply chains, characterized by high product variety, highly variable customer demand, and short product life cycle. Motivated by the strategic importance of response time in today’s global business environment, this thesis presents models and solution approaches for response time reduction and service-level differentiation in designing MTO and ATO supply chains. In the first part, we consider the problem of response time reduction in the design of MTO supply chains. More specifically, we consider an MTO supply chain design model that seeks to simultaneously determine the optimal location and the capacity of distribution centers (DCs) and allocate stochastic customer demand to DCs, so as to minimize the 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 DCs are modelled as M/G/1 queues and response times are computed using steady-state waiting time results from queueing theory. The problem is set up as a network of spatially distributed M/G/1 queues and modelled as a nonlinear mixed-integer program. We linearize the model using a simple transformation and a piece-wise linear and concave approximation. We present two solution procedures: an exact solution approach based on cutting plane method and a Lagrangean heuristic for solving large instances of the problem. While the cutting plane approach provides the optimal solution for moderate instances in few iterations, the Lagrangean heuristic succeeds in finding feasible solutions for large instances that are within 5% from the optimal solution in reasonable computation times. We show that the solution procedure can be extended to systems with multiple customer classes. Using a computational study, we also show that substantial reduction in response times can be achieved with minimal increase in total costs in the design of responsive supply chains. Furthermore, we find the supply chain configuration (DC location, capacity, and demand allocation) that considers congestion and its effect on response time can be very different from the traditional configuration that ignores congestion. The second part considers the problem of response time reduction in the design of a two-echelon ATO supply chain, where a set of plants and DCs are to be established to distribute a set of finished products with non-trivial bill-of-materials to a set of customers with stochastic demand. The model is formulated as a nonlinear mixed integer programming problem. Lagrangean relaxation exploits the echelon structure of the problem to decompose into two subproblems - one for the make-tostock echelon and the other for the MTO echelon. We use the cutting plane based approach proposed above to solve the MTO echelon subproblem. While Lagrangean relaxation provides a lower bound, we present a heuristic that uses the solution of the subproblems to construct an overall feasible solution. Computational results reveal that the heuristic solution is on average within 6% from its optimal. In the final part of the thesis, we consider the problem of demand allocation and capacity selection in the design of MTO supply chains for segmented markets with service-level differentiated customers. Demands from each customer class arrives according to an independent Poisson process and the customers are served from shared DCs with finite capacity and generally distributed service times. Service-levels of various customer classes are expressed as the fraction of their demand served within a specified response (sojourn) time. Our objective is to determine the optimal location and the capacity of DCs and the demand allocation so as to minimize the sum of the fixed cost of opening DCs and equipping them with sufficient capacity and the variable cost of serving customers subject to service-level constraints for multiple customer classes. The problem is set up as a network of spatially distributed M/M/1 priority queues and modelled as a nonlinear mixed integer program. Due to the lack of closed form solution for service-level constraints for multiple classes, we present an iterative simulation-based cutting plane approach that relies on discrete-event simulation for the estimation of the service-level function and its subgradients. The subgradients obtained from the simulation are used to generate cuts that are appended to the mixed integer programming model. We also present a near-exact matrix analytic procedure to validate the estimates of the service-level function and its subgradients from the simulation. Our computational study shows that the method is robust and provides an optimal solution in most of the cases in reasonable computation time. Furthermore, using computational study, we examine the impact of different parameters on the design of supply chains for segmented markets and provide some managerial insights