Response Time Reduction and Service Level Differentiation in Supply Chain Design: Models and Solution Approaches
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Date
2009-05-22T17:15:04Z
Authors
Vidyarthi, Navneet
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
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.