Abstract

Location of facilities such as plants, distribution centers in a supply chain plays critical role in efficient management of logistics activities. Real-life supply chains are generally large in size with multiple echelons, prone to disruptions and uncertainties, and constantly evolving to meet customer demands in a fast and reliable way. Therefore, it is quite challenging to identify these locations while balancing the trade-off between costs and service levels. In this thesis, we investigate three supply chain design problems addressing various issues that complicate the location of facilities in a supply chain.

The first paper investigates a multilevel capacitated facility location problem. Such problems commonly arise in large scale production-distribution supply chains with plants at one echelon, and distribution centers / warehouse at another, and there is hierarchy of flow between facilities and to the end customers such as retail stores. The operating costs at facilities and transportation costs on arcs are assumed to be concave. The concave functions model economies of scale in operations (such as production, handling, transportation) performed at large scale and emission of green house gases from transportation activities. The mathematical model for our problem is nonlinear (concave) for which we present two formulations. The first formulation is a prevalent mixed-integer nonlinear program, and second is a purely nonlinear programming problem. Extensive computations are performed to measure the efficiency of two formulations, and managerial insights are provided to understand the behavior of the model under different scenarios of concavities.

The second work focuses on e-commerce supply chains that have a common objective of providing fast and reliable deliveries of customers’ orders. The order delivery time primarily depends on the time taken to process the order at the facilities and travel time from facilities to customers. These two times are uncertain in practice, therefore, to capture the combined effect of both uncertainties, we introduce a mathematical model with a requirement that all customer orders should be delivered within a committed time with some probabilistic guarantee. The problem is formulated as a dynamic (multiperiod) capacitated facility location problem with modular capacities. The probabilistic service level constraints make the problem nonconvex. We present two linear binary programming reformulations, and develop an exact branch-and-cut algorithm utilizing the reformulations to solve large size instances. We also include sensitivity analysis to study the change in network configuration under various modeling parameters.

An increase in online sales every year is driving many brick-and-mortar retailers to follow an omni-channel retailing approach that would integrate their online sales channel with store sales. Omnichannel retailing requires a considerable change in current practices. For instance, a retailer generally decides if there is a need of new distribution facilities, which stores should be used as fulfillment centers as well, where to keep safety stocks, from where to serve online demand, among others. To study these aspect, in the third paper, we propose a novel mathematical model for the design of omnichannel distribution network along with allocation of safety stock to the facilities. The original problem is nonlinear which can be reformulated as conic quadratic mixed integer programming problem. The problem is solved using a branch-and-cut solution algorithm. Further, we present several managerial insights related to fulfillment and safety stock decisions using a small example.