Planning of network, production and distribution : approaches of chance constrained programming and adjustable robust counterpart

Abstract

When implementing a mathematical model in practical supply chain management, one of the most prominent challenges is to obtain all the model inputs, which are often beyond the available history data. Even if the inputs can be calibrated, small perturbations in the inputs can render the nominal optimal solution unsatisfactory or infeasible. This thesis attempts to address these issues through the approaches of chance constrained programming and adjustable robust counterpart. We focus on how to make robust strategical and operational decisions in planning supply chain network, production, and distribution when facing uncertain demand and production time.

The strategic problem studied in this thesis is to plan a multi-sourcing distribution network of retailers and distribution centers (DCs). Each retailer faces uncertain demand and can source products from more than one DC. A nonlinear mixed integer program, which includes a joint chance constraint to achieve certain service level, is constructed to simultaneously optimize DC locations and inventory levels, which set of DCs serves each retailer, and the amount of shipment from DCs to retailers. Two approaches, namely, the approximation based on linear decision rule and the set-wise approximation, are proposed to approximate conservatively the joint chance constraint based on incomplete demand information. According to extensive numerical experiments, both approaches yield sparse multi-sourcing distribution networks, which are effective in matching uncertain demand using on-hand inventory and hence successfully reach high service level. It is also verified through numerical experiments that the proposed approaches outperform other commonly adopted approximations of the chance constraint.

The operational problem considered in this thesis is the integrated production-distribution planning for distributed manufacturing systems, where multiple products are produced using certain manufacturing plants and shipped to customers in geographically disparate regions. This study is among the first to explicitly model the operational production, inventory, and transportation decisions of both the final products and the items in their bills of materials for every time period. The production decisions also capture the practical issues regarding production time, capacity, and precedence. This study starts with the single-facility production planning problem to analyze the production processes. In the deterministic setting, the problem is formulated as a mixed integer linear program (MILP), whose coefficient matrix is proved to be totally unimodular. When demand and production time are subject to random disturbances, we construct the robust adjustable counterparts that use inventory to hedge the uncertainty, propose equivalent MILP reformulations to ensure computational tractability, and study the computational complexities by showing total unimodularity or NP-hardness for some special cases. The single-facility problem is then generalized to the multi-facility production-distribution planning problem. Similar to the single-facility problem, the deterministic problem is modeled as an MILP. The robust adjustable counterparts, along with the equivalent MILP reformulations (and the conservative approximation if the equivalent reformulation is not compact), are proposed to handle uncertain demand and production time. Numerical experiments are conducted based on real data sets to demonstrate the excellent performance of the proposed approaches.