Khaled Hadj-Hamou

Integrated supply chain and product family architecture under highly customized demand

Mass customization efforts are challenged by an unpredictable growth or shrink in the market segments and shortened product life cycles which result in an opportunity loss and reduced profitability; hence we propose a concept of sustainable mass customization to address these challenges where an economically infeasible product for a market segment is replaced by an alternative superior product variant nearly at the cost of mass production. This concept provides sufficient time to restructure the product family architecture for the inclusion of a new innovative product variant while fulfilling the market segments with the customer delight and an extended profitability. To implement the concept of sustainable mass customization we have proposed the notions of generic-bill-Of-products (GBOP: list of product variants agreed for the market segments), its interface with generic-supply-chain-structure and strategic decisions about opening or closing of a market segment as an optimization MILP (mixed integer linear program) model including logistics and GBOP constraints. Model is tested with the varying market segments demands, sales prices and production costs against 1 to 40 market segments. Simulation results provide us an optimum GBOP, its respective segments and decisions on the opening or closing of the market segments to sustain mass customization efforts.

A convex optimization approach for solving the single-vehicle cyclic inventory routing problem

This paper investigates the mathematical structure of the Single-Vehicle Cyclic Inventory Routing Problem (SV-CIRP). The SV-CIRP is an optimization problem consisting of finding a recurring distribution plan, from a single depot to a selected subset of retailers, that maximizes the collected rewards from the visited retailers while minimizing transportation and inventory costs. It appears as fundamental building block for all variants of the cyclic inventory routing problem (CIRP). One of the main complications in developing solution methods for the SV-CIRP using the current formulations is the non-convexity of the objective function. We demonstrate how the problem can be reformulated so that its continuous relaxation is a convex optimization problem. We further examine its mathematical properties and compare our findings with statements previously done in literature. Based of these findings we propose an algorithm that solves the SV-CIRP more effectively. We present experimental results on well-known benchmark instances, for which we are able to find optimal solutions for 22 out of 50 instances and obtained new best known solutions to 23 other instances. HighlightsWe reformulate the Single-Vehicle Cyclic IRP as a convex optimization problem.The reformulations continuous relaxation is solved using convex optimization techniques.We propose a modified branch-and-bound procedure using these convex NLP relaxations.The convex NLP relaxations allows us to narrow the range of the complicating variable.New best results are found for 23 and optimality is proved for 22 out of 50 instances.

Analysis of an improved branch-and-cut formulation for the Inventory-Routing Problem with Transshipment

Abstract The Inventory-Routing Problem with Transshipment (IRPT) is an extension of the Inventory-Routing Problem (IRP), in which not only the supplier can deliver goods to the retailers, but also transshipments between retailers or between the supplier and a retailer are possible. In this paper, we investigate the branch-and-cut (B&C) formulation of the IRPT and propose four different types of improvements for it. We first develop two new sets of valid inequalities for the problem which greatly strengthen the linear relaxation of the problem. We then improve the bounds on the continuous delivery variables and use these improved bounds to tighten the inventory management constraints. Next, we reformulate the routing component of the problem by exploiting the possible presence of direct shipments in the optimal solution. Finally, we prove that some integer and continuous variables can be eliminated out of the mathematical formulation. Experimental results demonstrate that these improvements drastically reduce the computational burden for solving the IRPT to optimality. On a large set of benchmark instances our proposed branch-and-cut algorithm, which integrates these improvements, outperforms the current best results in the literature. In addition, we are able to find the optimal solutions for two instances whose optimal solution was not known until now.