Yun Fong Lim

Robust Storage Assignment in Unit-Load Warehouses

Assigning products to and retrieving them from proper storage locations are crucial decisions in minimizing the operating cost of a unit-load warehouse. The problem becomes intractable when the warehouse faces variable supply and uncertain demand in a multiperiod setting. We assume a factor-based demand model in which demand for each product in each period is affinely dependent on some uncertain factors. The distributions of these factors are only partially characterized. We introduce a robust optimization model that minimizes the worst-case expected total travel in the warehouse with distributional ambiguity of demand. Under a linear decision rule, we obtain a storage and retrieval policy by solving a moderate-size linear optimization problem. Surprisingly, despite imprecise specification of demand distributions, our computational studies suggest that the linear policy achieves close to the expected value given perfect information and significantly outperforms existing heuristics in the literature. This paper was accepted by Gerard P. Cachon, optimization.

Bucket brigades on in-tree assembly networks

In a network of subassembly lines, balance becomes more difficult to achieve as it requires that all subassembly lines be synchronized to produce at the same rate. We show how to adapt the ‘‘bucket brigade’’ protocol of work-sharing so that balance emerges spontaneously. 2004 Elsevier B.V. All rights reserved.

Dynamics of Dry Friction: A Numerical Investigation

We perform extended numerical simulation of the dynamics of dry friction, based on a model derived from the phenomenological description proposed by Baumberger et al. [Nature (London) 367, 544 (1994)] and Heslot et al. [Phys. Rev. E 49, 4973 (1994)]. Under a quasistationary approximation, the model is related to the Dieterich-Ruina aging (or slowness) law, which was introduced by Dieterich [Pure Appl. Geophys. 116, 790 (1978); J. Geophys. Res. 84, 2161 (1979); in Mechanical Behavior of Crustal Rocks, edited by N. L. Carter et al., Geophysics Monograph No. 24 (AGU, Washington, DC, 1981), p. 103] and Ruina [J. Geophys. Res. 88, 10 359 (1983)] on the basis of experiments on rocks. We obtain a dynamical phase diagram that agrees well with the experimental results on the paper-on-paper systems. In particular, the bifurcation between the stick-slip motion and steady sliding is shown to change from a direct (supercritical) Hopf type to an inverted (subcritical) one as the driving velocity increases, in agreement with the experiments.

TECHNICAL NOTE---Cellular Bucket Brigades

Workers in a bucket brigade production system perform unproductive travel when they walk to get more work from their colleagues. We introduce a new design of bucket brigades to reduce unproductive travel. Under the new design, each worker works on one side of an aisle when he proceeds in one direction and works on the other side when he proceeds in the reverse direction. We propose simple rules for workers to share work under the new design and find a sufficient condition for the system to self-balance. Numerical examples suggest that the improvement in throughput by the new design can be as large as 30%. Even with a 20% reduction in labor, the new design can still increase throughput by 7%.

Order-picking by cellular bucket brigades: A case study

Workers in bucket brigade order-picking perform unproductive travel when they walk back to receive work from their colleagues. The loss in productivity due to this unproductive travel can be significant especially if the order-picking line is long. We present a novel design alternative that may provide substantial improvement to the productivity of a bucket brigade. Under the new design, products are stored on both sides of an aisle. Each worker picks products to fulfill customer orders from one side of the aisle when he proceeds in one direction. The worker picks products, possibly for other customer orders, from the other side of the aisle when he proceeds in the reverse direction. We introduce new rules for workers to share work because they are not only required to pick products in both directions, but also to cross the aisle. In this study, we perform computer simulations based on data from a distributor of service parts in North America. Our results suggest that bucket brigade order-picking under the new design can be significantly more productive than a traditional bucket brigade, even if the latter is equipped with wireless technology to reduce travel.

Inventory Management Based on Target-Oriented Robust Optimization

We propose a target-oriented robust optimization approach to solve a multiproduct, multiperiod inventory management problem subject to ordering capacity constraints. We assume the demand for each product in each period is characterized by an uncertainty set that depends only on a reference value and the bounds of the demand. Our goal is to find an ordering policy that maximizes the sizes of all the uncertainty sets such that all demand realizations from the sets will result in a total cost lower than a prespecified cost target. We prove that a static decision rule is optimal for an approximate formulation of the problem, which significantly reduces the computation burden. By tuning the cost target, the resultant policy can achieve a balance between the expected cost and the associated cost variance. Numerical experiments suggest that although only limited demand information is used, the proposed approach performs comparably to traditional methods based on dynamic programming and stochastic programming. Mo...

Consignment Contracts with Revenue Sharing for a Capacitated Retailer and Multiple Manufacturers

We consider a retailer with limited storage capacity selling n independent products. Each product is produced by a distinct manufacturer, who is offered a consignment contract with revenue sharing by the retailer. The retailer first sets a common revenue share for all products, and each manufacturer then determines the retail price and production quantity for his product. Under certain conditions on price elasticities and cost fractions, we find a unique optimal revenue share for all products. Surprisingly, it is optimal for the retailer not to charge any storage fee in many situations even if she is allowed to do so. Both the retailer’s and manufacturers’ profits first increase and then remain constant as the capacity increases, which implies that an optimal capacity exists. We also find that the decentralized system requires no larger storage space than the centralized system at the expense of channel profit. If products are complementary, as the degree of complementarity increases, the retailer will decrease her revenue share to encourage the manufacturers to lower their prices.

Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches

This study considers a finite-horizon single-product periodic-review inventory management problem with demand distribution uncertainty. The problem is formulated as a dynamic program and the existence of an optimal (s, S) policy is proved. The corresponding dynamic robust counterpart models are then developed for the box and the ellipsoid uncertainty sets. These counterpart models are transformed into tractable linear and second-order cone programs, respectively. The effectiveness and practicality of the proposed robust optimization approaches are validated through a numerical study.

Solving Hierarchical Constraints over Finite Domains with Local Search

Many real world problems have requirements and constraints which conflict with each other. One approach for dealing with such over-constrained problems is with constraint hierarchies. In the constraint hierarchy framework, constraints are classified into ranks, and appropriate solutions are selected using a comparator which takes into account the constraints and their ranks. In this paper, we present a local search solution to solving hierarchical constraint problems over finite domains (HCPs). This is an extension of local search for over-constrained integer programs WSAT(OIP) to constraint hierarchies and general finite domain constraints.The motivation for this work arose from solving large airport gate allocation problems. We show how gate allocation problems can be formulated as HCPs using typical gate allocation constraints. Using the gate allocation benchmarks, we investigate how constraint heirarchy selection strategies and the problem formulation using two models: a 0–1 linear constraint hierarchy model and a nonlinear finite domain constraint hierarchy model.

Optimal Stackelberg strategies for financing a supply chain through online peer-to-peer lending

Abstract In recent years, supply chain finance (SCF) through online peer-to-peer (P2P) lending platforms has gained its popularity. We study an SCF system with a manufacturer selling a product to a retailer that faces uncertain demand over a single period. We assume that either the retailer or the manufacturer faces a capital constraint and must borrow capital through an online P2P lending platform. The platform determines a service rate for the loan, the manufacturer sets a wholesale price for the product, and the retailer chooses its order quantity for the product. We identify optimal Stackelberg strategies of the participants in the SCF system. For an SCF system with a capital-constrained retailer, we find that the retailers optimal order quantity and the manufacturers optimal wholesale price decrease with the platforms service rate. For an SCF system with a capital-constrained manufacturer, we find that as the platforms service rate increases, the manufacturers optimal wholesale price increases but the retailers optimal order quantity decreases. Our analysis suggests that it is important for the retailer and the manufacturer to take the online P2P lending platforms financial decisions (such as the service rate) into account when making their operational decisions.