Vernon Ning Hsu

Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography

We present a classified bibliography of the literature in the area of forecast, solution, and rolling horizons primarily in operations management problems. Each one of over 200 selected papers is categorized on five dimensions that identify the horizon type, the model type (deterministic or stochastic), the sources of the horizon, the methods used to obtain horizon results, and the subject area of the paper. The majority of the papers treat dynamic problems in inventory management, production planning, capacity expansion, machine replacement, and warehousing. We discuss the relationship of the horizon results with the theory and practice of rolling-horizon procedures and future research directions.

Dynamic Lot Sizing with Batch Ordering and Truckload Discounts

This paper studies two important variants of the dynamic economic lot-sizing problem that are applicable to a wide range of real-world situations. In the first model, production in each time period is restricted to a multiple of a constant batch size, where backlogging is allowed and all cost parameters are time varying. Several properties of the optimal solution are discussed. Based on these properties, an efficient dynamic programming algorithm is developed. The efficiency of the dynamic program is further improved through the use of Monge matrices. Using the results developed for the first model, an O(n3log n) algorithm is developed to solve the second model, which has a general form of product acquisition cost structure, including a fixed charge for each acquisition, a variable unit production cost, and a freight cost with a truckload discount. This algorithm can also be used to solve a more general problem with concave cost functions.

Optimal Component Stocking Policy for Assemble-to-Order Systems with Lead-Time-Dependent Component and Product Pricing

Short delivery time and the efficient management of component inventories are two crucial elements that determine the competitiveness of many contract assembly manufacturers, especially in the electronics industry. In this paper, we develop and analyze an optimization model to determine the optimal stocking quantities for components of an assemble-to-order product in an environment where demand is uncertain and the price for the final product and the costs of components depend on their delivery lead times. We provide an efficient solution procedure to solve the problem in which the manufacturer must deliver the full order quantity possibly in multiple shipments. We further extend our model to the situation where the manufacturer has the option of not delivering the full quantity but instead takes the penalty for a delivery shortage. We derive some analytical results that illustrate how different model parameters affect the optimal solution and provide useful insights for managing components in the assemble-to-order environment.

Dynamic lot size problems with one-way product substitution

Abstract We consider two multi-product dynamic lot size models with one-way substitution, where the products can be indexed such that a lower-index product may be used to substitute for the demand of a higher-index product. In the first model, the product used to meet the demand of another product must be physically transformed into the latter and incur a conversion cost. In the second model, a product can be directly used to satisfy the demand for another product without requiring any physical conversion. Both problems are generally computationally intractable. We develop dynamic programming algorithms that solve the problems in polynomial time when the number of products is fixed. A heuristic is also developed, and computational experiments are conducted to test the effectiveness of the heuristic and the efficiency of the optimal algorithm.

Inventory and Production Decisions for an Assemble-to-Order System with Uncertain Demand and Limited Assembly Capacity

This paper considers an inventory and production-planning problem for a contract manufacturer who anticipates an order of a single product, but with uncertain quantity. To meet the challenges of long component procurement lead times and limited assembly capacity, which may render production time insufficient to assemble total order quantity, the manufacturer may need to procure components or even assemble some quantities of the final product before receiving the confirmation of the actual order quantity. We present profit-maximization models that make optimal inventory and production decisions in the above assemble-to-order environment. We also consider the option of outsourcing, so that the manufacturer can outsource part of his production to an external facility that also has limited capacity. We establish structural properties of optimal solutions and develop efficient solution procedures for the proposed problems. We also provide sensitivity analysis of the optimal decisions, and some managerial insights.

Distribution Coordination Between Suppliers and Customers with a Consolidation Center

We study a problem faced by a third-party logistics provider (3PL) who needs to coordinate shipments between suppliers and customers through a consolidation center in a distribution network. Products from a supplier have one release time and are consolidated into a single shipment to the consolidation center. At the center, products to the same destination are also consolidated into a single shipment, and the consolidation time can be as early as possible or as late as possible, depending on the customer requirement and cost structure. The 3PL needs to determine the pickup times from the suppliers, delivery times to the customers, and the transportation options while considering product release times, latest arrival times, different consolidation policies, and the transportation and storage costs involved. In this paper, we formulate this problem as a nonlinear optimization problem, show it is an NP-hard problem, and develop a dual-based solution method for the general problem. Utilizing the problem’s special structure, we show that the Lagrangian dual of the general problem can be solved optimally as a linear program, thus allowing us to accelerate the computation of a lower bound to the optimal objective function value. The experimental results show that the dual-based algorithm provides solutions with objective function values, which are on average within 3.24% of optimality. We also consider a version of the problem where each customer orders products from all suppliers, for which we develop a polynomial-time algorithm. Subject classifications: shipment consolidation; distribution network optimization; logistics coordination. Area of review: Transportation. History: Received July 2006; revisions received March 2007, May 2007; accepted June 2007. Published online in Articles in Advance May 15, 2008.

An Economic Lot Size Model for Perishable Products with Age-Dependent Inventory and Backorder Costs

This paper presents an Economic Lot Size (ELS) model for perishable products where the costs of holding inventory stocks (having backorders) in each period depend on the age of inventories (backorders). We propose a polynomial-time dynamic programming algorithm to solve two structured problems, one with non-decreasing demands and the other with non-decreasing marginal backorder cost with respect to the age of the backorder. Our results generalize a recent study on an ELS model for perishable product but without backorders.

Tool selection for optimal part production: a Lagrangian relaxation approach

This paper extends previous work on implementation problems associated with a flexible system that produces flat sheet-metal parts with interior holes. The paper makes four main contributions. First, we formulate the problem of selecting tooling and design standards to minimize the cost of producing parts as an optimization model. Second, we develop a projected subgradient algorithm for the Lagrangian relaxation of the problem by using the models special structure to develop relationships between the Lagrangian multipliers. Third, we demonstrate that the algorithm produces close to optimal solutions (duality gap less than 2%) very quickly on a number of problems derived using a substantial data set obtained from a Chicago area firm. Fourth, an important variant of the traditional repair kit problem is shown to be a special case of the tool selection problem.

Structured p-facility location problems on the line solvable in polynomial time

In this paper we give an O(pn^2) algorithm for solving the p-facility location problem on the line when the cost of serving any customer is a unimodal function of the location of the serving facilities. One application of our model is a generalization of the economic lot-sizing problem with backlogging allowed.

Dynamic Economic Lot Size Models with Period-Pair-Dependent Backorder and Inventory Costs

Inventory and backorder cost functions in the classical Wagner-Whitin economic lot size (ELS) models are typically period-pair-independent ( pp-independent) in the sense that inventoried units carried (or backorders in existence) in a given period are treated the same regardless of the periods in which they are produced (placed) or the periods in which they are used (filled). We consider versions of the problem where inventory and backorder costs arepp-dependent, as well as versions where backorder costs, but not inventory costs, are pp-dependent. Recognizing that the problems considered are NP-hard, we provide cases where the cost structure allows polynomial solvability via dynamic programming.