Hark-Chin Hwang

Parallel machine scheduling under a grade of service provision

Abstract We consider the problem of scheduling parallel machines that process service requests from various customers who are entitled to many different grade of service (GoS) levels. We propose and analyze one simple way to ensure such differentiated service. In particular, we investigate how the longest processing time first algorithm (LPT) would perform in the worst case and show that a slight modification of LPT could significantly improve its worst-case performance.

The effect of machine availability on the worst-case performance of LPT

We consider the makespan minimization parallel machine scheduling problem where each machine may be unavailable for a known time interval. For this problem, we investigate how the worst-case behavior of the longest processing time first algorithm (LPT) is affected by the availability of machines. In particular, for given m machines, we analyze the cases where arbitrary number, λ, ranging from one to m - 1, machines are unavailable simultaneously. Then, we show that the makespan of the schedule generated by LPT is never more than the tight worst-case bound of 1 + ½ ⌊m/(m - λ)⌋ times the optimum makespan.

Dynamic lot-sizing model with demand time windows and speculative cost structure

We consider a deterministic lot-sizing problem with demand time windows, where speculative motive is allowed. Utilizing an untraditional decomposition principle, we provide an optimal algorithm that runs in O(nT^3) time, where n is the number of demands and T is the length of the planning horizon.

Note on “An efficient approach for solving the lot-sizing problem with time-varying storage capacities”

In a recent paper Gutierrez et al. (2008) show that the lot-sizing problem with inventory bounds can be solved in O(T log T) time. In this note we show that their algorithm does not lead to an optimal solution in general.

Economic Lot-Sizing for Integrated Production and Transportation

In this study, improved and new algorithms are developed for economic lot-sizing problems with integrated production and transportation operations. To model the economies of scale in production with the effect of shipment consolidation in transportation, we assume concave production costs and stepwise transportation costs. More specifically, we consider concave/fixed-charge/nonspeculative cost functions in production, and nonstationary/stationary delivery cost functions in transportation. The cost functions in production are always assumed to be nonstationary. To achieve a cost-effective production and shipment schedule over time, inventories are considered for carrying and backlogging items. Efficient solution procedures are provided for all the models with or without backlogging under assumed cost structures.

A two-dimensional vector packing model for the efficient use of coil cassettes

We consider the problem of efficiently packing steel products, known as coils, into special containers, called cassettes for shipping. The objective is to minimize the number of cassettes used for packing all the given coils where each cassette has capacity limits on both total payload weight and size. We model this problem as a two-dimensional vector packing problem and propose a heuristic. We also analyze the worst-case performance of the proposed algorithm under a special condition which, in fact, holds for the particular real-world case that we handled. Our computational experiment with real production data shows that the proposed algorithm performs quite satisfactorily in practice.

Inventory Replenishment and Inbound Shipment Scheduling Under a Minimum Replenishment Policy

An effective supply system for a vendor-managed inventory (VMI) warehouse requires collaboration between a supplier and a customer, and coordination between production and distribution functions. We study a dynamic lot-sizing model for production and inbound transportation to the VMI warehouse under a policy, based on mutual benefit of the supplier and the customer, that each replenishment quantity should be no less than a predetermined minimum size. To take advantage of economies of scale in replenishment operations as well as in shipment consolidation operations, the problem in this study assumes a concave replenishment cost structure in general for which optimal algorithms are presented. By computational experiments, we show that the most important parameter on the system is the minimum replenishment quantity. We also show that the minimum replenishment policy is successful only when large-size demands are guaranteed based on collaborations.

Dynamic lot-sizing model for major and minor demands

Abstract This paper deals with a lot-sizing model for major and minor demands in which major demands are specified by time windows while minor demands are given by periods. For major demands, the agreeable time window structure is assumed where each time window is not strictly nested in any other time windows. To incorporate the economy of scale of large production quantity, especially from major demands, concave cost structure in production must be considered. Investigating the optimality properties, we propose optimal solution procedures based on dynamic program. For a simple case when only major demands exist, we propose an optimal procedure with running time of O ( n 2 T ) where n is the number of demands and T is the length of the planning horizon. Extending the algorithm to the model with major and minor demands, we propose an algorithm with complexity O ( n 2 T 2 ) .

An Efficient Procedure for Dynamic Lot-sizing Model with Demand Time Windows

We consider a dynamic lot-sizing model with demand time windows where n demands need to be scheduled in T production periods. For the case of backlogging allowed, an O(T3) algorithm exists under the non-speculative cost structure. For the same model with somewhat general cost structure, we propose an efficient algorithm with O(max {T2, nT}) time complexity.

The economic lot-sizing problem with lost sales and bounded inventory

This article considers an economic lot-sizing problem with lost sales and bounded inventory. The structural properties of optimal solutions under different assumptions on the cost functions are proved. Using these properties, new and improved algorithms for the problem are presented. Specifically, the first polynomial algorithm for the general lot-sizing problem with lost sales and bounded inventory is presented, and it is shown that the complexity can be reduced considerably in the special case of non-increasing lost sales costs. Moreover, with the additional assumption that there is no speculative motive for holding inventory, an existing result is improved by providing a linear time algorithm.