Unbalanced production line scheduling with partial job specialization

This article presents a mathematical model for manpower scheduling for unbalanced production lines in order to minimize in-process inventory cost. The model extends prior work by adding workers' skill limitations to the system. The model is formulated for a one-period schedule and then extended for multiperiod schedules. An example problem is solved for both single and multiperiods. A heuristic algorithm is also presented for multiperiod and large-scale problems, and computational experiences are reported.     

Order-statistic calculation,costs, and service in an (s,Q) inventory system

A retailer or distributor of finished goods, or the manager of a spare-parts inventory system, must generally forecast the major portion of demand. A specific customer-service level p (fraction of replenishment intervals with no stockout) implies two challenges: achieve the service within a small interval plus or minus, and do so with a minimum-cost investment in inventory. The pth fractile of lead-time demand (LTD) is the reorder point (ROP) for this service measure, and is often approximated by that fractile of a normal distribution. With this procedure, it is easy to set safety stocks for an (s, Q) inventory system. However, Bookbinder and Lordahl [2] and others have identified cases where the normal approximation yields excessive costs and/or lower service than desired. This article employs an order-statistic approach. Using available LTD data, the ROP is simply estimated from one or two of the larger values in the sample. This approach is sufficiently automatic and intuitive for routine implementation in industry, yet is distribution free. The order-statistic method requires only a small amount of LTD data, and makes no assumptions on the form of the underlying LTD distribution, nor even its parameters μ and ρ. We compare the order-statistic approach and the normal approximation, first in terms of customer service and then using a model of expected annual cost. Based upon characteristics of the available LTD data, we suggest a procedure to aid a practitioner in choosine between the normal and order-statistic method. © 1994 John Wiley & Sons, Inc.     

Heuristic procedure for a multiproduct dynamic lot-sizing problem with coordinated replenishments

In this article we develop a heuristic procedure for a multiproduct dynamic lot-sizing problem. In this problem a joint setup cost is incurred when at least one product is ordered in a period. In addition to the joint setup cost a separate setup cost for each product ordered is also incurred. The objective is to determine the product lot sizes, over a finite planning horizon, that will minimize the total relevant cost such that the demand in each period for each product is satisfied without backlogging. In this article we present an effective heuristic procedure for this problem. Computational results for the heuristic procedure are also reported. Our computational experience leads us to conclude that the heuristic procedure may be of considerable value as a decision-making aid to production planners in a real-world setting. © 1994 John Wiley & Sons, Inc.     

Optimal replacement policies for multistate deteriorating systems

We consider state-age-dependent replacement policies for a multistate deteriorating system. We assume that operating cost rates and replacement costs are both functions of the underlying states. Replacement times and sojourn times in different states are all state-dependent random variables. The optimization criterion is to minimize the expected long-run cost rate. A policy-improvement algorithm to derive the optimal policy is presented. We show that under reasonable assumptions, the optimal replacement policies have monotonic properties. In particular, when the failure-rate functions are nonincreasing, or when all the replacement costs and the expected replacement times are independent of state, we show that the optimal policies are only state dependent. Examples are given to illustrate the structure of the optimal policies in the special case when the sojourntime distributions are Weibull. © 1994 John Wiley & Sons, Inc.     

Initial point search on weighted trees

An initial point search game on a weighted graph involves a searcher who wants to minimize search and travel costs seeking a hider who wants to maximize these costs. The searcher starts from a specified vertex 0 and searches each vertex in some order. The hider chooses a nonzero vertex and remains there. We solve the game in which the graph is a simple tree, and use this solution to solve a search game on a tree in which each branch is itself a weighted graph with a certain property, and the searcher is obliged to search the entire branch before departing. © 1994 John Wiley & Sons, Inc.     

A new surrogate dual multiplier search procedure

Efficient computation of tight bounds is of primary concern in any branch-and-bound procedure for solving integer programming problems. Many successful branch-and-bound approaches use the linear programming relaxation for bounding purposes. Significant interest has been reported in Lagrangian and surrogate duals as alternative sources of bounds. The existence of efficient techniques such as subgradient search for solving Lagrangian duals has led to some very successful applications of Lagrangian duality in solving specially structured problems. While surrogate duals have been theoretically shown to provide stronger bounds, the difficulty of surrogate dual-multiplier search has discouraged their employment in solving integer programs. Based on the development of a new relationship between surrogate and Lagrangian duality, we suggest a new strategy for computing surrogate dual values. The proposed approach allows us to directly use established Lagrangian search methods for exploring surrogate dual multipliers. Computational experience with randomly generated capital budgeting problems validates the economic feasibility of the proposed ideas.     

On the (S − 1, S) lost sales inventory model with priority demand classes

In this paper an inventory model with several demand classes, prioritised according to importance, is analysed. We consider a lot‐for‐lot or (S ? 1, S) inventory model with lost sales. For each demand class there is a critical stock level at and below which demand from that class is not satisfied from stock on hand. In this way stock is retained to meet demand from higher priority demand classes. A set of such critical levels determines the stocking policy. For Poisson demand and a generally distributed lead time, we derive expressions for the service levels for each demand class and the average total cost per unit time. Efficient solution methods for obtaining optimal policies, with and without service level constraints, are presented. Numerical experiments in which the solution methods are tested demonstrate that significant cost reductions can be achieved by distinguishing between demand classes. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 593–610, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10032     

The value of losing control: Competition in markets for complements

When selling complementary products, manufacturers can often benefit from considering the resulting cross‐market interdependencies. Although using independent retailers makes it difficult to internalize these positive externalities, the ensuing double marginalization can mitigate within‐market competition. We use standard game theoretic analysis to determine optimal distribution channel strategies (through independent retailers or integrated) for competing manufacturers who participate in markets for complements. Our results suggest that a firm's optimal channel choice is highly dependent on its competitive positioning. A firm with a competitive advantage in terms of product characteristics (customer preferences) or production capabilities (cost) might benefit from selling through company‐controlled stores, allowing coordinated pricing across the two markets, whereas a less competitive firm might be better off using independent channel intermediaries to mitigate price competition. We consider two scenarios depending on whether the two firms make their distribution channel decisions sequentially or simultaneously. Although firms are unlikely to make such decisions at exactly the same instant, the simultaneous model also serves as a proxy for the scenario where firms decide sequentially, but where they cannot observe each other's strategic channel choices. For the sequential case, we find that the sequence of entry can have tremendous impact on the two firms'profits; whereas in some cases, the first mover can achieve substantially higher profits, we find that when the two markets are of sufficiently different size and only loosely related, a firm with a competitive advantage might be better off as a follower. Interestingly, our results suggest that, when the markets are of rather similar size, both firms are better off if they enter the industry sequentially. In those cases, the first entrant has incentive to reveal its planned channel strategies, and the follower has incentive to seek out and consider this information. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Strategic capacity decision‐making in a stochastic manufacturing environment using real‐time approximate dynamic programming

In this study, we illustrate a real‐time approximate dynamic programming (RTADP) method for solving multistage capacity decision problems in a stochastic manufacturing environment, by using an exemplary three‐stage manufacturing system with recycle. The system is a moderate size queuing network, which experiences stochastic variations in demand and product yield. The dynamic capacity decision problem is formulated as a Markov decision process (MDP). The proposed RTADP method starts with a set of heuristics and learns a superior quality solution by interacting with the stochastic system via simulation. The curse‐of‐dimensionality associated with DP methods is alleviated by the adoption of several notions including “evolving set of relevant states,” for which the value function table is built and updated, “adaptive action set” for keeping track of attractive action candidates, and “nonparametric k nearest neighbor averager” for value function approximation. The performance of the learned solution is evaluated against (1) an “ideal” solution derived using a mixed integer programming (MIP) formulation, which assumes full knowledge of future realized values of the stochastic variables (2) a myopic heuristic solution, and (3) a sample path based rolling horizon MIP solution. The policy learned through the RTADP method turned out to be superior to polices of 2 and 3. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010