Models for production planning under power interruptions

We present a robust optimization model for production planning under the assumption that electricity supply is subject to uncertain interruptions caused by participation in interruptible load contracts (ILCs). The objective is to minimize the cost of electricity used for production while providing a robust production plan which ensures demand satisfaction under all possible interruption scenarios. The combinatorial size of the set of interruption scenarios makes this a challenging problem. Furthermore, we assume that no probabilistic information is known about the supply uncertainty: we only use the information given in the ILC to identify an uncertainty set that captures the possible scenarios. We construct a general robust framework to handle this uncertainty and present a heuristic to compute a good feasible solution of the robust model. We provide computational experiments on a real‐world example and compare the performance of an exact solver applied to the robust model with that of the heuristic procedure. Finally, we include the operational impact of interruptions such as “recovery modes” in the definition of the uncertainty set. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

The capital supply curve in capacity expansion models: Some economic and algorithmic aspects

Capacity expansion models typically minimize the discounted cost of acquisition and operation over a given planning horizon. In this article we generalize this idea to one in which a capital supply curve replaces the usual discount rate. A capital supply curve is a means to model financial outlook, investment limits, and risk. We show that when such a curve is included in a capacity expansion model, it will, under certain conditions, provide a less capital intensive solution than one which incorporates a discount rate. In this article, we also provide an algorithm that solves capacity expansion models that incorporate a capital supply curve. The attractive feature of this algorithm is that it provides a means to utilize the “discount rate” models efficiently. Throughout, we give applications in power generation planning and computational experience for this application is also presented.     

Risk‐sensitive sizing of responsive facilities

We develop a risk‐sensitive strategic facility sizing model that makes use of readily obtainable data and addresses both capacity and responsiveness considerations. We focus on facilities whose original size cannot be adjusted over time and limits the total production equipment they can hold, which is added sequentially during a finite planning horizon. The model is parsimonious by design for compatibility with the nature of available data during early planning stages. We model demand via a univariate random variable with arbitrary forecast profiles for equipment expansion, and assume the supporting equipment additions are continuous and decided ex‐post. Under constant absolute risk aversion, operating profits are the closed‐form solution to a nontrivial linear program, thus characterizing the sizing decision via a single first‐order condition. This solution has several desired features, including the optimal facility size being eventually decreasing in forecast uncertainty and decreasing in risk aversion, as well as being generally robust to demand forecast uncertainty and cost errors. We provide structural results and show that ignoring risk considerations can lead to poor facility sizing decisions that deteriorate with increased forecast uncertainty. Existing models ignore risk considerations and assume the facility size can be adjusted over time, effectively shortening the planning horizon. Our main contribution is in addressing the problem that arises when that assumption is relaxed and, as a result, risk sensitivity and the challenges introduced by longer planning horizons and higher uncertainty must be considered. Finally, we derive accurate spreadsheet‐implementable approximations to the optimal solution, which make this model a practical capacity planning tool.© 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Expansion planning for waste‐to‐energy systems using waste forecast prediction sets

We consider an expansion planning problem for Waste‐to‐Energy (WtE) systems facing uncertainty in future waste supplies. The WtE expansion plans are regarded as strategic, long term decisions, while the waste distribution and treatment are medium to short term operational decisions which can adapt to the actual waste collected. We propose a prediction set uncertainty model which integrates a set of waste generation forecasts and is constructed based on user‐specified levels of forecasting errors. Next, we use the prediction sets for WtE expansion scenario analysis. More specifically, for a given WtE expansion plan, the guaranteed net present value (NPV) is evaluated by computing an extreme value forecast trajectory of future waste generation from the prediction set that minimizes the maximum NPV of the WtE project. This problem is essentially a multiple stage min‐max dynamic optimization problem. By exploiting the structure of the WtE problem, we show this is equivalent to a simpler min‐max optimization problem, which can be further transformed into a single mixed‐integer linear program. Furthermore, we extend the model to optimize the guaranteed NPV by searching over the set of all feasible expansion scenarios, and show that this can be solved by an exact cutting plane approach. We also propose a heuristic based on a constant proportion distribution rule for the WtE expansion optimization model, which reduces the problem into a moderate size mixed‐integer program. Finally, our computational studies demonstrate that our proposed expansion model solutions are very stable and competitive in performance compared to scenario tree approaches. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 47–70, 2016     

Quay crane scheduling at container terminals to minimize the maximum relative tardiness of vessel departures

In this paper, we study the problem of scheduling quay cranes (QCs) at container terminals where incoming vessels have different ready times. The objective is to minimize the maximum relative tardiness of vessel departures. The problem can be formulated as a mixed integer linear programming (MILP) model of large size that is difficult to solve directly. We propose a heuristic decomposition approach to breakdown the problem into two smaller, linked models, the vessel‐level and the berth‐level models. With the same berth‐level model, two heuristic methods are developed using different vessel‐level models. Computational experiments show that the proposed approach is effective and efficient. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Information technology (IT) infrastructure relies on a globalized supply chain that is vulnerable to numerous risks from adversarial attacks. It is important to protect IT infrastructure from these dynamic, persistent risks by delaying adversarial exploits. In this paper, we propose max‐min interdiction models for critical infrastructure protection that prioritizes cost‐effective security mitigations to maximally delay adversarial attacks. We consider attacks originating from multiple adversaries, each of which aims to find a “critical path” through the attack surface to complete the corresponding attack as soon as possible. Decision‐makers can deploy mitigations to delay attack exploits, however, mitigation effectiveness is sometimes uncertain. We propose a stochastic model variant to address this uncertainty by incorporating random delay times. The proposed models can be reformulated as a nested max‐max problem using dualization. We propose a Lagrangian heuristic approach that decomposes the max‐max problem into a number of smaller subproblems, and updates upper and lower bounds to the original problem via subgradient optimization. We evaluate the perfect information solution value as an alternative method for updating the upper bound. Computational results demonstrate that the Lagrangian heuristic identifies near‐optimal solutions efficiently, which outperforms a general purpose mixed‐integer programming solver on medium and large instances.     

Disruption management in production planning

We study the problem of recovering a production plan after a disruption, where the disruption may be caused by incidents such as power failure, market change, machine breakdown, supply shortage, worker no‐show, and others. The new recovery plan we seek after has to not only suit the changed environment brought about by the disruption, but also be close to the initial plan so as not to cause too much customer unsatisfaction or inconvenience for current‐stage and downstream operations. For the general‐cost case, we propose a dynamic programming method for the problem. For the convex‐cost case, a general problem which involves both cost and demand disruptions can be solved by considering the cost disruption first and then the demand disruption. We find that a pure demand disruption is easy to handle; and for a pure cost disruption, we propose a greedy method which is provably efficient. Our computational studies also reveal insights that will be helpful to managing disruptions in production planning. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

The discrete max-min problem

The historic max-min problem is examined as a discrete process rather than in its more usual continuous mode. Since the practical application of the max-min model usually involves discrete objects such as ballistic missiles, the discrete formulation of the problem seems quite appropriate. This paper uses an illegal modification to the dynamic programming process to obtain an upper bound to the max-min value. Then a second but legal application of dynamic programming to the minimization part of the problem for a fixed maximizing vector will give a lower bound to the max-min value. Concepts of optimal stopping rules may be applied to indicate when sufficiently near optimal solutions have been obtained.     

A continuous‐time strategic capacity planning model

Capacity planning decisions affect a significant portion of future revenue. In the semiconductor industry, they need to be made in the presence of both highly volatile demand and long capacity installation lead‐times. In contrast to traditional discrete‐time models, we present a continuous‐time stochastic programming model for multiple resource types and product families. We show how this approach can solve capacity planning problems of reasonable size and complexity with provable efficiency. This is achieved by an application of the divide‐and‐conquer algorithm, convexity, submodularity, and the open‐pit mining problem. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

赋双权二部图中最大权最小权完美匹配

本文涉及的是在赋双权的二部图中求关于第一个权最大的限制下、第二个权最小的完美匹配的网络模型,给出了这一模型的有效算法,并用此算法解决了企业的优化组合分工中的挖潜问题。     

Robust shortest path problems with two uncertain multiplicative cost coefficients

We consider a robust shortest path problem when the cost coefficient is the product of two uncertain factors. We first show that the robust problem can be solved in polynomial time by a dual‐variable enumeration with shortest path problems as subproblems. We also propose a path enumeration approach using a K ‐shortest paths finding algorithm that may be efficient in many real cases. An application in hazardous materials transportation is discussed, and the solution methods are illustrated by numerical examples. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Rescheduling to minimize makespan on a changing number of identical processors

We consider the problem of rescheduling n jobs to minimize the makespan on m parallel identical processors when m changes value. We show this problem to be NP-hard in general. Call a list schedule totally optimal if it is optimal for all m = 1, …,n. When n is less than 6, there always exists a totally optimal schedule, but for n ≥ 6 this can fail. We show that an exact solution is less robust than the largest processing time first (LPT) heuristic and discuss implications for polynomial approximation schemes and hierarchical planning models.     

Scheduling jobs and maintenance activities on parallel machines

Most machine scheduling models assume that the machines are available all of the time. However, in most realistic situations, machines need to be maintained and hence may become unavailable during certain periods. In this paper, we study the problem of processing a set of n jobs on m parallel machines where each machine must be maintained once during the planning horizon. Our objective is to schedule jobs and maintenance activities so that the total weighted completion time of jobs is minimized. Two cases are studied in this paper. In the first case, there are sufficient resources so that different machines can be maintained simultaneously if necessary. In the second case, only one machine can be maintained at any given time. In this paper, we first show that, even when all jobs have the same weight, both cases of the problem are NP-hard. We then propose branch and bound algorithms based on the column generation approach for solving both cases of the problem. Our algorithms are capable of optimally solving medium sized problems within a reasonable computational time. We note that the general problem where at most j machines, 1 ≤ j ≤ m, can be maintained simultaneously, can be solved similarly by the column generation approach proposed in this paper. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 145–165, 2000     

Approximation algorithms for general one‐warehouse multi‐retailer systems

Logistical planning problems are complicated in practice because planners have to deal with the challenges of demand planning and supply replenishment, while taking into account the issues of (i) inventory perishability and storage charges, (ii) management of backlog and/or lost sales, and (iii) cost saving opportunities due to economies of scale in order replenishment and transportation. It is therefore not surprising that many logistical planning problems are computationally difficult, and finding a good solution to these problems necessitates the development of many ad hoc algorithmic procedures to address various features of the planning problems. In this article, we identify simple conditions and structural properties associated with these logistical planning problems in which the warehouse is managed as a cross‐docking facility. Despite the nonlinear cost structures in the problems, we show that a solution that is within ε‐optimality can be obtained by solving a related piece‐wise linear concave cost multi‐commodity network flow problem. An immediate consequence of this result is that certain classes of logistical planning problems can be approximated by a factor of (1 + ε) in polynomial time. This significantly improves upon the results found in literature for these classes of problems. We also show that the piece‐wise linear concave cost network flow problem can be approximated to within a logarithmic factor via a large scale linear programming relaxation. We use polymatroidal constraints to capture the piece‐wise concavity feature of the cost functions. This gives rise to a unified and generic LP‐based approach for a large class of complicated logistical planning problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Machine scheduling with an availability constraint and job delivery coordination

In this paper we study the scheduling problem that considers both production and job delivery at the same time with machine availability considerations. Only one vehicle is available to deliver jobs in a fixed transportation time to a distribution center. The vehicle can load at most K jobs as a delivery batch in one shipment due to the vehicle capacity constraint. The objective is to minimize the arrival time of the last delivery batch to the distribution center. Since machines may not always be available over the production period in real life due to preventive maintenance, we incorporate machine availability into the models. Three scenarios of the problem are studied. For the problem in which the jobs are processed on a single machine and the jobs interrupted by the unavailable machine interval are resumable, we provide a polynomial algorithm to solve the problem optimally. For the problem in which the jobs are processed on a single machine and the interrupted jobs are nonresumable, we first show that the problem is NP‐hard. We then propose a heuristic with a worst‐case error bound of 1/2 and show that the bound is tight. For the problem in which the jobs are processed on either one of two parallel machines, where only one machine has an unavailable interval and the interrupted jobs are resumable, we propose a heuristic with a worst‐case error bound of 2/3. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case

The dynamics of the environment in which supply chains evolve requires that companies frequently redesign their logistics distribution networks. In this paper we address a multiperiod single‐sourcing problem that can be used as a strategic tool for evaluating the costs of logistics network designs in a dynamic environment. The distribution networks that we consider consist of a set of production and storage facilities, and a set of customers who do not hold inventories. The facilities face production capacities, and each customer's demand needs to be delivered by a single facility in each period. We deal with the assignment of customers to facilities, as well as the location, timing, and size of inventories. In addition, to mitigate start and end‐of‐study effects, we view the planning period as a typical future one, which will repeat itself. This leads to a cyclic model, in which starting and ending inventories are equal. Based on an assignment formulation of the problem, we propose a greedy heuristic, and prove that this greedy heuristic is asymptotically feasible and optimal in a probabilistic sense. We illustrate the behavior of the greedy heuristic, as well as some improvements where the greedy heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 412–437, 2003     

Solution algorithms for the parallel replacement problem under economy of scale

We consider the parallel replacement problem in which machine investment costs exhibit economy of scale which is modeled through associating both fixed and variable costs with machine investment costs. Both finite- and infinite-horizon cases are investigated. Under the three assumptions made in the literature on the problem parameters, we show that the finite-horizon problem with time-varying parameters is equivalent to a shortest path problem and hence can be solved very efficiently, and give a very simple and fast algorithm for the infinite-horizon problem with time-invariant parameters. For the general finite-horizon problem without any assumption on the problem parameters, we formulate it as a zero-one integer program and propose an algorithm for solving it exactly based on Benders' decomposition. Computational results show that this solution algorithm is efficient, i.e., it is capable of solving large scale problems within a reasonable cpu time, and robust, i.e., the number of iterations needed to solve a problem does not increase quickly with the problem size. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 279–295, 1998     

Assessing the value of demand sharing in supply chains

We consider the problem of assessing the value of demand sharing in a multistage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order‐up‐to policy. We demonstrate how a typical supply chain player can determine the extent of its available information in the presence of demand sharing by studying the properties of the moving average polynomials of adjacent supply chain players. The retailer's demand is driven by the random shocks appearing in the autoregressive moving average representation for its demand. Under the assumptions we will make in this article, to the retailer, knowing the shock information is equivalent to knowing the demand process (assuming that the model parameters are also known). Thus (in the event of sharing) the retailer's demand sequence and shock sequence would contain the same information to the retailer's supplier. We will show that, once we consider the dynamics of demand propagation further up the chain, it may be that a player's demand and shock sequences will contain different levels of information for an upstream player. Hence, we study how a player can determine its available information under demand sharing, and use this information to forecast leadtime demand. We characterize the value of demand sharing for a typical supply chain player. Furthermore, we show conditions under which (i) it is equivalent to no sharing, (ii) it is equivalent to full information shock sharing, and (iii) it is intermediate in value to the two previously described arrangements. Although it follows from existing literature that demand sharing is equivalent to full information shock sharing between a retailer and supplier, we demonstrate and characterize when this result does not generalize to upstream supply chain players. We then show that demand propagates through a supply chain where any player may share nothing, its demand, or its full information shocks (FIS) with an adjacent upstream player as quasi‐ARMA in—quasi‐ARMA out. We also provide a convenient form for the propagation of demand in a supply chain that will lend itself to future research applications. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 515–531, 2014     

基于级库存的维修器材整合供应策略研究

针对传统器材供应模式效率低的问题,借助供应链管理的思想提出了多需求点整合供应模式,并建立了基于级库存策略的整合优化模型,对成本各组成部分分析求解,得到了最优总成本对应的策略参数,其中总成本考虑了供应中心补货成本、库存持有成本、供应成本和供应延迟成本．最后通过算例与直接供应策略进行了比较,证明了整合供应策略的有效性．     

Inventory management with advance capacity information

An important aspect of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced if a company is able to obtain advance capacity information (ACI) about future supply/production capacity availability from its supplier. We address a periodic‐review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state‐dependent base‐stock policy characterized by a base‐stock level that is a function of ACI. We establish a link with inventory models that use advance demand information (ADI) by developing a capacitated inventory system with ADI, and we show that equivalence can only be set under a very specific and restrictive assumption, implying that ADI insights will not necessarily hold in the ACI environment. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there is sufficient flexibility to react to anticipated demand and supply capacity mismatches. Further, most of the benefits can be achieved with only limited future visibility. We also show that the system parameters affecting the value of ACI interact in a complex way and therefore need to be considered in an integrated manner. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011