Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

Sensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are not changed. Linear one-parameter perturbations of the objective function or of the so-called ”right-hand side” of linear programs and their effect on the optimal value is very well known and can be found in most college textbooks on Management Science or Operations Research. In contrast, no explicit formulas have been established that describe the behavior of the optimal value under linear one-parameter perturbations of the constraint coefficient matrix. In this paper, such explicit formulas are derived in terms of local expressions of the optimal value function and intervals on which these expressions are valid. We illustrate this result using two simple examples

Sustainable supply chain governance:A literature review

Governance is one of the core concepts underlying sustainable supply chain (SC). Although governance practices are widely acknowledged and implemented, literature discussing those practices is not as thoroughly organized. The purpose of this paper is therefore to investigate the forms, dynamics, and development of sustainable supply chain governance (SSCG). We reviewed a total of 126 articles in operations and SC management peer-reviewed journals spanning 15 years of recent research. Our literature analysis unveils several key themes concerning the popularity of contractual and relational governance, the role of SC lead firms, the network perspective, and the dynamics of governance mechanisms. At a higher conceptual level, we conclude that there exists a mutually dependent relationship between SSCG and SC complexity. The study summarizes and conceptualizes the recent scholarly conversations about SSCG and offers an agenda for further research.</p

Sustainable supply chain governance:A literature review

Governance is one of the core concepts underlying sustainable supply chain (SC). Although governance practices are widely acknowledged and implemented, literature discussing those practices is not as thoroughly organized. The purpose of this paper is therefore to investigate the forms, dynamics, and development of sustainable supply chain governance (SSCG). We reviewed a total of 126 articles in operations and SC management peer-reviewed journals spanning 15 years of recent research. Our literature analysis unveils several key themes concerning the popularity of contractual and relational governance, the role of SC lead firms, the network perspective, and the dynamics of governance mechanisms. At a higher conceptual level, we conclude that there exists a mutually dependent relationship between SSCG and SC complexity. The study summarizes and conceptualizes the recent scholarly conversations about SSCG and offers an agenda for further research.</p

Mathematical models for planning support

In this paper we describe how computer systems can provide planners with active planning support, when these planners are carrying out their daily planning activities. This means that computer systems actively participate in the planning process by automatically generating plans or partial plans. Active planning support by computer systems requires the application of mathematical models and solution techniques. In this paper we describe the modeling process in general terms, as well as several modeling and solution techniques. We also present some background information on computational complexity theory, since most practical planning problems are hard to solve. We also describe how several objective functions can be handled, since it is rare that solutions can be evaluated by just one single objective. Furthermore, we give an introduction into the use of mathematical modeling systems, which are useful tools in a modeling context, especially during the development phases of a mathematical model. We finish the paper with a real life example related to the planning process of the rolling stock circulation of a railway operator

The Value of Information in Container Transport: Leveraging the Triple Bottom Line

Planning the transport of maritime containers from the sea port to final destinations while using multiple transport modes is challenged by uncertainties regarding the time the container is released for further transport or the transit time from the port to its final destination. This paper assesses the value of information in container transport in terms of multiple performance dimensions, i.e. logistics costs, reliability, security, and emissions. The analysis is done using a single period model where a decision maker allocates arriving containers to two transport modes (slow, low price, no flexible departure times, versus fast, high price, flexible departure times). We construct a frontier of Pareto optimal decisions under each of the information scenarios and show that these frontiers move in a favorable direction when the level of information progresses. Each of the Pareto frontiers help strike the balance between the aforementioned performance dimensions. The mathematical results are illustrated using two numerical examples involving barge transport and train transport

Joint Design and Pricing of Intermodal Port - Hinterland Network Services: Considering Economies of Scale and Service Time Constraints

Maritime container terminal operating companies have extended their role from node operators to that of multimodal transport network operators. They have extended the gates of their seaport terminals to the gates of inland terminals in their network by means of frequent services of high capacity transport modes such as river vessels (barges) and trains.

How Much is Location Information Worth? A Competitive Analysis of the Online Traveling Salesman Problem with Two Disclosure Dates

In this paper we derive the worst-case ratio of an online algorithm for the Traveling Salesman Problem (TSP) with two disclosure dates. This problem, a variant of the online TSP with release dates, is characterized by the disclosure of a job’s location at one point in time followed by the disclosure of that job’s release date at a later point in time. We present an online algorithm for this problem restricted to the positive real number line. We then derive the worst-case ratio of our algorithm and show that it is best-possible in two contexts – the first, one in which the amount of time between the disclosure events and release time are fixed and equal for all jobs; and a second in which the time between disclosure events va

Optimal competitive capacity strategies:Evidence from the container shipping market

For nearly two decades, ocean carriers have been locked in an arms race for capacity, which has led to huge losses for many and even bankruptcy for some. We investigate the nature of this investment race by studying a long-term capacity investment problem in a duopoly under demand uncertainty. In our model, two firms make sequential capacity decisions, responding to each other’s current and future capacity. We consider two types of strategies which differ in terms of how a firm considers the opponent’s future capacity in its own strategy: a proactive strategy where the firm assumes that the opponent will respond using a certain strategy, or a reactive strategy where the firm assumes that the opponent’s future capacity remains unchanged. In the proactive case, we allow the firm to have different assumptions on the opponent’s strategy, representing different amounts of information the firm has on the opponent. For each type of strategies, we derive the firm’s optimal decisions on both the timing and size of capacity adjustments, specified by an array of intervals for the optimal capacity in a given capacity space in each period. Using detailed data from the container shipping market (2000–2015), we illustrate how to plan competitive capacity investments, following our model. By comparing the optimal decisions specified by our model with the reality, we show that the realized capacity decisions of the leading carriers, which were often questioned as irrational, are close to optimal, assuming these carriers follow proactive strategies. By revealing the underlying structures of different strategies, that is, the stayput intervals, we show how a specific strategy brings value to firms under competition. Based on our results, we provide practical guidelines to carriers and firms which operate in a similar competitive market for implementing an effective competitive capacity strategy.<br/