Methodology for determining the acceptability of system designs in uncertain environments

In practice, managers often wish to ascertain that a particular engineering design of a production system meets their requirements. The future environment of this design is likely to differ from the environment assumed during the design. Therefore it is crucial to find out which variations in that environment may make this design unacceptable (unfeasible). This article proposes a methodology for estimating which uncertain environmental parameters are important (so managers can become pro-active) and which combinations of parameter values (scenarios) make the design unacceptable. The proposed methodology combines simulation, bootstrapping, design of experiments, and linear regression metamodeling. This methodology is illustrated through a simulated manufacturing system, including fourteen uncertain parameters of the input distributions for the various arrival and service times. These parameters are investigated through the simulation of sixteen scenarios, selected through a two-level fractional–factorial statistical design. The resulting simulation Input/Output (I/O) data are analyzed through a first-order polynomial metamodel and bootstrapping. A second experiment with other scenarios gives some outputs that turn out to be unacceptable. In general, polynomials fitted to the simulation’s I/O data can estimate the border line (frontier) between acceptable and unacceptable environments.     

Measurement and optimization of robust stability of multiclass queueing networks: Applications in dynamic supply chains

Multiclass queueing networks are an essential tool for modeling and analyzing complex supply chains. Roughly speaking, stability of these networks implies that the total number of customers/jobs in the network remains bounded over time. In this context robustness characterizes the ability of a multiclass queueing network to remain stable, if the expected values of the interarrival and service times distributions are subject to uncertain shifts. A powerful starting point for the stability analysis of multiclass queueing networks is the associated fluid network. Based on the fluid network analysis we present a measure to quantify the robustness, which is indicated by a single number. This number will be called the stability radius. It represents the magnitude of the smallest shift of the expected value of the interarrival and/or service times distributions so that the associated fluid network looses the property of stability. The stability radius is a worst case measure and is a conceptual adaptation from the dynamical systems literature. Moreover, we provide a characterization of the shifts that destabilize the network. Based on these results, we formulate a mathematical program that minimizes the required network capacity, while ensuring a desired level of robustness towards shifts of the expected values of the interarrival times distributions. This approach provides a new view on long-term robust production capacity allocation in supply chains. The capabilities of our method are demonstrated using a real world supply chain.     

Minmax robustness for multi-objective optimization problems

In real-world applications of optimization, optimal solutions are often of limited value, because disturbances of or changes to input data may diminish the quality of an optimal solution or even render it infeasible. One way to deal with uncertain input data is robust optimization, the aim of which is to find solutions which remain feasible and of good quality for all possible scenarios, i.e., realizations of the uncertain data. For single objective optimization, several definitions of robustness have been thoroughly analyzed and robust optimization methods have been developed. In this paper, we extend the concept of minmax robustness (Ben-Tal, Ghaoui, & Nemirovski, 2009) to multi-objective optimization and call this extension robust efficiency for uncertain multi-objective optimization problems. We use ingredients from robust (single objective) and (deterministic) multi-objective optimization to gain insight into the new area of robust multi-objective optimization. We analyze the new concept and discuss how robust solutions of multi-objective optimization problems may be computed. To this end, we use techniques from both robust (single objective) and (deterministic) multi-objective optimization. The new concepts are illustrated with some linear and quadratic programming instances.     

Robust improvement schemes for road networks under demand uncertainty

This paper is concerned with development of improvement schemes for road networks under future travel demand uncertainty. Three optimization models, sensitivity-based, scenario-based and min–max, are proposed for determining robust optimal improvement schemes that make system performance insensitive to realizations of uncertain demands or allow the system to perform better against the worst-case demand scenario. Numerical examples and simulation tests are presented to demonstrate and validate the proposed models.     

The impact of two-product joint lifecycles on capacity planning of remanufacturing networks

Capacity planning in the reverse channel of closed-loop supply chains (CLSCs) involves complex issues due to the different lifecycles of product offerings in combination with the variability regarding product usage time, quality level of used products and return patterns. (Georgiadis, P., Vlachos, D., Tagaras, G., 2006. The impact of product lifecycle on capacity planning of closed-loop supply chains with remanufacturing. Production and Operations Management 15; 514–527) developed a system dynamics (SD) model to study a CLSC with remanufacturing for a single product which incorporates a dynamic capacity modeling approach. We extend this SD model for two sequential product-types under two alternative scenarios regarding the market preferences over the product-types; in the first scenario, the market is considered showing no preferences, while in the second scenario, the demand over a product-type can be satisfied only by providing units of the specific type. We study how the joint lifecycles of two product-types, entry time of the second product-type to the market and used product return patterns affect the optimal policies regarding expansion and contraction of collection and remanufacturing capacities. The results of extensive numerical investigation are tested for their statistical significance using analysis of variance (ANOVA). In the first scenario, the results show that the system performs best when the two lifecycles form a trapezoid pattern for total demand while in the second scenario, when the two lifecycles form a triangular pattern.     

Variable-sized uncertainty and inverse problems in robust optimization

In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at finding a set of robust solutions that covers all possible uncertainty set outcomes. We refer to these problems as robust optimization with variable-sized uncertainty. We discuss how to construct smallest possible sets of min–max robust solutions and give bounds on their size.A special case of this perspective is to analyze for which uncertainty sets a nominal solution ceases to be a robust solution, which amounts to an inverse robust optimization problem. We consider this problem with a min–max regret objective and present mixed-integer linear programming formulations that can be applied to construct suitable uncertainty sets.Results on both variable-sized uncertainty and inverse problems are further supported with experimental data.     

Real-time production planning and control system for job-shop manufacturing: A system dynamics analysis

Much attention has been paid to production planning and control (PPC) in job-shop manufacturing systems. However, there is a remaining gap between theory and practice, in the ability of PPC systems to capture the dynamic disturbances in manufacturing process. Since most job-shop manufacturing systems operate in a stochastic environment, the need for sound PPC systems has emerged, to identify the discrepancy between planned and actual activities in real-time and also to provide corrective measures. By integrating production ordering and batch sizing control mechanisms into a dynamic model, we propose a comprehensive real-time PPC system for arbitrary capacitated job-shop manufacturing. We adopt a system dynamics (SD) approach which is proved to be appropriate for studying the dynamic behavior of complex manufacturing systems. We study the system’s response, under different arrival patterns for customer orders and the existence of various types real-time events related to customer orders and machine failures. We determine the near-optimal values of control variables, which improve the shop performance in terms of average backlogged orders, work in process inventories and tardy jobs. The results of extensive numerical investigation are statistically examined by using analysis of variance (ANOVA). The examination reveals an insensitivity of near-optimal values to real-time events and to arrival pattern and variability of customer orders. In addition, it reveals a positive impact of the proposed real-time PPC system on the shop performance. The efficiency of PPC system is further examined by implementing data from a real-world manufacturer.     

Modelling recruitment training in mathematical human resource planning

This paper deals with mathematical human resource planning; more specifically, it suggests a new model for a manpower‐planning system. In general, we study a k‐classed hierarchical system where the workforce demand at each time period is satisfied through internal mobility and recruitment. The motivation for this work is based on various European Union incentives, which promote regional or local government assistance programs that could be exploited by firms not only for hiring and training newcomers, but also to improve the skills and knowledge of their existing personnel. In this respect, in our augmented mobility model we establish a new ‘training/standby’ class, which serves as a manpower inventory position for potential recruits. This class, which may very well be internal or external to the system, is incorporated into the framework of a non‐homogeneous Markov chain model. Furthermore, cost objectives are employed using the goal‐programming approach, under different operating assumptions, in order to minimize the operational cost in the presence of system's constraints and regulations. Copyright © 2002 John Wiley & Sons, Ltd.     

A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a fuzzy linear programming model for tactical supply chain planning in a multi-echelon, multi-product, multi-level, multi-period supply chain network. In this approach, the demand, process and supply uncertainties are jointly considered. The aim is to centralize multi-node decisions simultaneously to achieve the best use of the available resources along the time horizon so that customer demands are met at a minimum cost. This proposal is tested by using data from a real automobile SC. The fuzzy model provides the decision maker (DM) with alternative decision plans with different degrees of satisfaction.     

A fuzzy optimization approach for procurement transport operational planning in an automobile supply chain

We consider a real-world automobile supply chain in which a first-tier supplier serves an assembler and determines its procurement transport planning for a second-tier supplier by using the automobile assembler’s demand information, the available capacity of trucks and inventory levels. The proposed fuzzy multi-objective integer linear programming model (FMOILP) improves the transport planning process for material procurement at the first-tier supplier level, which is subject to product groups composed of items that must be ordered together, order lot sizes, fuzzy aspiration levels for inventory and used trucks and uncertain truck maximum available capacities and minimum percentages of demand in stock. Regarding the defuzzification process, we apply two existing methods based on the weighted average method to convert the FMOILP into a crisp MOILP to then apply two different aggregation functions, which we compare, to transform this crisp MOILP into a single objective MILP model. A sensitivity analysis is included to show the impact of the objectives weight vector on the final solutions. The model, based on the full truck load material pick method, provides the quantity of products and number of containers to be loaded per truck and period. An industrial automobile supply chain case study demonstrates the feasibility of applying the proposed model and the solution methodology to a realistic procurement transport planning problem. The results provide lower stock levels and higher occupation of the trucks used to fulfill both demand and minimum inventory requirements than those obtained by the manual spreadsheet-based method.     

On the impact of suboptimal decisions in the newsvendor model

We study the impact of suboptimal decisions in the newsvendor model, one of the popular inventory models. We establish a lower bound for the deviation of inventory cost from its minimum, when the order quantity is suboptimal. Demonstration of the bound shows the model to be sensitive to suboptimal decisions.     

Sensitivity analysis for product design selection with an implicit value function

In product design selection the decision maker (DM) often does not have enough information about the end users’ needs to state the “preferences” with precision, as is required by many of the existing selection methods. We present, for the case where the DM gives estimates of the preferences, a concept for calculating a “robustness index.” The concept can be used with any iterative selection method that chooses a trial design for each iteration, and uses the DM’s preference parameters at that trial design to eliminate some design options which have lower value than the trial design. Such methods, like our previously published method, are applicable to cases where the DM’s value function is implicit. Our robustness index is a metric of the allowed variation between the actual and estimated preferences for which the set of non-eliminated trial designs (which could be singleton) will not change. The DM, through experience, can use the robustness index and other information generated in calculating the index to determine what action to take: make a final selection from the present set of non-eliminated designs; improve the precision of the preference estimates; or otherwise cope with the imprecision. We present an algorithm for finding the robustness index, and demonstrate and verify the algorithm with an engineering example and a numerical example.     

Managing critical success strategies for an enterprise resource planning project

This paper develops an innovative objectives-oriented approach with one evaluation model and three optimization models for managing the implementation of a set of critical success strategies (CSSs) for an enterprise resource planning (ERP) project in an organization. To evaluate the CSSs based on their contribution to the organizational objectives, the evaluation model addresses an important issue of measuring the relationship between objectives in a three-level hierarchy involving the organization, its functional departments, and the ERP project. To determine the optimal management priority for implementing the CSSs from the organization’s perspective, the three optimization models maximize their total implementation value by integrating individual departments’ management preferences. An empirical study is conducted to demonstrate how these models work and how their outcomes can provide practical insights and implications in planning and managing the implementation of the CSSs for an ERP project.     

A sensitivity analysis algorithm for hierarchical decision models

In this paper, a comprehensive algorithm is developed to analyze the sensitivity of hierarchical decision models (HDM), including the analytic hierarchy process and its variants, to single and multiple changes in the local contribution matrices at any level of the decision hierarchy. The algorithm is applicable to all HDM that use an additive function to derive the overall contribution vector. It is independent of pairwise comparison scales, judgment quantification techniques and group opinion combining methods. The allowable range/region of perturbations, contribution tolerance, operating point sensitivity coefficient, total sensitivity coefficient and the most critical decision element at a certain level are identified in the HDM SA algorithm. An example is given to demonstrate the application of the algorithm and show that HDM SA can reveal information more significant and useful than simply knowing the rank order of the decision alternatives.     

Sensitivity analysis of the newsvendor model

Quality of decisions in inventory management models depends on the accuracy of parameter estimates used for decision making. In many situations, error in decision making is unavoidable. In such cases, sensitivity analysis is necessary for better implementation of the model. Though the newsvendor model is one of the most researched inventory models, little is known about its robustness. In this paper, we perform sensitivity analysis of the classical newsvendor model. Conditions for symmetry/skewness of cost deviation (i.e., deviation of expected demand–supply mismatch cost from its minimum) have been identified. These conditions are closely linked with symmetry/skewness of the demand density function. A lower bound of cost deviation is established for symmetric unimodal demand distributions. Based on demonstrations of the lower bound, we found the newsvendor model to be sensitive to sub-optimal ordering decisions, more sensitive than the economic order quantity model. Order quantity deviation (i.e., deviation of order quantity from its optimum) is explored briefly. We found the magnitude of order quantity deviation to be comparable with that of parameter estimation error. Mean demand is identified as the most influential parameter in deciding order quantity deviation.     

Robust nonlinear optimization with conic representable uncertainty set

The robust optimization methodology is known as a popular method dealing with optimization problems with uncertain data and hard constraints. This methodology has been applied so far to various convex conic optimization problems where only their inequality constraints are subject to uncertainty. In this paper, the robust optimization methodology is applied to the general nonlinear programming (NLP) problem involving both uncertain inequality and equality constraints. The uncertainty set is defined by conic representable sets, the proposed uncertainty set is general enough to include many uncertainty sets, which have been used in literature, as special cases. The robust counterpart (RC) of the general NLP problem is approximated under this uncertainty set. It is shown that the resulting approximate RC of the general NLP problem is valid in a small neighborhood of the nominal value. Furthermore a rather general class of programming problems is posed that the robust counterparts of its problems can be derived exactly under the proposed uncertainty set. Our results show the applicability of robust optimization to a wider area of real applications and theoretical problems with more general uncertainty sets than those considered so far. The resulting robust counterparts which are traditional optimization problems make it possible to use existing algorithms of mathematical optimization to solve more complicated and general robust optimization problems.     

A minmax regret median problem on a tree under uncertain locations of the demand points

This paper deals with the location of a new facility on a tree according to the minimization of the weighted distance to the customers. The weights represent demands of the set of nodes. The exact location of each customer will be assumed unknown but close   to its corresponding node. In this context, an algorithm to find a minmax regret median is proposed and its complexity is shown to be O(nlog(n))$O(nlog\left(n\right))$, where n$n$ is the number of nodes of the tree     

Radio resource management for the UMTS enhanced uplink in presence of QoS radio bearers

The next step in the evolution of UMTS is the Enhanced Uplink or high speed uplink packet access (HSUPA), which is designed for the efficient transport of packet switched data. We propose an analytic modeling approach for the performance evaluation of the UMTS uplink with best-effort users over the enhanced uplink and QoS-users over dedicated channels. The model considers two different scheduling disciplines for the enhanced uplink: parallel scheduling and one-by-one scheduling. Resource Management in such a system has to consider the requirements of the dedicated channel users and the enhanced uplink users on the shared resource, i.e. the cell load. We evaluate the impact of two resource management strategies, one with preemption for dedicated channels and one without, on key QoS-indicators like blocking and dropping probabilities as well as user and cell throughput.     

Multi-period planning and uncertainty issues in cellular manufacturing: A review and future directions

In this paper we review research that has been done to address cellular manufacturing under conditions of multi-period planning horizons, with demand and resource uncertainties. Most traditional cell formation procedures ignore any changes in demand over time caused by product redesign and uncertainties due to volume variation, part mix variation, and resource unreliability. However in today’s business environment, product life cycles are short, and demand volumes and product mix can vary frequently. Thus cell design needs to address these issues. It is only recently that researchers have been modelling uncertainty and multi-period issues. In this paper we conduct a comprehensive review of the work that addresses these issues. We present mathematical programming formulations as well as a taxonomy of existing models. Finally we suggest some directions for future research.