Developing real option game models

By mixing concepts from both game theoretic analysis and real options theory, an investment decision in a competitive market can be seen as a “game” between firms, as firms implicitly take into account other firms’ reactions to their own investment actions. We review two decades of real option game models, suggesting which critical problems have been “solved” by considering game theory, and which significant problems have not been yet adequately addressed. We provide some insights on the plausible empirical applications, or shortfalls in applications to date, and suggest some promising avenues for future research.     

Closed-form solution to a real option problem with regime switching

I investigate the optimal investment timing model in which investment is feasible in only one of the two regimes, which shift at Poisson jump times. I derive the option value and investment threshold in closed forms. I also prove that some solutions in previous models are obtained as the limits of the solution. The closed-form solution can be useful as a new framework to study real option problems with the illiquidity of option exercise opportunities.     

The equitable location problem on the plane

This paper considers the problem of locating M facilities on the unit square so as to minimize the maximal demand faced by each facility subject to closest assignments and coverage constraints. Focusing on uniform demand over the unit square, we develop upper and lower bounds on feasibility of the problem for a given number of facilities and coverage radius. Based on these bounds and numerical experiments we suggest a heuristic to solve the problem. Our computational results show that the heuristic is very efficient, as the average gap between its solutions and the lower bound is 4.34%.     

Robust optimization of internal transports at a parcel sorting center operated by Deutsche Post World Net

Competitiveness in global markets requires the ongoing identification and full utilization of improvement potential. To cut costs by means of process optimization, logistics service providers need to focus on efficient planning — not only for external but also for internal transports. This contribution will demonstrate that significant reductions in internal transports at one of the Deutsche Post World Net’s main parcel sorting centers can be achieved by applying the robust solution of a modified three-dimensional linear assignment model.     

A travel time estimation model for a high-level picker-to-part system with class-based storage policies

Most previous related studies on warehouse configurations and operations only investigated single-level storage rack systems where the height of storage racks and the vertical movement of the picking operations are both not considered. However, in order to utilize the space efficiently, high-level storage systems are often used in warehouses in practice. This paper presents a travel time estimation model for a high-level picker-to-part system with the considerations of class-based storage policy and various routing policies. The results indicate that the proposed model appears to be sufficiently accurate for practical purposes. Furthermore, the effects of storage and routing policies on the travel time and the optimal warehouse layout are discussed in the paper.     

Branch and bound algorithm for a transfer line design problem: Stations with sequentially activated multi-spindle heads

In this paper, a new transfer line balancing problem is considered. The main difference from the simple assembly line balancing problem is that the operations are grouped into blocks (batches). All the operations of the same block are carried out simultaneously by one piece of equipment (multi-spindle head). Nevertheless, the blocks assigned to the same workstation are executed in series. The line cost consists of the sum of block and workstation costs. At the considered line design stage, the set of all available blocks is given. The aim is to find a subset from the given set of available blocks and to find a partition of this subset to workstations such that each operation is executed once and the line cost is minimal while all the precedence, cycle time, and compatibility (operation inclusion and block exclusion) constraints are respected. A new lower bound based on solving a special set partitioning problem is presented and a branch and bound algorithm is developed. The experimental results prove the quality of the lower bound and applicability of the suggested branch and bound algorithm for medium sized industrial cases.     

A multicut L-shaped based algorithm to solve a stochastic programming model for the mobile facility routing and scheduling problem

This paper considers the mobile facility routing and scheduling problem with stochastic demand (MFRSPSD). The MFRSPSD simultaneously determines the route and schedule of a fleet of mobile facilities which serve customers with uncertain demand to minimize the total cost generated during the planning horizon. The problem is formulated as a two-stage stochastic programming model, in which the first stage decision deals with the temporal and spatial movement of MFs and the second stage handles how MFs serve customer demands. An algorithm based on the multicut version of the L-shaped method is proposed in which several lower bound inequalities are developed and incorporated into the master program. The computational results show that the algorithm yields a tighter lower bound and converges faster to the optimal solution. The result of a sensitivity analysis further indicates that in dealing with stochastic demand the two-stage stochastic programming approach has a distinctive advantage over the model considering only the average demand in terms of cost reduction.     

A travel-time model for a person-onboard order picking system

The design of an order picking system in a distribution center depends on several decisions, where a key decision is determining the optimal storage system configuration (the number, length, and height of the storage aisles). To make this decision, a throughput model that considers vertical, as well as horizontal, travel is needed. In this paper we extend prior research that considers horizontal travel for a given number and length of the storage aisles so that we are also able to consider the height of the aisles as well. Such a model will provide a more accurate estimate of the throughput of an order picker and it will also permit an examination of the tradeoff between the length and height of the aisles. The analytical model we develop to estimate throughput is based on probability models and order statistics results assuming random storage. It is intended for person-onboard order picking systems and we consider both Tchebychev and rectilinear travel. We illustrate the use of our travel-time model by incorporating it into a simple, cost-based optimization model to recommend the height of a one-pallet-deep storage system.     

Warehouse design: A structured approach

In spite of the importance of warehousing to the customer service and cost levels of many businesses, there is currently not a comprehensive systematic method for designing warehouses. In this paper, the current literature on the overall methodology of warehouse design is explored, together with the literature on tools and techniques used for specific areas of analysis. The general results from the literature have then been validated and refined with reference to warehouse design companies. The output is a general framework of steps, with specific tools and techniques that can be used for each step. This is intended to be of value to practitioners and to assist further research into the development of a more comprehensive methodology for warehouse design.     

A real options approach to labour shifts planning under different service level targets

Firms that experience uncertainty in demand as well as challenging service levels face, among other things, the problem of managing employee shift numbers. Decisions regarding shift numbers often involve significant expansions or reductions in capacity, in response to changes in demand. In this paper, we quantify the impact of treating shifts in workforce expansion as investments, while considering required service level improvements. The decision to increase shifts, whether by employing temporary workers or hiring permanent employees, is one that involves significant risks. Traditional theories typically consider reversible investments, and thus do not capture the idiosyncrasies involved in shift management, in which costs are not fully reversible. In our study, by using real options theory, we quantify managers’ ability to consider this irreversibility, aiming to enable them to make shift decisions under conditions of uncertainty with the maximum level of flexibility. Our model aims to help managers make more accurate decisions with regard to shift expansion under service level targets, and to defer commitment until future uncertainties can be at least partially resolved. Overall, our investigation contributes to studies on the time required to introduce labour shift changes, while keeping the value of service level improvements in mind.     

Tabu search for the single row facility layout problem using exhaustive 2-opt and insertion neighborhoods

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, while minimizing the weighted sum of the distances between all pairs of facilities. The problem is NP-hard. In this paper, we present two tabu search implementations, one involving an exhaustive search of the 2-opt neighborhood and the other involving an exhaustive search of the insertion neighborhood. We also present techniques to significantly speed up the search of the two neighborhoods. Our computational experiments show that the speed up techniques are effective, and our tabu search implementations are competitive. Our tabu search implementations improved previously known best solutions for 23 out of the 43 large sized SRFLP benchmark instances.     

Batch picking in narrow-aisle order picking systems with consideration for picker blocking

This paper develops strategies to control picker blocking that challenge the traditional assumptions regarding the tradeoffs between wide- and narrow-aisle order picking systems. We propose an integrated batching and sequencing procedure called the indexed batching model (IBM), with the objective of minimizing the total retrieval time (the sum of travel time, pick time and congestion delays). The IBM differs from traditional batching formulations by assigning orders to indexed batches, whereby each batch corresponds to a position in the batch release sequence. We develop a mixed integer programming solution for exact control, and demonstrate a simulated annealing procedure to solve large practical problems. Our results indicate that the proposed approach achieves a 5–15% reduction in the total retrieval time primarily by reducing picker blocking. We conclude that the IBM is particularly effective in narrow-aisle picking systems.     

Two-worker blocking congestion model with walk speed m in a no-passing circular passage system

This paper introduces a blocking model and closed-form expression of two workers traveling with walk speed m (m = integer) in a no-passing circular-passage system of n stations and assuming n = m + 2, 2m + 2, …. We develop a Discrete-Timed Markov Chain (DTMC) model to capture the workers’ changes of walk, pick, and blocked states, and quantify the throughput loss from blocking congestion by deriving a steady state probability in a closed-form expression. We validate the model with a simulation study. Additional simulation comparisons show that the proposed throughput model gives a good approximation of a general-sized system of n stations (i.e., n > 2), a practical walk speed system of real number m (i.e., m ? 1), and a bucket brigade order picking application.     

Strategic robust supply chain design based on the Pareto-optimal tradeoff between efficiency and risk

The strategic design of a robust supply chain has to determine the configuration of the supply chain so that its performance remains of a consistently high quality for all possible future conditions. The current modeling techniques often only consider either the efficiency or the risk of the supply chain. Instead, we define the strategic robust supply chain design as the set of all Pareto-optimal configurations considering simultaneously the efficiency and the risk, where the risk is measured by the standard deviation of the efficiency. We model the problem as the Mean–Standard Deviation Robust Design Problem (MSD-RDP). Since the standard deviation has a square root expression, which makes standard maximization algorithms based on mixed-integer linear programming non-applicable, we show the equivalency to the Mean–Variance Robust Design Problem (MV-RDP). The MV-RDP yields an infinite number of mixed-integer programming problems with quadratic objective (MIQO) when considering all possible tradeoff weights. In order to identify all Pareto-optimal configurations efficiently, we extend the branch-and-reduce algorithm by applying optimality cuts and upper bounds to eliminate parts of the infeasible region and the non-Pareto-optimal region. We show that all Pareto-optimal configurations can be found within a prescribed optimality tolerance with a finite number of iterations of solving the MIQO. Numerical experience for a metallurgical case is reported.     

Simulated annealing and tabu search approaches for the Corridor Allocation Problem

In the Corridor Allocation Problem, we are given n facilities to be arranged along a corridor. The arrangements on either side of the corridor should start from a common point on the left end of the corridor. In addition, no space is allowed between two adjacent facilities. The problem is motivated by applications such as the arrangement of rooms in office buildings, hospitals, shopping centers or schools. Tabu search and simulated annealing algorithms are presented to minimize the sum of weighted distances between every pair of facilities. The algorithms are evaluated on several instances of different sizes either randomly generated or available in the literature. Both algorithms reached the optimal (when available) or best-known solutions of the instances with n ? 30. For larger instances with size 42 ? n ? 70, the simulated annealing implementation obtained smaller objective values, while requiring a smaller number of function evaluations.     

Global facility network design in the presence of competition

We study the facility network design problem for a global firm that is a monopolist seller in its domestic market but faces local competition in its foreign market. The global firm produces in the face of demand and exchange rate uncertainty but can postpone localization and distribution of the output until after uncertainties are resolved. The competitor in the foreign market, however, enjoys the flexibility of postponing all production activities until after uncertainties are resolved. The two firms engage in an ex-post Cournot competition in the foreign market. We consider three potential network configurations for the global firm. Under a linear demand function, we provide the necessary and sufficient condition that one of the three networks is the global firm’s optimal choice, and explore how the presence of foreign competition affects the sensitivity of the global firm’s design to various cost parameters and market uncertainties.     

Robust placement of sensors in dynamic water distribution systems

Designing a robust sensor network to detect accidental contaminants in water distribution systems is a challenge given the uncertain nature of the contamination events (what, how much, when, where and for how long) and the dynamic nature of water distribution systems (driven by the random consumption of consumers). We formulate a set of scenario-based minimax and minimax regret models in order to provide robust sensor-placement schemes that perform well under all realizable contamination scenarios, and thus protect water consumers. Single-and multi-objective versions of these models are then applied to a real water distribution system. A heuristic solution method is applied to solve the robust models. The concept of “sensitivity region” is used to visualize trade-offs between multiple objectives.     

Bayesian semiparametric analysis for a single item maintenance optimization

We address the problem of a finite horizon single item maintenance optimization structured as a combination of preventive and corrective maintenance in a nuclear power plant environment. We present Bayesian semiparametric models to estimate the failure time distribution and costs involved. The objective function for the optimization is the expected total cost of maintenance over the pre-defined finite time horizon. Typically, the mathematical modeling of failure times are based on parametric models. These models fail to capture the true underlying relationships in the data; indeed, under a parametric assumption, the hazard rates are treated as unimodal, which, as shown in this paper, is incorrect. Importantly, assuming an increasing failure rate, as is typically done, we show, is way off the mark in the present context. Since hazard and cost estimates feed into the optimization phase, from a risk management perspective, potentially gross errors, resulting from purely parametric models, can be obviated. We show the effectiveness of our approach using real data from the South Texas Project Nuclear Operating Company (STPNOC) located in Bay City, Texas.     

A constructive aisle design model for unit-load warehouses with multiple pickup and deposit points

We develop a network-based warehouse model of individual pallet locations and their interactions with appropriate cross aisles in order to evaluate the expected travel distance of a given design. The model is constructive in that it uses Particle Swarm Optimization to determine the best angles of cross aisles and picking aisles for multiple, pre-determined pickup and deposit (P&D) points in a unit-load warehouse. Our results suggest that alternative designs offer reduced expected travel distance, but at the expense of increased storage space. The opportunity for benefit also seems to decline as P&D points increase in number and dispersion.     

Balancing stochastic two-sided assembly lines: A chance-constrained,piecewise-linear,mixed integer program and a simulated annealing algorithm

Two-sided assembly lines are often designed to produce large-sized products, such as automobiles, trucks and buses. In this type of a production line, both left-side and right-side of the line are used in parallel. In all studies on two-sided assembly lines, the task times are assumed to be deterministic. However, in real life applications, especially in manual assembly lines, the tasks may have varying execution times defined as a probability distribution. The task time variation may result from machine breakdowns, loss of motivation, lack of training, non-qualified operators, complex tasks, environment, etc. In this paper, the problem of balancing two-sided assembly lines with stochastic task times (STALBP) is considered. A chance-constrained, piecewise-linear, mixed integer program (CPMIP) is proposed to model and solve the problem. As a solution approach a simulated annealing (SA) algorithm is proposed. To assess the effectiveness of CPMIP and SA algorithm, a set of test problems are solved. Finally, computational results indicating the effectiveness of CPMIP and SA algorithm are reported.