Strategic Acquisition Management: A Multi-Objective Synergistic Approach

Of all the strategic planning and decision-making a corporation undertakes, a merger or acquisition of another company is one of the most important and complex. The complexity is due not only to the volume of accounting, finance, marketing and management factors that need to be considered, but also to synergistic factors that are not adequately incorporated in current acquisition planning models. This paper presents a goal-programming modelling approach to deal with the problem of strategic acquisition planning for mergers, acquisitions or joint ventures. A goal-programming model is developed and applied to illustrate its use in acquisition decision-making. The results of the paper demonstrate the model's informational efficiency of application and unique ability to include synergistic decision-making factors.     

Probabilistic programming models for traffic incident management operations planning

This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for the planning of traffic incident management operations. For the incident response planning, we use the concept of quality of service during a potential incident to give the decision-maker the flexibility to determine the optimal policy in response to various possible situations. An integer programming model with probabilistic constraints is also proposed to address the incident response problem with stochastic resource requirements at the sites of incidents. For the resource allocation planning, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the resource requirements of the incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. A detailed case study for the incident resource allocation problem is included to demonstrate the use of proposed model in a real-world context. The paper concludes with a summary of results and recommendations for future research.     

A successive convex approximation method for multistage workforce capacity planning problem with turnover

Workforce capacity planning in human resource management is a critical and essential component of the services supply chain management. In this paper, we consider the planning problem of transferring, hiring, or firing employees among different departments or branches of an organization under an environment of uncertain workforce demands and turnover, with the objective of minimizing the expected cost over a finite planning horizon. We model the problem as a multistage stochastic program and propose a successive convex approximation method which solves the problem in stages and iteratively. An advantage of the method is that it can handle problems of large size where normally solving the problems by equivalent deterministic linear programs is considered to be computationally infeasible. Numerical experiments indicate that solutions obtained by the proposed method have expected costs near optimal.     

A Multi-Attribute Assignment Goal-Programming Model with Incentives

A multi-attribute assignment goal-programming model is developed in this paper for the selection and assignment of transfer personnel. Attributes and incentives are used to select the correct type of people from surplus personnel and assign them to vacant positions. The model is illustrated in a simple, exemplary case problem, and the results are interpreted. The model is solved by using a sequential linear goal-programming algorithm and a mixed-integer programming subroutine.     

The municipal financial planning model: A simultaneous regression equations and goal programming approach

Most of today's city managers are concerned about municipal financial problems. In trying to resolve these problems, scientific planning tools are needed to examine the optimality of resource allocation. For the municipal financial policy planners, the following two points are important.

• 1.(1) Statistical aspects. Since there are many economic variables in municipal financial problems, it is necessary to clarify the relationship among these variables and to infer the parameters through a statistical approach.
• 2.(2) Mathematical aspects. Policy-planners must specify the optimal value of these variables so as to attain the multiple goals of a local government.

Econometric models, especially the simultaneous equations approach, are appropriate for statistical analysis; whereas a goal-programming formulation may be used for mathematical aspects of the problem.In this paper, we propose and show that these two models can be combined. We call this the GPE model.The GPE model is applied to Urawa City. The Urawa model is composed of 6 structural equations 9 variables and 4 scenarios from the standpoint of future insight of Urawa City.From the Urawa Case, we conclude that the GPE model may be a practical tool for the municipal financial planning of other local governments.     

A stochastic programming approach for planning horizons of infinite horizon capacity planning problems

Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for general stochastic cost and demand data (non-Markovian and non-stationary). We give sufficient conditions for the existence of an optimal solution. Furthermore, we study the monotonicity property of the finite horizon approximation of the original problem. We show that, the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem, when the time horizon goes to infinity. These convergence results, together with the integrality of decision variables, imply the existence of a planning horizon. We also develop a useful formula to calculate an upper bound on the planning horizon. Then by decomposition, we show the existence of a planning horizon for a class of very general stochastic capacity planning problems, which have complicated decision structure.     

The multivariate non-homogeneous Markov manpower system in a departmental mobility framework

The present paper proposes a non-homogeneous multivariate Markov manpower system in the general category of mathematical human resource planning. More specifically, we suggest a model, which takes into account the divisions existing in an organization categorizing its employees into several groups (departments). In this context, it considers not only possible transitions within the departments (intra-department transitions), but also, transfers of personnel between departments (inter-department transitions). Additionally, the proposed modeling structure is accompanied by cost and stocks (personnel) objectives which are set and in the sequel could be achieved by controlling either the recruitment policy or the allocation policy of employees transferred to other departments (or both). We use a minmax fuzzy goal-programming approach, under different operating assumptions, in order to keep the operational cost below desired aspiration levels and reach desirable stock structures in the presence of system’s constraints and regulations. The paper concludes with a numerical illustration.     

A Process for Determining Priorities and Weights for Large-Scale Linear Goal Programmes

Many planning models can be formulated as large-scale linear goal-programming problems in which the analyst and user must establish thousands of objective-function weights that reflect the priorities of the many goals. How to select such weights so as to have the resulting optimal solution be a suitable compromise solution is the main focus of this paper. We first describe the problem setting that gave rise to the need, here military personnel planning, and then a process by which a set of goal priorities and objective-function weights can be developed using Saaty's analytic hierarchy process.     

Path planning for robots under stochastic uncertainty *

In order to reduce large online measurement and correction expenses, the a priori informations on the random variations of the model parameters of a robot and its working environment are taken into account already at the planning stage. Thus, instead of solving a deterministic path planning problem with a fixed nominal parameter vector, here, the optimal velocity profile along a given trajectory in work space is determined by using a stochastic optimization approach. Especially, the standard polygon of constrained motion-depending on the nominal parameter vector-is replaced by a more general set of admissible motion determined by chance constraints or more general risk constraints. Robust values (with respect to stochastic parameter variations) of the maximum, minimum velocity, acceleration, deceleration, resp., can be obtained then by solving a univariate stochastic optimization problem Considering the fields of extremal trajectories, the minimum-time path planning problem under stochastic uncertainty can be solved now by standard optimal deterministic path planning methods     

An application of Lagrangian relaxation to a capacity planning problem under uncertainty

A supply chain network-planning problem is presented as a two-stage resource allocation model with 0-1 discrete variables. In contrast to the deterministic mathematical programming approach, we use scenarios, to represent the uncertainties in demand. This formulation leads to a very large scale mixed integer-programming problem which is intractable. We apply Lagrangian relaxation and its corresponding decomposition of the initial problem in a novel way, whereby the Lagrangian relaxation is reinterpreted as a column generator and the integer feasible solutions are used to approximate the given problem. This approach addresses two closely related problems of scenario analysis and two-stage stochastic programs. Computational solutions for large data instances of these problems are carried out successfully and their solutions analysed and reported. The model and the solution system have been applied to study supply chain capacity investment and planning.     

Production planning with uncertainty in the quality of raw materials: a case in sawmills

Motivated by sawmill production planning, this paper investigates multi-period, multi-product (MPMP) production planning in a manufacturing environment with non-homogeneous raw materials, and consequently random process yields. A two-stage stochastic program with recourse is proposed to address the problem. The random yields are modelled as scenarios with stationary probability distributions during the planning horizon. The solution methodology is based on the sample average approximation (SAA) scheme. The stochastic sawmill production planning model is validated through the Monte Carlo simulation. The computational results for a real medium capacity sawmill highlight the significance of using the stochastic model as a viable tool for production planning instead of the mean-value deterministic model, which is a traditional production planning tool in many sawmills.     

Stochastic multi-site capacity planning of TFT-LCD manufacturing using expected shadow-price based decomposition

This paper presents a stochastic optimization model and efficient decomposition algorithm for multi-site capacity planning under the uncertainty of the TFT-LCD industry. The objective of the stochastic capacity planning is to determine a robust capacity allocation and expansion policy hedged against demand uncertainties because the demand forecasts faced by TFT-LCD manufacturers are usually inaccurate and vary rapidly over time. A two-stage scenario-based stochastic mixed integer programming model that extends the deterministic multi-site capacity planning model proposed by Chen et al. (2010) [1] is developed to discuss the multi-site capacity planning problem in the face of uncertain demands. In addition a three-step methodology is proposed to generate discrete demand scenarios within the stochastic optimization model by approximating the stochastic continuous demand process fitted from the historical data. An expected shadow-price based decomposition, a novel algorithm for the stage decomposition approach, is developed to obtain a near-optimal solution efficiently through iterative procedures and parallel computing. Preliminary computational study shows that the proposed decomposition algorithm successfully addresses the large-scale stochastic capacity planning model in terms of solution quality and computation time. The proposed algorithm also outperforms the plain use of the CPLEX MIP solver as the problem size becomes larger and the number of demand scenarios increases.     

A matheuristic algorithm for stochastic home health care planning

Efficient human resource planning is the cornerstone of designing an effective home health care system. Human resource planning in home health care system consists of decisions on districting/zoning, staff dimensioning, resource assignment, scheduling, and routing. In this study, a two-stage stochastic mixed integer model is proposed that considers these decisions simultaneously. In the planning phase of a home health care system, the main uncertain parameters are travel and service times. Hence, the proposed model takes into account the uncertainty in travel and service times. Districting and staff dimensioning are defined as the first stage decisions, and assignment, scheduling, and routing are considered as the second stage decisions. A novel algorithm is developed for solving the proposed model. The algorithm consists of four phases and relies on a matheuristic-based method that calls on various mixed integer models. In addition, an algorithm based on the progressive hedging and Frank and Wolf algorithms is developed to reduce the computational time of the second phase of the proposed matheuristic algorithm. The efficiency and accuracy of the proposed algorithm are tested through several numerical experiments. The results prove the ability of the algorithm to solve large instances.     

A stochastic model for operating room planning with elective and emergency demand for surgery

This paper describes a stochastic model for Operating Room (OR) planning with two types of demand for surgery: elective surgery and emergency surgery. Elective cases can be planned ahead and have a patient-related cost depending on the surgery date. Emergency cases arrive randomly and have to be performed on the day of arrival. The planning problem consists in assigning elective cases to different periods over a planning horizon in order to minimize the sum of elective patient related costs and overtime costs of operating rooms. A new stochastic mathematical programming model is first proposed. We then propose a Monte Carlo optimization method combining Monte Carlo simulation and Mixed Integer Programming. The solution of this method is proved to converge to a real optimum as the computation budget increases. Numerical results show that important gains can be realized by using a stochastic OR planning model.     

基于二元联系数距离的不确定语言多属性决策模型

研究了属性权重范围已知,方案主观偏好值为语言变量,决策信息为不确定语言决策矩阵的多属性决策问题.在给出不确定语言变量转换为二元联系数的公式以及二元联系数距离公式的基础上,将方案主观偏好语言评价值转换为二元联系数,将不确定语言决策矩阵转换为二元联系数决策矩阵,从而得到方案的二元联系数综合属性值,通过最小化方案的二元联系数综合属性值和主观偏好值之间距离,建立多目标优化模型,并将其转换为一个单目标规划模型计算出属性权重.然后,通过对方案的二元联系数综合属性值进行不确定性分析,得到各方案的排序总数,利用排序总数对方案进行排序择优.应用实例表明该决策方法可行有效.     

Comments on “An Algorithm for Solving the Linear Goal-Programming Problem by Solving Its Dual”

Goal Programming within a pre-emptive priority structure has been one of the most widely used multi-objective mathematical model formulations. By considering its dual problem, Ignizio has shown that a very efficient computational procedure for solving linear goal-programming problems can be problems can be implemented with any conventional large-scale simplex system. This note gives an overview of Ignizio's dual formulation, and identifies when a certain dual variable must be incorporated in the model to preserve the pre-emptive priority structure.     

Sales and operations planning in systems with order configuration uncertainty

This paper addresses the problem of aligning demand and supply in configure-to-order systems. Using stochastic programming methods, this study demonstrates the value of accounting for the uncertainty associated with how orders are configured. We also demonstrate the value of component supply flexibility in the presence of order configuration uncertainty. We present two stochastic models: an explosion problem model and an implosion problem model. These models are positioned sequentially within a popular business process called sales and operations planning. Both models are formulated as two-stage stochastic programs with recourse and are solved using the sample average approximation method. Computational analyses were performed using data obtained from IBM System and Technology Group. The problem sets used in our analysis are created from actual industry data and our results show that significant improvements in revenue and serviceability can be achieved by appropriately accounting for the uncertainty associated with order configurations.     

Fractionation in radiation treatment planning

Radiotherapy treatment is often delivered in a fractionated manner over a period of time. Emerging delivery devices are able to determine the actual dose that has been delivered at each stage facilitating the use of adaptive treatment plans that compensate for errors in delivery. We formulate a model of the day-to-day planning problem as a stochastic program and exhibit the gains that can be achieved by incorporating uncertainty about errors during treatment into the planning process. Due to size and time restrictions, the model becomes intractable for realistic instances. We show how heuristics and neuro-dynamic programming can be used to approximate the stochastic solution, and derive results from our models for realistic time periods. These results allow us to generate practical rules of thumb that can be immediately implemented in current planning technologies.     

Simultaneous Optimization in Process Quality Control via Prediction-interval Constrained Programming

A challenging problem in process control is the selection of input levels which will produce desirable output quality. This problem is complicated by the unsure relationships of cause and effect and by the trade-offs between meeting conflicting output specifications. This paper proposes a new approach, which incorporates prediction-interval constraints into a goal-programming model. A process-control problem, originally solved by the desirability-function approach, is solved using this new model. Comparisons between the two approaches are discussed.