An integer programming approach to short-term production scheduling in a tobacco plant

In this paper, a mathematical model is developed that facilitates daily production scheduling in a tobacco processing plant. The implied objectives are to meet specific horizon production targets (obtained from a master production schedule), to maintain safety stock requirements and to ensure that the demand for labour lies within given limits. The express objective is to minimise the number of machines used in the production process. Additionally, the model incorporates work-in-progress, aspects of the demand for product transportation within the plant and machine capacity (utilisation) reduction effects associated with production sequencing. These aspects are relevant when dealing with time intervals as small as a day but can be averaged out when dealing with monthly time intervals. The developments in this paper represents stage II of the modelling of the tobacco plant, where stage I (already completed) was centred on obtaining a monthly master production schedule for a year ahead and assisting in macro planning activities. This paper also sees the development of a simple user-friendly heuristic which facilitates production sequencing on a daily basis given the master production schedule obtained from Stage I.     

Learning effects and the phenomenon of moving bottlenecks in a two-stage production system

This paper studies the effects of learning and forgetting on a two-stage production system and the position of a potential bottleneck in the system. We start with developing a model for a two-stage serial production system where semi-finished items are fed by the first stage to the second stage, which, in turn, processes the items to their final state. The finished items are transferred either to a subsequent stage or to customers. The paper assumes that both stages of the production system considered are subject to learning and forgetting effects. Learning quickens the production rate as more experience is gained (i.e., when the number of repetitions increases), while forgetting has the opposite effect when production is intermittent (i.e., experience is lost over production breaks). The paper studies how different values of the learning and forgetting parameters influence the ratio of the production rates of both stages and the flow of material in the system. The results of the paper indicate that learning may cause a bottleneck to shift its position in a production system. This happens when an initially slower stage overtakes a previously faster stage over time due to a higher learning rate. The paper thus contributes to the literature on moving bottlenecks and provides practitioners with a model that helps predicting where bottlenecks may arise in the production system, and which enables the system to flexibly react to moving bottlenecks.     

Multi-plant production planning in capacitated self-configuring two-stage serial systems

This research deals with a capacitated master production planning and capacity allocation problem for a multi-plant manufacturing system with two serial stages in each plant. We consider both cases in which a decoupling buffer is allowed or not between the two stages. Peculiar to the system considered is the capability of dynamically self-configuring its layout when buffering is disallowed, in the sense that, for each production run, different parallel machines in the second stage are grouped together and serially connected to a machine in the first stage. Although setup times and costs are considered negligible in our model, yet binary setup variables are introduced in order to account for minimum lot-sizes. The resulting mixed {0,1} linear programming model is solved by means of LP-based heuristic algorithms. The proposed modeling and solution procedure has been applied to problem instances originating from a real-world application, showing good results in practice.     

Optimal Short Horizon Distribution Operations in Reusable Container Systems

Manufacturers in many countries are facing increasing market pressures to use returnable containers. Few studies address the day-to-day operational problems of controlling production and distribution that are inherent in closed systems that reuse containers. In this paper we present a formulation of an optimal configuration of this type of system. In particular, we model the reusable bottle production and distribution activities of a large soft drink manufacturer located in Mexico City, Mexico. Two types of operational research models are combined to form the overall optimization system. A pair of linear programs (one aggregated, the other disaggregated) determines a master plan that is subsequently fined-tuned on a shift-by-shift basis using a difference equation simulation model. The simulation model mimics the heuristic ‘rules of thumb’ used by production planners for product distribution and container reuse planning. The results of our study indicate that this formulation provides a timely response in the field to key operational problems addressed by no previous approach. Included are better organizational control (through providing one-week production and distribution plans), feedback allowing modification of heuristic rules previously used in controlling the distribution of product and container reuse, and improvement in inventory behaviour such as avoiding shortages. These improvements have resulted in considerable market share gains since the models were implemented.     

On the Mean Production-rate Analysis of a Two-stage Production System with End Buffer and Random Demand

This paper deals with the transient fluctuations of the mean production rate of a two-stage production system subject to interstage and end inspections and end buffer. The interstage and end inspections are instantaneous, and the end buffer is with finite capacity of size N. A stochastic model is developed to describe the system, and analytical expressions to evaluate the mean production rate (MPR) of machine j (=I, II) in [0, t] with arbitrary distributions of processing times at the stages of production and exponential supply and demand pattern have been obtained by using the state-space method and the regeneration-point technique. A particular case is investigated, and numerical results are presented.     

A quantitative analysis of the Greek soft-drink market,or: How your advertisement will help your competitor's sales

This paper is deailing with the application of quantitative methods in analysing the Greek soft drink market. Single equation and simultaneous-equation regression models are developed and tested against real time-series data. The use of these methods in a real life case brought out the serious problem of interelationships existing between advertising and sales of products with minor differences and also marked the need of its further investigation.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.     

A dynamic inventory model with supplier selection in a serial supply chain structure

Considering the inherent connection between supplier selection and inventory management in supply chain networks, this article presents a multi-period inventory lot-sizing model for a single product in a serial supply chain, where raw materials are purchased from multiple suppliers at the first stage and external demand occurs at the last stage. The demand is known and may change from period to period. The stages of this production–distribution serial structure correspond to inventory locations. The first two stages stand for storage areas for raw materials and finished products in a manufacturing facility, and the remaining stages symbolize distribution centers or warehouses that take the product closer to customers. The problem is modeled as a time-expanded transshipment network, which is defined by the nodes and arcs that can be reached by feasible material flows. A mixed integer nonlinear programming model is developed to determine an optimal inventory policy that coordinates the transfer of materials between consecutive stages of the supply chain from period to period while properly placing purchasing orders to selected suppliers and satisfying customer demand on time. The proposed model minimizes the total variable cost, including purchasing, production, inventory, and transportation costs. The model can be linearized for certain types of cost structures. In addition, two continuous and concave approximations of the transportation cost function are provided to simplify the model and reduce its computational time.     

Converging Branch Multi-Stage Production Schedules with Finite Production Rates and Start-up Delays

This article considers scheduling production in a multi-stage system with converging branches and assumes an infinite time horizon, deterministic parameters, finite production rates, and constant lot sizes at each stage. The objective is the minimization of total time-averaged setup-shutdown and holding cost.The interdependence of successive stages is accounted for by delaying the initial startup at one stage relative to that at its immediate predecessors, to prevent shortages between the stages. Analytical expressions are found for such delay times and written under an "integer multiple" assumption on the cycle times at adjacent stages. Total cost is then minimized for a given set of integer multiples, and a heuristic search procedure for finding the optimal integer multiple values is described. Extensions of this procedure are then discussed.     

Determining Net Requirements for Material Requirements Planning

This paper presents a design guideline for netting systems that determine net requirements, for push-type production ordering. Two alternative netting systems (full and single) are formulated in an N stage production and inventory system. The performances of the two alternatives are discussed through numerically analysing production ordering variations and inventory level variations at each stage in the processes. The results obtained suggest that: (1) the full netting system is preferable at the production stages, where variance in the accumulated forecast consumption error by the immediately succeeding stage is smaller than the variance in the accumulated forecast market demand error over a production ordering interval and the lead time for the stage. (2) The single netting system may be preferable at the other stages, particularly in regard to production ordering variations.     

Widening requirements capture with soft methods: an investigation of hybrid M&S studies in health care

A simulation study consists of several stages: problem formulation, model implementation, verification and validation, experimentation and output data analysis. The application of multiple techniques in the model implementation stage is referred to as hybrid simulation, which we distinguish in this paper from a hybrid M&S study, the latter referring to studies that apply methods and techniques from disciplines like Operations Research (OR), Systems Engineering and Computer Science to one or more stages of a simulation study. Our paper focuses on the contribution of soft OR methods in the problem formulation stage of a simulation study (and by extension a hybrid M&S study). Soft Systems Methodology (SSM) has, arguably, been the most widely used qualitative approach for eliciting system requirements. In this paper, we present Qualitative System Dynamics (QSD), a soft systems method, as having potential use in the problem formulation stage of a healthcare M&S study. The contribution of this paper is thus twofold: (1) a review of the literature in SSM for healthcare operations management and (2) an examination of QSD as an additional soft OR method, complementing (rather than supplanting) existing approaches, which can further aid the understanding of the system in the problem formulation/conceptual modelling stage of a hybrid M&S study.     

基于Projection Pursuit-RAGA-NK-GERT的质量绩效提升路径优化——以组织质量特异性免疫和产品生命周期为主导逻辑的解释框架

依据组织免疫和组织质量特异性免疫的相关理论,引入情境变量产品生命周期,构建基于组织质量监视、组织质量防御软要素、组织质量防御硬要素和组织质量记忆的质量绩效提升路径理论框架。使用基于RAGA的投影寻踪模型、适应度景观和NK模型对产品生命周期不同阶段的质量绩效提升路径进行实证分析,实证结果表明:产品生命周期不同阶段有不同的质量绩效提升路径,产品导入期遵循的质量绩效提升路径为组织质量监视→组织质量防御→组织质量记忆,产品成长期遵循的质量绩效提升路径为组织质量防御软要素→组织质量防御硬要素→组织质量监视→组织质量记忆,产品成熟期遵循的质量绩效提升路径为组织质量防御硬要素→组织质量防御软要素→组织质量监视→组织质量记忆,产品衰退期遵循的质量绩效提升路径为组织质量记忆→组织质量监视→组织质量防御。并建立产品生命周期不同阶段质量绩效提升路径优化的GERT网络,优化产品生命周期不同阶段的质量绩效提升路径。     

PROMETHEE: an extension through fuzzy mathematical programming

PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are very close to each other. PROMETHEE V applies Integer Linear Programming in order to select the subset of alternatives that maximizes the sum of PROMETHEE II scorings, subject to a set of constraints. In order to make the model more realistic, this paper proposes that some constraints are soft and some coefficients are estimated by fuzzy numbers. Fuzzy Integer Linear Programming is applied, using the PROMETHEE III scorings as objective function coefficients, in order to find the subsets of non-outranked alternatives that best satisfy the soft constraints. The new model is more realistic and fits better the fuzzy philosophy of PROMETHEE. The method is illustrated with an example.     

Multilevel Scheduling of Multistage Production with Limited In-Process Inventory

A multistage, multiproduct production scheduling with limited in-process buffers between the successive stages is considered. Each stage is made up of identical parallel machines. The problem objective is to determine an assignment of products to machines over a scheduling horizon, which minimizes the completion time of the production order, with the in-process inventory holding costs as low as possible. The problem is modelled by multilevel integer programmes, each of which is concerned with scheduling a different stage of production. The interactions among the stages are modelled by additional constraints, which take into account the semi-finished product's availability and the limited storage capacity of the intermediate buffers. An hierarchical scheduling algorithm is presented, and an illustrative example for a three-stage production is included.     

Spatial competition and collaboration networks

We model the formation of collaboration networks among firms that are located in a circular city as a two-stage game. In the first stage, the firms form collaboration links, and in the second stage, they engage in price competition. If two firms form a link, their production costs in the second stage are reduced. The second stage is a generalization of Salop??s (Bell J Econ 10(1):141?C156, 1979) circular city model. We provide a complete characterization of equilibrium prices of the model. We show that a firm prefers forming a link with a more distant firm if the cost-reducing effects are the same. We discuss the stability and social efficiency of the collaboration networks. When link costs are small, there is no conflict between efficiency and stability of networks. When link costs are significant, there is a conflict between efficiency and stability of networks. We also examine the average distances between linked firms.     

A dynamic programming approach for batch sizing in a multi-stage production process with random yields

This paper proposes a dynamic programming approach to modeling and determining batch sizes in a single period, multi-stage production process with random yields for each stage. To improve the computational performance of the proposed approach, a statistical bound is developed. A key decision incorporated into the model is whether to continue onto the next stage of processing or to scrap the entire current batch of product. This decision is based on the expected total profit from the remaining items for processing following the removal of all defectives. The decisions involving the locations of test stations after stages are also incorporated into the modeling approach.     

The role of CD4 T cells in immune system activation and viral reproduction in a simple model for HIV infection

CD4 T cells play a fundamental role in the adaptive immune response including the stimulation of cytotoxic lymphocytes (CTLs). Human immunodeficiency virus (HIV) which infects and kills CD4 T cells causes progressive failure of the immune system. However, HIV particles are also reproduced by the infected CD4 T cells. Therefore, during HIV infection, infected and healthy CD4 T cells act in opposition to each other, reproducing virus particles and activating and stimulating cellular immune responses, respectively. In this investigation, we develop and analyze a simple system of four ordinary differential equations that accounts for these two opposing roles of CD4 T cells. The model illustrates the importance of the CTL immune response during the asymptomatic stage of HIV infection. In addition, the solution behavior exhibits the two stages of infection, asymptomatic and final AIDS stages. In the model, a weak immune response results in a short asymptomatic stage and faster development of AIDS, whereas a strong immune response illustrates the long asymptomatic stage. A model with a latent stage for infected CD4 T cells is also investigated and compared numerically with the original model. The model shows that strong stimulation of CTLs by CD4 T cells is necessary to prevent progression to the AIDS stage.     

A leader-follower model and analysis for a two-stage network of oligopolies

This paper is concerned with the existence, uniqueness and computation of leader-follower equilibrium solutions for an industry involved with two major stages of production. We assume that there exists one set of firms performing the first stage of production, which produces a semi-finished product. This semi-finished product is converted to a final good by a second set of firms performing the second stage of production. Furthermore, also competing in the final product market is a third set of firms, which are vertically integrated through the two stages of production and which are assumed to lead the second set of firms by explicitly considering the reaction or response of these latter firms to their own outputs. We model such an industry as a two-stage network of oligopolies, and define equilibrium solutions based on assumed market structures. Our analysis examines the existence and uniqueness of such equilibrium solutions, characterizes the nature of the production strategies of the various firms at an equilibrium, and prescribes algorithms to compute such solutions. This provides the machinery required to perform sensitivity analyses for studying the effects of various mergers or integrations on individual firm profits, and on the industry outputs and prices at equilibrium. The presentation is self-contained, and does not necessarily require any significant prior preparation in economic theory on the part of the reader.This paper is based on work done for the Minerals and Mining Resources Research Institute, under the sponsorship of the Bureau of Mines, Department of the Interior.