Hierarchical production planning at a multiproduct multiprocessor fibreglass manufacturing facility

Abstract

Abstract. A hierarchical production planning model is developed for a forming facility of a major fibreglass manufacturer. The model establishes aggregate quarterly quantities for families of products, monthly disaggregate production quantities for end-items within these families, and a weekly sequencing schedule of end-items. A key feature of the planning system is its ability to decompose total set-up cost into primary and secondary components and to account appropriately for each component at a distinct level of the planning hierarchy. The mathematical programming formulations, the accompanying solution algorithms, and the results of their application to nine months of actual company demand and cost data are presented.     

Cost/quality tradeoffs for control procedures in information systems

An analytical framework is presented to study the cost/benefit tradeoffs of alternative internal control scenarios designed to ensure quality of outputs from information systems. A mathematical model is used to evaluate the impact that various alternatives have on system performance and cost. The model can be used to compare the benefits gained from enhanced processing with those arising from more effective internal control procedures. Model variables under the control of system designers include placement and effectiveness of internal control procedures, cost and quality of processing activities, both manual and computerized, and cost and quality of correction procedures. The model incorporates a penalty cost incurred by failure to detect and correct errors. The analytical process is illustrated through application to a specific information system.     

The effects of learning and forgetting on the optimal lot size quantity of intermittent production runs

This paper studies the effects of learning and forgetting on the production lot size problem with infinite and finite planning horizons. It is assumed that the determination of the economic manufactured quantity (EMQ) in the succeeding production run is dependent on: (1) the maximum inventory accumulated prior to interruption; (2) the length of the interruption period which incurs total forgetting; and (3) the level of experience in equivalent units remembered at the start-up of the next production run. The optimum operating inventory doctrines is obtained by trading off procurement cost per unit time and the inventory carrying cost per unit time, so that their sum will be a minimum. A numerical example is presented to demonstrate the application of learning and forgetting to the determination of the EMQ.     

Inventory Positioning/Partitioning for Backorders Optimization for a Class of Multi-Echelon Inventory Problems*

Inventory management has undergone significant philosophical changes in recent decades such as the advent of the zero inventory concept. However, as attractive as the concept of minimal inventories may be, it is often unrealistic in application. Attention to basic features of inventory control systems such as order quantities, base stock levels, and reorder points remain crucial to ensure customer service at minimal cost. A nonlinear optimization model for determining base stock levels in a multi-echelon inventory network is presented. Lagrangian relaxation results in (1) newsboy-style relations that provide the optimal solutions, and (2) instantaneous shadow prices for the budget constraint. Sensitivity analysis of this model will facilitate making decisions concerning the desired investment in inventory for the entire system. This model may be solved on standard nonlinear programming software and is generalizable to problems in both production and distribution settings.     

Simultaneous determination of production lot size and process parameters under process deterioration and process breakdown

The purpose of this study is to combine production-inventory management with process-quality design for determining production lot size and process parameters under the possibility of process deterioration and breakdown. The total cost of such an integrated model includes: the combined setup cost (production setup and process resetting), the costs of quality loss, tolerance and mean costs for processes established, a penalty cost for process breakdown and carrying costs for cumulated inventory. The quadratic quality loss function is introduced to assess quality loss within the system. Decision variables include the initial setting (process mean) and process tolerance for process parameters determination, and production lot size for production-inventory management. The cycle time for production-inventory management is assumed to be the same as the resetting cycle for the new process-quality system. The contribution of this study lies in its development of an integrated model that enables process parameters, production lot size, and cycle time to be determined concurrently for quality and economic considerations, and at an earlier time in the process design and production management stage. An example is presented to demonstrate the proposed model.     

A goal programming approach to production planning for flexible manufacturing systems

The increased use of flexible manufacturing systems (FMS) reduces production time variability as the fixed processing time of automated systems replaces the variable processing time of human resources in production systems. This reduction in the variability permits the application of deterministic, constrained optimization models that recognize the conflicting multi-objective nature of resource utilization in an FMS environment. One such multi-objective optimization model is linear goal programming. Unlike most linear programming models, linear goal programming is designed to handle conflicting multi-objective problems. A goal programming model is developed a and presented in this paper as an aid in FMS planning. An application is also presented to illustrate the informational benefits of using the proposed model.     

The effects of the warranty cost on the imperfect EMQ model with general discrete shift distribution

In this paper, we investigate the effect of the warranty cost on optimization of the economic manufacturing quality (EMQ). This is done for a deteriorating process where the production process shifts from the in-control state to the out-of-control state following a general discrete probability distribution. Once the production process goes out of control, the production process produces some defective items. The defective item cost includes reworking and warranty costs. Thus, in order to economically operate a production-inventory system with products sold under warranty, the tradeoffs among the production setup, inventory, and defective item cost, including the reworked cost before sale and the warranty cost after sale, needed to be analysed. This objective in this paper is to determine the production lot size while minimizing the total cost per unit of time per unit of time. Various special cases are presented. Two of them are extensions of results obtained previously in the literature. Finally, a numerical example is given which uses a discrete Weibull probability distribution. Sensitivity analysis of the model with respect to cost and time parameters is also performed.     

A multistage approach for production and workforce planning in long-cycle product environments

Aggregate production planning (APP) has been studied extensively for the past two decades. The APP problem, also called production and workforce scheduling, is to determine the optimal workforce and production level in each period of the planning horizon in order to satisfy demand forecasts for these periods. The advantages of the APP are low cost of data collection and computational cost of the running model; the accuracy of data; and, effective managerial understanding of the results. If the product of concern takes longer than one period, it is called a long-cycle product. Examples of long-cycle products are aircraft, ships, buildings and special machines. A detailed model incorporating dynamic productivity and long-cycle products considerations is presented to solve the problem of production and workforce planning. Using a multistage production system approach, a search technique is developed to solve this class of problems where the objective function is linear and some of the constraint coefficients are dynamically nonlinear. The model provides a better solution than an aggregate production planning model, often used to solve these problems.     

A note on an economic production quantity model and just-in-time production

In this paper an economic production quantity (EPQ) model in which the production rate is variable is studied. An analysis is presented of the impact of a variable production rate on the optimal production quantity and the total relevant cost. It is observed that this EPQ production and inventory system, in which the production rate is close to the demand rate, possesses many characteristics that are similar to a just-in-time (JIT) production system. It is shown that the normal prerequisites and benefits of JIT production can be identified from an analysis of such an EPQ system.     

Integrated production strategy and reuse scenario: A CoFAQ model and case study of mail server system development

One of the core problems in software product family (SPF) is the coordination of product building and core asset development, specifically the integration of production strategy decision and core asset scenario selection. In the current paper, a model of Cost Optimization under Functional And Quality (CoFAQ) goal satisfaction constraints is developed. It provides a systematic mechanism for management to analyze all possible products and evaluate various reuse alternatives at the organizational level. The CoFAQ model facilitates decision-makers to optimize the SPF development process by determining which products are involved in the SPF (i.e. production strategy) and which reuse scenario for each module should be selected to implement the SPF toward minimum total developing cost under the constraints of satisfying functional and quality goals. A two-phase algorithm with heuristic (TPA) is developed to solve the model efficiently. Based on the TPA, the CoFAQ is reduced to a weighted set-covering problem for production strategy decision and a knapsack problem for the reuse scenario selection. An application of the model in mail server domain development is presented to illustrate how it has been used in practice.     

Materials receiving capacity and inventory management

This paper analyses the optimal level of materials receiving capacity for a manufacturer that receives deliveries from many suppliers. Inventory levels and inventory carrying costs depend on the frequency of deliveries and thus, on the materials receiving capacity. An analytic model that captures the tradeoff between inventory costs and materials receiving costs is presented and discussed. The receiving cost is modeled as increasing in discrete jumps of varying sizes whenever materials receiving resources are added. Practical issues in implementing the model are highlighted and methods to reduce the marginal materials receiving cost are discussed. The paper also discusses connections to the JIT approach for production environments where materials receiving is heavily automated.     

SIMULTANEOUS BATCHING AND SCHEDULING FOR CHEMICAL PROCESSING WITH EARLINESS AND TARDINESS PENALTIES

We consider the problem of determining the allocation of demand from different customer orders to production batches and the schedule of resulting batches to minimize the total weighted earliness and tardiness penalties in context of batch chemical processing. The problem is formulated as a mixed-integer nonlinear programming model. An iterative heuristic procedure that makes use of the network nature of the problem formulation is presented to approximate an optimal solution. An algorithm polynomial in the number of batches to produce is also presented that optimally solves the problem under special cost structures.     

THE USE OF FORECAST ERROR MEASURES AS SURROGATES FOR AN ERROR COST CRITERION IN THE PRODUCTION SMOOTHING PROBLEM

This paper presents research on the problem of selecting a proper surrogate for a forecast error cost criterion in the production smoothing problem. Various forecast models estimated future selected demand process values. Resultant error costs were computed and the coincidence of the selection of a forecast model on the basis of least error cost and the various error measures was noted. The error measures used were the mean absolute deviation, average algebraic error(bias), and the mean squared error. Computations necessary to develop the mathematical form of the error cost criterion are presented in an Appendix. Also presented are the penalty costs of using an error measure as a surrogate for an error cost criterion.     

A possibilistic aggregate production planning model for brass casting industry

This article discusses a possibilistic aggregate production planning (APP) model for blending problem in a brass factory; the problem computing optimal amounts of raw materials for the total production of several types of brass in a planning period. The model basically has a multi-blend model formulation in which demand quantities, percentages of the ingredient in some raw materials, cost coefficients, minimum and maximum procurement amounts are all imprecise and have triangular possibility distributions. A mathematical model and a solution algorithm are proposed for solving this model. In the proposed model, the Lai and Hwang's fuzzy ranking concept is relaxed by using ‘Either-or’ constraints. An application of the brass casting APP model to a brass factory demonstrates that the proposed model successfully solves the multi-blend problem for brass casting and determines the optimal raw material purchasing policies.     

A new EPQ model: integrating lower pricing,rework and reject situations

The economic production quantity (EPQ) is a well-known and commonly used inventory control technique. It has been used for well over 50 years to optimize lot sizes in transportation/production. The standard results are easy to apply but are based on a number of assumptions. A common assumption in the EPQ model is that all units produced are of perfect quality, this will underestimate the actual required quantity. Many researchers have studied the effects after relaxing this assumption on the EPQ model. The previous studies had considered that imperfect quality and defective items are either to be reworked instantaneously and kept in stock or rejected at a cost. The objective of this paper is to provide a framework to integrate lower pricing, rework and reject situations into a single EPQ model. A 100% inspection is performed in order to identify the amount of good quality items, imperfect quality items and defective items in each lot. This model assumes that items of imperfect quality, not necessarily defective, could be used in another production situation or sold to a particular purchaser at a lower price. The electronic and clothing industries give good examples for such situations. A mathematical model is developed and a numerical example is presented to illustrate the solution procedures. It is found that the time factor of when to sell the imperfect items is critical, as this decision will affect the inventory cost and the batch quantities.     

Process Mean Determination with Quantity Discounts in Raw Material Cost*

Setting the mean (target value) for a container-filling process is an important decision for a producer when the material cost is a significant portion of the production cost. Because the process mean determines the process conforming rate, it affects other production decisions, including, in particular, the production setup and raw material procurement policies. In this paper, we consider the situation in which quantity discounts exist in the raw material acquisition cost, and incorporate the quantity-discount issue into an existing model that was developed for simultaneously determining the process mean, production setup, and raw material procurement policies for a container-filling process. The product of interest is assumed to have a lower specification limit, and the items that do not conform to the specification limit are scrapped with no salvage value. The production cost of an item is proportional to the amount of the raw material used in producing the item. A two-echelon model is formulated for a single-product production process, and an algorithm is developed for finding the optimal solution. A sensitivity analysis is performed to study the effects of the model parameters on the optimal solution.     

基于分布式工厂的供应链二级分销网络生产计划优化模型

从供应链的集成和协作角度出发,提出了在多工厂、多分销商条件下二级分销网络生产计划制定的双层规划模型,模型考虑了二级网络中制造商和分销商之间的信息共享,从而降低了整个链上的费用。同时设计了启发式求解算法,并给出了一个数值例子。     

A robust optimization model for stochastic aggregate production planning

The aggregate production planning (APP) problem considers the medium-term production loading plans subject to certain restrictions such as production capacity and workforce level. It is not uncommon for management to often encounter uncertainty and noisy data, in which the variables or parameters are stochastic. In this paper, a robust optimization model is developed to solve the aggregate production planning problems in an environment of uncertainty in which the production cost, labour cost, inventory cost, and hiring and layoff cost are minimized. By adjusting penalty parameters, decision-makers can determine an optimal medium-term production strategy including production loading plan and workforce level while considering different economic growth scenarios. Numerical results demonstrate the robustness and effectiveness of the proposed model. The proposed model is realistic for dealing with uncertain economic conditions. The analysis of the tradeoff between solution robustness and model robustness is also presented.     

需求和零售商购买成本同时扰动的供应链应急协调

供应链的契约协调机制是供应链管理的重要内容,突发事件下的供应链协调机制是近年来的研究热点。 研究了在单制造商单零售商组成的供应链中,假设生产成本是其生产数量的凸函数下,当市场需求为零售价格的非线性函数,突发事件造成需求和零售商购买成本同时发生扰动时,集权、分权供应链应对突发事件的最优策略。 首先证明了稳定环境下的数量折扣契约可以实现该供应链的协调,在集权式决策下,供应链的原有生产计划对突发事件具有一定的鲁棒性,但是当突发事件造成的扰动超过一定幅度时,供应链的协调将会被打破,供应链系统必须改变生产计划才能实现其利润最大化。 在分权式决策下,供应链的原数量折扣契约不能使扰动后的供应链达到协调,因此,设计了新的数量折扣契约来使扰动后的供应链达到协调。最后给出一个算例验证了相关结论。     

An optimal set-up policy for control charts

A model of a production process, using an unscheduled set-up policy and utilizing fraction-defective control charts to control current production is developed taking into consideration all the costs; namely cost of sampling, cost of not detecting a change in the process, cost of a false indication of change, and the cost of re-adjusting detected changes. The model is based on the concept of the expected time between detection of changes calling for set-ups. It is shown that the combination of unscheduled set-ups and control charts can be utilized in an optimal way if those combinations of sample size, sampling interval and extent of control limits from process average will be used that provide the minimum expected total cost per unit of time. The costs when a production process with unscheduled set-up is controlled by using the appropriate optimal control charts is compared to the cost of a production process using scheduled set-ups at optimum intervals in conjunction with its appropriate control charts. This comparison indicates the criteria for selecting production processes with scheduled set-ups using optimal set-up intervals over unscheduled set-ups. Suggestions are made to evaluate the optimal process set-up strategy and the accompanying decision parameters, for any specific cost data, by use of computer enumeration.