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.     

Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives

Aggregate production planning (APP) addresses matching supply to forecast demand, with varying customer orders over the intermediate planning horizon. In real-world APP problems, input data and related parameters are commonly imprecise because information is incomplete or unavailable, and the decision maker (DM) must simultaneously consider conflicting objectives. This study develops an interactive possibilistic linear programming (i-PLP) approach to solve multi-product and multi-time period APP problems with multiple imprecise objectives and cost coefficients by triangular possibility distributions in uncertain environments. The imprecise multi-objective APP model designed here seeks to minimise total production costs and changes in work-force level with reference to imprecise demand, cost coefficients, available resources and capacity. Additionally, the proposed i-PLP approach provides a systematic framework that helps the decision-making process to solve fuzzy multi-objective APP problems, enabling a DM to interactively modify the imprecise data and parameters until a set of satisfactory solutions is derived. An industrial case demonstrates the feasibility of applying the proposed approach to a practical multi-objective APP problem.     

Multi-site aggregate production planning with multiple objectives: A goal programming approach

This paper addresses the problem of aggregate production planning (APP) for a multinational lingerie company in Hong Kong. The multi-site production planning problem considers the production loading plans among manufacturing factories subject to certain restrictions, such as production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers' preferences, as well as production capacity, workforce level, storage space and resource conditions of the factories. In this paper, a multi-objective model is developed to solve the production planning problems, in which the profit is maximized but production penalties resulting from going over/under quotas and the change in workforce level are minimized. To enhance the practical implications of the proposed model, different managerial production loading plans are evaluated according to changes in future policy and situation. Numerical results demonstrate the robustness and effectiveness of the developed model.     

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.     

Aggregate production planning with workforce transferring plan for multiple product types

This paper presents the aggregate production planning for multiple product types where the worker resource can be transferred among the production lines. A mathematical model was formulated in spreadsheet format. Then the spreadsheet-solver technique was used as a tool to solve the model. A real situation of a manufacturing company was selected as a case study. The actual data was used to test and validate the proposed model. The optimal aggregate production plan provides the information on managing the available production capacity together with the useful workforce transferring plan. The obtained solutions were compared to those of another approach where the workers cannot be transferred among the production lines. The total cost is significantly reduced when the workers are allowed to transfer among the production lines.     

A disaggregation problem for a multiplant,multiproduct scheduling application

Abstract

This paper discusses an integer programming technique for planning production when there are multiple plants involved in the production of a number of products and the plants are relatively close. This allows for the closing of one plant during a planning period with a shift of the mobile resources, mainly labour, to other plants. The model is introduced and then an example problem is given. Finally, there is a discussion of why this method improves upon other techniques proposed to solve this problem. Some actual case studies are cited.     

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.     

A stochastic programming model for production planning of perishable products with postponement

This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilise the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilisation of resources. The impact of unit shortage cost under different probability distribution of economic scenarios on the total cost is analyzed. Comparative analysis of solutions with and without postponement strategies is also performed.     

Concurrent consideration of product design,process planning and production planning activities

In manufacturing engineering, product design, process planning and production planning activities are often considered independently. However, in order to effectively respond to changes in business situations, such as changes in demand forecast, product mix and technology, it is desirable to consider them concurrently. For this purpose, a large-scale linear programming model has been developed. The model considers minimization of the sum of processing cost, late shipment cost and inventory holding cost as the objective, and concurrently selects product designs, and generates process plans and production plans. The number of columns in the formulation can be large and, hence, an efficient column generation scheme is developed to solve the model. The model and solution procedure are illustrated with examples.     

Inventory Control and Scheduling of Multiple Products in a Common Facility*

Consider a set of chemical products to be produced in a single facility. Each product has its own unique reaction time (which is assumed to be independent of its batch size), as well as other cost and demand values. In this paper, we address the problem of determining the optimal number of batches, batch sizes, and an accompanying production schedule for these products in the single facility that will minimize the total cost. Two different algorithms have been developed for this problem, the performances of which are contrasted with classical cyclic production schedules. Finally, some guidelines for the application of these methods to real-life problems are outlined.     

Cloud manufacturing system for sheet metal processing

Abstract

Cloud computing is changing the way industries and enterprises run their businesses. Cloud manufacturing is emerging as an approach to transform the traditional manufacturing business model, while helping the manufacturer to align production efficiency with its business strategy, and creating intelligent factory networks that enable collaboration across the whole enterprise. Many production planning and control (PPC) problems are essentially optimisation problems, where the objective is to develop a plan that meets the demand at minimum cost or maximum profit. Because the underlying optimisation problem will vary in the different business and operation phases, it is important to think about optimisation in a dynamic mechanism and in a number of interlinked sub-problems at the same time. Cloud manufacturing has the potential to offer decision support as a service and medium of communication in PPC. To solve these problems and produce collaboration across the supply chain, this paper provides an overview of the state of the art in cloud manufacturing and presents a model of cloud-based production planning and production system for sheet metal processing.     

Linear programming and financial cost models for industrial enterprises

Linear programming models of complex interrelated manufacturing enterprises have improved production planning decisions. With a linear programming formulation, the planning engineer concerned with specifying levels of production activity need not be concerned with cost accounting formulations of product costs to make his production decisions. He is only concerned with examining alternative production activities in terms of the added production costs the activity incurs, and the amount of product that is fed or consumed. The financial analyst, however, is concerned with development of budgetted average product costs. He must roll the costs of feed and intermediate products down to the final stage products. This paper bridges these two interests by demonstrating a methodology for the direct translation of the solution of the linear programming model to the development of rolled product standard costs.     

Tactical production and distribution planning with dependency issues on the production process

Tactical production-distribution planning models have attracted a great deal of attention in the past decades. In these models, production and distribution decisions are considered simultaneously such that the combined plans are more advantageous than the plans resolved in a hierarchical planning process. We consider a two-stage production process, where in the first stage raw materials are transformed into continuous resources that feed the discrete production of end products in the second stage. Moreover, the setup times and costs of resources depend on the sequence in which they are processed in the first stage. The minimum scheduling unit is the product family which consists of products sharing common resources and manufacturing processes. Based on different mathematical modelling approaches to the production in the first stage, we develop a sequence-oriented formulation and a product-oriented formulation, and propose decomposition-based heuristics to solve this problem efficiently. By considering these dependencies arising in practical production processes, our model can be applied to various industrial cases, such as the beverage industry or the steel industry. Computation tests on instances from an industrial application are provided at the end of the paper.     

An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming

In this paper, we present an aggregate production planning (APP) model applied to a Portuguese firm that produces construction materials. A multiple criteria mixed integer linear programming (MCMILP) model is developed with the following performance criteria: (1) maximize profit, (2) minimize late orders, and (3) minimize work force level changes. It includes certain operational features such as partial inflexibility of the work force, legal restrictions on workload, work force size (workers to be hired and downsized), workers in training, and production and inventory capacity. The purpose is to determine the number of workers for each worker type, the number of overtime hours, the inventory level for each product category, and the level of subcontracting in order to meet the forecasted demand for a planning period of 12 months. Additionally, a decision support system (DSS) based on the MCMILP model is proposed. It will help practitioners find the “best” solution for an APP problem without having to familiarize themselves with the mathematical complexities associated with the model. An example to illustrate the use of the DSS is also included.     

Notes and Communications REPLANNING FREQUENCIES FOR MASTER PRODUCTION SCHEDULES

Updating production plans typically is achieved by rolling the planning horizon forward one period at a time, each time including the latest information in order to determine the best course of action to pursue in the present period. Theoretical planning-horizon studies have identified the conditions by which the production decisions in the current and some specified number of future periods remain optimal given some set of future demands. Motivated by these findings, this study addresses the replanning frequency in a hierarchical production planning problem where no planning-horizon theorems are available. In this problem the aggregate production plan and the master production schedule are linked by a rolling-horizon practice. Empirical experimentation indicates that under certain cost and demand conditions the master production schedule need not be updated every period. If a schedule does not need to be updated for several periods, the schedule for these periods can be frozen to provide stability for planning components at lower levels in the bill of material of the products. The results of this study thus provide some reference for the determination of the frozen portion of the master production schedule.     

Decision support for multi-family aggregate production planning

Aggregate production planning decisions are inter mediate range decisions that can have a significant impact on both productivity and profitability. In this paper, we examine an interactive computer-based method that provides decision support for the aggregate planner. The proposed approach combines the judgement of the planner with the optimization of subproblems to arrive at an effective solution for multi-family aggregate production planning problems. In the interactive approach, the planner exercises direct control over sensitive workforce levels and production capacities. A network flow sub-problem solver is used to generate optimal production plans and inventory levels given the user-specified production capacities. Decision aids are provided to help the planner achieve a cost-effective solution that is consistent with judgement concerning workforce levels. Computational testing on five test problems indicates that very cost-effective solutions can be obtained. The results of applying the interactive method to a real-world problem are also reported.     

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.     

Product sequencing in multiple-piece-flow assembly lines

Modern markets demand mass customization, that is, the manufacture of customized products at low cost. Mass customization represents a major challenge for the organization of assembly lines, which were originally designed for the manufacture of homogeneous products. The multiple-piece-flow assembly line is an organizational innovation that can address this challenge. Here, several customized workpieces, each associated with a separate customer order and, hence, a separate due date, are handled simultaneously in one cycle. Consequently, the idle times decrease as do the manufacturing costs. Multiple-piece-flow assembly lines are used, for instance, in manufacturing industrial equipment.To the best of our knowledge, this paper is the first to investigate product sequencing in multiple-piece-flow assembly lines. We formalize the underlying planning problem, establish a mixed-integer model, examine its relation to several classic optimization problems, and describe useful problem properties. We leverage these properties to design an effective iterative variable neighborhood heuristic (IVNH). A detailed simulation based on real-world data and the rolling-horizon planning framework confirms that the IVNH is well suited for practical use. Furthermore, extensive computational experiments on well-structured randomly generated data sets show that the IVNH identifies optimal or near-optimal solutions within short run times. It outperformed an off-the-shelf optimization software, and in certain practice settings, the IVNH was even able to substantially reduce average order delays.     

Simultaneous production and logistics operations planning in semicontinuous food industries

The production and logistics operations planning in real-life single- or multi-site semicontinuous food industries is addressed in this work. A discrete/continuous-time mixed integer programming model, based on the definition of families of products, is developed for the problem in question. A remarkable feature of the proposed approach is that in the production planning problem timing and sequencing decisions are taken for product families rather than for products. However, material balances are realized for every specific product, thus permitting the detailed optimization of production, inventory, and transportation costs. Changeovers are also explicitly taken into account and optimized. Moreover, alternative transportation modes are considered for the delivery of final products from production sites to distribution centers. The efficiency and the applicability of the proposed approach is demonstrated by solving to optimality two industrial-size case studies, for an emerging real-life Greek dairy industry.     

Coordinating pricing and production decisions for multiple products

We consider a dynamic problem of joint pricing and production decisions for a profit-maximizing firm that produces multiple products. We model the problem as a mixed integer nonlinear program, incorporating capacity constraints, setup costs, and dynamic demand. We assume demand functions to be convex, continuous, differentiable, and strictly decreasing in price. We present a solution approach which is more general than previous approaches that require the assumption of a specific demand function. Using real-world data from a manufacturer, we study problem instances for different demand scenarios and capacities and solve for optimal prices and production plans. We present analytical results that provide managerial insights on how the optimal prices change for different production plans and capacities. We extend some of the earlier works that consider single product problems to the case of multiple products and time variant production capacities. We also benchmark performance of proposed algorithm with a commercial solver and show that it outperforms the solver both in terms of solution quality and computational times.