Production planning with uncertain demands

Hierarchical model for production planning in the case of uncertain demand

In this paper, we are interested in a production planning process in collaborative supply chains. More precisely, we consider supply chains, where actors use Manufacturing Resource Planning process (MRPII). Moreover, these actors collaborate by sharing procurement plans.We focus on a supplier, who applies the Periodic Order Quantity (POQ) rule to plan a production integrating the uncertain procurement plan sent by her/his customer. The uncertainty of the procurement plan is expressed by closed intervals on the cumulative demands. In order to choose a robust production plan, under the interval uncertainty representation, the min-max criterion is applied. We propose algorithms for determining the set of possible costs of a given production plan - due to the uncertainty on the cumulative demands.We then construct algorithms for computing a robust production plan with respect to the min-max criterion: the algorithm based on iterative adding constraints and the polynomial algorithms under certain realistic assumptions.

Robust production planning and capacity control for flexible assembly lines

The aim of the paper is to develop an optimization model to support the analysis of decision-making on Macedonian family farms. For this purpose, normative linear programming paradigm is applied, utilising its optimization potential. The model is tested and presented on vegetable farm level. Hence, the model provides optimal vegetable productions plan, taking into consideration relevant technological and resource limitations faced by the farm. The results are given in base scenario format and are compared with the optimum production plans within the alternative model scenarios. The optimal production structure in all scenarios indicates that the optimal solution is given on production of tomato, pepper, cabbage, carrot and bean, thus corresponding to the most frequent types of vegetables in the Macedonian agriculture. The optimal production plan also confirms the diversification as a characteristic of the Macedonian agriculture. The base scenario reveals a total net return over the variable costs of 17,924 € which is highest compared to other scenarios. The working capital available is a binding constraint in second and third scenario, where the optimal solution reveals that the land resource is not exhausted i.e. an arable land of about 3 ha remains. Furthermore, the analysis of the crop rotation reflects the seasonal character of the vegetable production. Gross margin sensitivity was examined using the working capital parameterisation. The model is quite flexible thus enabling different crop enterprises to be added additionally.

Production planning in the case of uncertain individual demand Extension for an MRP II concept

A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

The market demands and financial constraints in medium- to long-term production planning are often subject to uncertainties. As an extension of the author's previous paper, this paper focuses on a formulation and simulation analysis for multi-product aggregate production-planning problems with fuzzy demands and fuzzy capacities. The fuzzy production–inventory balance equation is formulated as a soft equation and can be interpreted as the possibility level of meeting the market demands, which is more meaningful and accepted by the practitioner than the previous one. With this interpretation, a fuzzy multi-product aggregate production-planning model is transformed into a parametric programming model. A simulation of a practical instance is conducted to illustrate the model and demonstrate the performance and effect of various parameters on the optimal aggregate production plan. The proposed formulation and simulation analysis can help the decision-maker make a reasonable and preferred aggregate plan to guarantee feasibility of the downstream family disaggregation plans.

A mathematical programming approach to optimize process plant performance subject to equipment failure is presented. The optimal production planning and scheduling in multipurpose process plants involves the efficient utilization of assets and resources to produce a number of products so as to satisfy market demands while optimizing a performance criterion. However, the degree of utilization of process plant components, within the time horizon of operation, critically depends on the level of equipment availability. The interactions between production and maintenance planning as well as the necessary links to quantify the strong interactions between them are studied. The preventive maintenance planning and crew allocation problem are used to demonstrate the effectiveness of the proposed approach. The overall problem is first formulated as an optimal control problem by integrating an aggregate production planning model with a continuous time Markov chain maintenance model. The resulting problem is then transformed into a mixed-integer linear programming model by using an Euler discretization scheme and appropriate linearizations of bilinear terms. Finally, extensions to include design aspects are also discussed. The applicability of the proposed approach is demonstrated by a number of illustrative examples.

This paper uses a mixed integer programming model to study a production and inventory planning problem faced by a manufacturer who utilizes Inventory-Based Financing (IBF) to capture additional demands during peak seasons that otherwise will not be met due to a shortage of working capital. By exploiting the problem's inherent structure of three distinct but related manufacturer decisions, i.e., the production, financing and working capital allocation decisions, the paper develops a branch-and-bound procedure to solve the model which is shown to be NP-hard. Through a series of numerical experiments, our study provides a number of interesting managerial insights into how the manufacturer's optimal production and inventory plans could differ with and without IBF. Specifically, we find that (a) the manufacturer would strategically overstock his inventory for the purpose of securing more loans, and this overstocking behavior is more acute in periods immediately prior to the peak demand period; and (b) the manufacturer could take advantage of the difference in peak and non-peak seasons of product demands by partially financing the production of one product through pledging the cycle inventory of another product.

The processes of optimization of the production plan according to certain criteria by modeling were investigated. Achieving effective results directly depends on the optimal production plan. The most important thing in determining the optimal production plan is the choice of modeling criteria. For the most part, the quality of decisions is characterized not by one but by many incomparable criteria. Therefore, it is necessary to make decisions based not on one but on many criteria. This so-called multi-objective optimization problem. For solving such problems is widely used mathematical methods. Mathematical approach can be used to solve problems in any particular activity as mathematics abstracted from specific features characteristic of a particular solution. Therefore, from the point of view of mathematics, the optimal result can be obtained with various established criteria, but from the economic point of view it is important to choose the ones that are of decisive importance. That is, their weight is important for the consumer when making a purchase decision, and for the manufacturer – in terms of production capabilities of certain types and results (production efficiency). The basis of the operation of any enterprise is a production program (production and sales plan). The main task of the production plan is to meet the needs of consumers in high-quality products, which are produced with the best use of resources, on the one hand, and the enterprise to get the maximum profit, on the other. With this in mind, a two-criteria optimization model that allows to make a production plan was proposed. The plan ensures that products are produced with the best use of available resources and at the same time ensures maximum quality of manufactured products and maximum profit from sales of these products. The solution of the problem with two objective functions and linear constraints is achieved by step-by-step solution of the proposed mathematical model of optimization of the production plan using the method of sequential restrictions. The simplex method was also used. An example shows an algorithm for solving the optimization problem.

Demand forecasting is essential for businesses, particularly in the fashion industry, because it predicts future demand for clothing and accessories, thereby aiding in informed production decisions. However, the continuous increase in inventory stock outages, inaccurate forecasting, and inefficient supply chain coordination in the Nigerian fashion industry offers a valid opportunity for empirical investigation. This study examines the effect of the weighted moving average (WMA) demand forecasting on production planning and resource optimization in the fashion industry. A cross-sectional survey of 105 fashion industry professionals was conducted. Data collected through the structured questionnaire were analyzed using partial least squares structural equation modeling (PLS-SEM). The study found that accurate demand forecasting using the WMA positively impacts resource optimization and production planning. Effective resource optimization measures significantly enhance production outcomes. Emphasizing adaptive forecasting methods and dynamic resource management capabilities strengthens the relationship between demand forecasting and production planning. The findings provide valuable insights for fashion industry operation managers to improve demand forecasting practices and resource management, leading to better production planning and enhanced operational efficiency.

Increasing productivity of palm oil company could be done by solving problems in the company such as non-optimal production quantity, over range of production cost, stagnation of production activity, and unplanned of production condition. Those problems can be solved by managing production planning. The purpose of this research is to focus on production planning by determining the optimal production planning, determining the best production condition, and determining criticality of crude palm oil components process. Determination of optimal production planning using goal programming shows five goals formulation: minimize the production cost of crude palm oil (CPO) and fresh fruit bunch (FFB), minimize the deficiency of FFB, maximize production to fulfil demand capacity and maximize the number of FFB processed into CPO. The result of scenario simulation shows that by increasing the productivity of palm oil plantation (11-12%), increasing the yield of CPO (0.21-0.23%), decreasing the effect of maturity rate of FFB (2.5%), and fulfill the requirement of number of truck could decrease free fatty acids by 2.43% and increase number of production by 8408247 in January 2020. The result of the analysis of the assessment of critical components of the palm oil production process results in four classifications. The four classifications of equipment criticality rating (ECR) respectively, ECR 1 at station of boiler, thrasher, and digester, ECR 2 at station of sterilizer, ECR 3 at station of clarification and engine room, and ECR 4 at receiving station, fat pit, and water treatment.

Production planning is a tactical scheme in the supply chain management of product that aims to provide optimal solutions based on the inventory stock of the company in terms of fulfilling the production demand. The variable of demand, supply, and production amount is used in this research as an input to determine the production by the implementation of Fuzzy-Mamdani Logic (FML). This research aims to obtain the optimal production and supply planning for several periods, which later comparing the total cost through the Fuzzy-Mamdani Logic implementation with the method used by the company. The objects for this research are the 7’ and 10’ big-corrugation types of zinc sheets manufactured by PT Y, which is the highest demand product of the company. The result shows that the implementation of FML outlined as an appropriate solution for the decision making to determine the production amount. The amount production itself for the 7’ and 10’ big-corrugation type of zinc sheets during June 2017 - May 2018 were 663,700 and 640,400 quantities for each model, while production in June 2017 was only 18,100 and 32,800 quantities.

In this paper, we propose a decomposition procedure for constructing robust optimal production plans for reverse inventory systems. Our method is motivated by the need of overcoming the excessive computational time requirements, as well as the inaccuracies caused by imprecise representations of problem parameters. The method is based on a min-max formulation that avoids the excessive conservatism of the dualization technique employed by Wei et al. (2011). We perform a computational study using our decomposition framework on several classes of computer generated test instances and we report our experience. Bienstock and Ozbay (2008) computed optimal base stock levels for the traditional lot sizing problem when the production cost is linear and we extend this work here by considering return inventories and setup costs for production. We use the approach of Bertsimas and Sim (2004) to model the uncertainties in the input.

Agricultural production and farm management are inextricable, since managerial aspects for safe and of high-quality food products have led to the development of successful production plans but multifaceted controversies as well. These controversies arise from the focus of policymakers, especially in the EU, to the environmental aspects of agricultural production, creating conflicting objectives for farmers. Energy from biomass derivatives could play a significant role in the dispute for economic and environmental sustainability in agriculture, along with the formulation of agro-energy districts. In this context, an MCDM model was developed integrating LCA data for the assessment of economic, environmental and energy sustainability regarding thirteen major crops in the Region of Central Macedonia in Greece. The model's objectives consist of maximization of farmers' gross income, minimization of emissions coming from farming practices and maximization of energy potentially coming from biomass. Furthermore, three different scenario-based directions allocate different weights to the respective objectives, creating different managerial strategies. The optimal production plan was the scenario in which the weights were allocated by goal programming. The optimal plan proposes the cultivation expansion of energy crops, tree crops, alfalfa and hard wheat to a higher degree. Moreover, a significant reduction to the cultivated areas of tobacco, rice, barley and soft wheat could lead to a potentially viable production plan.