Aggregate planning problems and solutions pdf backorders

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aggregate planning

Performed the experiments: OS. Analyzed the data: OS MT. Wrote the paper: OS MT. All data is supplied in S1 and S2 Tables. The optimization model and the implementation of the epsilon-constraint algorithm used in this the study is supplied in GAMS format as S1 Model.

Supply chain management that considers the flow of raw materials, products and information has become a focal issue in modern manufacturing and service systems. Supply chain management requires effective use of assets and information that has far reaching implications beyond satisfaction of customer demand, flow of goods, services or capital.

Aggregate planning, a fundamental decision model in supply chain management, refers to the determination of production, inventory, capacity and labor usage levels in the medium term. Traditionally standard mathematical programming formulation is used to devise the aggregate plan so as to minimize the total cost of operations.

However, this formulation is purely an economic model that does not include sustainability considerations. In this study, we revise the standard aggregate planning formulation to account for additional environmental and social criteria to incorporate triple bottom line consideration of sustainability. We show how these additional criteria can be appended to traditional cost accounting in order to address sustainability in aggregate planning. We analyze the revised models and interpret the results on a case study from real life that would be insightful for decision makers.

Supply chain management has become one of the most important core functions of companies in manufacturing and service sectors. Supply chain management considers all of the stages from raw material procurement to consumption by the end users in fulfilling the demand for a certain product or service.

In the simplest terms, whenever there is a demand either for a product or a service and supply to fulfill this demand, a supply chain emerges. Material and information flow both up and down the supply chain. In particular, a supply process receives certain inputs that are then turned into desired outputs via a transformational process to satisfy the demand. Therefore, any activity in fulfilling the demand is in the scope of the supply chain system under consideration. Any business entity either being a manufacturing or a service business has an underlying supply chain system and in the core of this system is what is called the production or operations function of the business.

Production and operations functions focus on the flow of information, and material between stages of the supply chain. Complexity of supply chains shows significant varieties depending on its structure, products and services provided by companies. For example, Apple Corp. Then, in the Pre-Launch stage involves mainly building up inventories for the products in accordance with the expected demand.

The launch stage involves forecasting the demand for the next two quarters and resolving backlog problems. The quarterly reviews focuses on managing inventory levels, adjusting demand forecast and monitoring sales, demand and product life cycle. The last three stages that include Pre-Launch, Launch and quarterly review is considered as part of the Aggregate Planning activity. The supply chain management problems deal with long-term, medium-term and short-term decision.

The medium-term decisions affect the system performance between 3—9 months and generally include the capacity utilization, workforce management and inventory management decisions. In general, these decisions are considered simultaneously in aggregate planning problem [ 2 ].

The aggregate planning problem sets production capacities, labor utilization, inventory profiles, backordering in the case of not being able to satisfy the demand on time, and subcontracting. Therefore, the aggregate planning problem is a key instrument in applying the strategic level decisions while determining the principles of operational level problems.

In addition, the aggregate planning problem encompasses economic, environmental and social factors. In managing the supply chains, integrating sustainability in the decision-making process had become one of the focal subjects due to increasing awareness from the customers who use the products supplied by companies. In this paper, we propose a methodological approach to incorporate sustainability considerations in the aggregate planning problem of supply chain management and illustrate our approach on household refrigerator industry in Turkey.

Sustainability is used either as the ability to sustain a practice or process or to refer to environmental consciousness in the literature and most non-academic resources. Both comprehensions are valid but incomplete. The traditional method for posing the aggregate planning problem is based on a purely economic model. To address the sustainability in supply chain management, the decision maker should incorporate these three pillars of sustainability simultaneously into the decision-making process.

The application of the triple bottom line accounting on economic order quantity EOQ was shown to provide very useful insights [ 5 ]. It was shown that inclusion of environmental and social factors in addition to economic considerations allows the decision makers to assess their decisions from sustainability perspective.

In this paper, a methodological approach to incorporate sustainability considerations in the aggregate planning problem is presented. The standard model is extended to according to additional environmental and social criteria. The revised models are then analyzed to drive insights into the aggregate planning problem from sustainability perspective.

The analysis shows how environmental and social criteria can be appended to traditional cost accounting in order to address sustainability in supply chain management with the aggregate planning problem. The literature on sustainability of supply chains focus on reviews and also a number ideas to incorporate sustainability. However, most of the existing literature considers only economic and environmental aspects of sustainability.

Beamon [ 6 ] and Handfield et al. These papers consider sustainability from environmental perspective only. They analyze the impact of environmental policies on the supply chains.

They show that environmental policies must be considered in the decision-making framework in order to have greener supply chains. Toptal et al. An important consideration is the cap-and-trade policy that allows trading of carbon emissions through a system such as EU Emissions Trading System. The firms have two options: they either buy or sell carbon allowances at a specified market price or they pay their carbon emissions costs as taxes.

Boulanger and Breechet [ 9 ] survey the genetic methods that can be used by the policy-makers in assessing the sustainability performance of their policies. They also discuss the appropriateness of these methods using sector-based applications and conclude that the multi-agent simulation models are best suited with decision-making for sustainability.

Turkay [ 10 ] reviews methods for environmentally conscious supply chain management and categorizes them as product centric closed-loop supply chains , production system centric environmentally conscious production and transportation system centric sustainable transportation approaches. Under environmentally conscious production, supply chain systems with environmental extensions are studied.

Carter [ 11 ] deals with purchasing social responsibility PSR as an application of corporate social responsibility CSR to supply chains. Carter and Jennings [ 12 ] analyze the effect of social responsibility projects on supply chain performance and conclude that these projects enhance the supply chain performance. The main message in [ 11 ] and [ 12 ] is the necessity to include social factors in the models in order to achieve sustainability along with the environmental factors.

It is clear from the literature that inclusion of social factors in the aggregate planning of sustainable supply chains has not attracted attention and we aim to fill this gap in this paper.

The standard aggregate planning problem aims to determine the production levels, inventory kept in the supply chain, hiring and firing employees, overtime production, backorders and demand satisfaction levels with the objective of having the minimum cost or maximum profit.

It is the most widely solved supply chain management problem. In this paper, the standard aggregate planning model is extended to include carbon footprint, energy consumption, employee job-security and morale-motivation, employee health and work-family balance, and customer satisfaction considerations with the purpose of incorporating the triple bottom line accounting of sustainability. On the other hand, hiring and firing quantify employee job-security and morale-motivation factors whereas employee health and work-family balance factors are considered by the overtime hours.

Finally, the customer satisfaction consideration is quantified by the fill rate of the demand metric. Based on these metrics we develop six models: two environmentally revised models emissions cap and energy consumption cap , three socially revised models smoothing and layoff limits, overtime limit, and service level target , and one TBL accounting model. For all of the revised models, mathematical programming formulations are analyzed with data from real-life along with numerical sensitivity analyses.

In aggregate planning, the decision maker first estimates aggregate cost components including labor costs, capacity changing costs, production costs, inventory holding costs, stock-out and backlogging costs, and subcontracting costs. The estimation of these costs is not an easy task; however, it is a prerequisite for aggregate planning.

Apart from the cost components, other factors including the demand forecast, D t , for each period, t ; the number of working days in each period, labor hours required per item of production, and the initial inventory, backlog and workforce levels are required to devise the aggregate plan.

Once all these inputs are determined, the aggregate planning problem can be formulated as a mathematical programming problem and solved. In other words, the aggregate planning is a prerequisite for many operations including production planning, scheduling, and inventory management. The decision maker not only reveals information on production, inventory, and capacity levels but also on the required capital, machinery, and warehouse space, sourcing decisions and supplier purchase level, customer service levels, and product pricing by deducing the aggregate plan.

Clift [ 14 ] proposes metrics for sustainability in all aspects; i. The author argues that social metrics are not so common and a public consensus is needed to define and use them in decision-making processes.

Moreover, aggregation across the dimensions such as expressing ecological impact through monetary units is both unnecessary and undesirable. Koplin et al. Sarkis [ 16 , 17 ] presents a decision-making framework for environmentally conscious business management using analytic network process ANP. Arslan and Turkay [ 5 ] examine the sustainability considerations in the inventory management problems.

They include the economic, environmental and social factors of the triple bottom line accounting of sustainability in the deterministic inventory management problem using the EOQ model. Bonney and Jaber [ 18 ] provide a list of non-cost metrics for incorporating environmental footprint in the inventory context. Although [ 18 ] uses similar models that are available in [ 5 ], [ 18 ] focuses on the environmental factors of the EOQ model. Cai et al. They observe the trade-offs between system costs and GHG emission for the system under consideration.

They also state that their model enables analysis of alternative technologies over a number of periods and may be extended to cover a large variety of complexities common in energy systems. Letmathe and Balakrishnan [ 20 ] present a linear and a mixed-integer program for firms to determine the optimal product mix and production quantities under environmental constraints in addition to the production constraints.

Lineras and Romeo [ 21 ] give a multi criteria decision-making method for electricity planning and model GHG emissions as well as radioactive waste as minimization objectives. Penkuhn et al. It is necessary to consider the social factors in addition to the environmental and economic ones in order to analyze supply chains from sustainability perspective.

Past literature on sustainable supply chains mainly focuses on the environmental factors. The main conclusion from these papers is to include carbon tax as the environmental factor that gives favorable results in terms of environmental dimension of sustainability. The social factors, on the other hand, has not attracted attention due to lack of understanding and data on their impact on the performance of sustainable supply chains. This paper presents three novel contributions to the aggregate planning problem: the introduction of sustainability through triple bottom line accounting that includes social aspects in addition to economic and environmental aspects, the use of the learning curve in reflecting the workers performance on the production efficiency with time, and the smoothing limit that decreases the hiring and firing employees on the system performance.

Then, the effects of all of the aggregate planning decisions with the realistic model are analyzed from sustainability perspective.

From environmental perspective, carbon footprint and carbon tax are added to the classical model. Carbon footprint is used for greenhouse gases emission per unit production and its cost effect is calculated by carbon tax perspective.

The electricity usage is also added to traditional model from environmental perspective because electricity used for production is a major source of environmental pollution.

Enhanced Simulated Annealing for Solving Aggregate Production Planning

In the present study, a multi-period multi-product aggregate production planning model is developed under uncertainty, considering some important aspects of real-world production systems. In order to apply environmental concerns and control the pollution arising from machines, environmental improvement planning is included as a periodic decision variable. Also, the pollution caused by the production is restricted to an allowable level. A light robust optimization approach is employed in which demands and processing times of operations are uncertain parameters. An illustrative example is presented to demonstrate the model validity and some test problems are designed to analyze the impact of uncertainty on the objective function. Several sensitivity analyses are carried out to provide useful managerial insights.

Simulated annealing has been an effective means that can address difficulties related to optimisation problems. Due to the fact that aggregate production planning is one of the most considerable problems in production planning, in this paper, we present multiobjective linear programming model for APP and optimised by. During the course of optimising for the APP problem, it uncovered that the capability of was inadequate and its performance was substandard, particularly for a sizable controlled problem with many decision variables and plenty of constraints. Since this algorithm works sequentially then the current state will generate only one in next state that will make the search slower and the drawback is that the search may fall in local minimum which represents the best solution in only part of the solution space. In order to enhance its performance and alleviate the deficiencies in the problem solving, a modified is proposed. We attempt to augment the search space by starting with solutions, instead of one solution.

Aggregate production planning, abbreviated as APP, is useful for operation management. It is associated with the determination of production, inventory, and personnel levels to fulfil varying demand over a planning perspective that ranges from a period of six months to one year. Aggregate production plans are needed to exploit workforce opportunity and represent a crucial part of operations management. Aggregate production plans facilitate matching of supply and demand while reducing costs. Process of Aggregate production planning applies the upper-level predictions to lower-level, production-floor scheduling and is most successful when applied to periods 2 to 18 months in the future. Plans generally either "chase" demand, adjusting workforce accordingly, or are "level" plans, meaning that labour is comparatively constant with fluctuations in demand being met by inventories and back orders. Concept of aggregate production planning denotes to the process of determine the overall quantities of products to be manufactured or produced in a plant or other manufacturing facility during a medium term planning period such as a month, or a quarter.

Aggregate Planning Practice Problems

Performed the experiments: OS. Analyzed the data: OS MT. Wrote the paper: OS MT. All data is supplied in S1 and S2 Tables. The optimization model and the implementation of the epsilon-constraint algorithm used in this the study is supplied in GAMS format as S1 Model.

Similarly production, resources, such as distinct machines or labor pools, are aggregated into an aggregate, machine or labor resource. Another example is when the firm works multiple shifts, and the variable costs differ between these shifts. The variable production cost is usually more during overtime, as, workers earn a rate premium. Then we prove the existence and uniqueness of the optimal solution of the acquisition quantity and derive the formulation of the optimal solution.

Aggregate Production Planning

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