انتقال الگوریتم سهم عادلانه از یک توزیع به یک محیط برنامه ریزی تولید

This paper investigates the ability to migrate the fair share algorithm from a distribution to a production planning environment. In a semi-process-based production system, such as that of the photographic film producer Agfa, the availability of the intermediate product is then the limiting constraint steering the fair share algorithm for the end-product lotsizing decision process. The manufacturing model of Agfa is typically semi-process, where a first stage produces a limited number of intermediate products. The second stage is flow oriented and converts the intermediates into many distinct end-products. The planning method currently implemented within Agfa is a two-level scheduling approach. First, it establishes a cyclical volume plan at the intermediate product level, which is then used as an input constraint for the secondary problem of determining end-product lotsizes. As an alternative to the traditional model, where the end-product lotsizes are determined based on the standard EOQ formula, this investigation suggests the end-product mix decisions to be governed by a tuned fair share algorithm. The paper discusses this algorithm with its parameter settings, the impact on stock values, on service levels, and on set-up and inventory holding costs. The results of both algorithms are compared. This investigation proves that the combination of a cyclical volume plan, at the intermediate product level, combined with fair share mix decisions for the end-product lotsizes, delivers the needed service level with lower inventory levels and reduced operational costs. The main benefit of the model integrating volume planning and mix decisions is its ability to reduce demand amplifications, prohibiting market demand nervousness (amplified by the Forrester effect) from entering into upstream operations. The reduced nervousness allows a major reduction in needed safety stock at the intermediate product level.

The task of production planning is to get supply and demand in balance. Within the planning process a company should treat volume and mix problems separately. If volume planning is handled effectively, it will be less difficult to deal with mix problems. If on the other hand volume is not planned well, then mix issues become substantially more difficult to cope with. Therefore questions of volume precede those of mix. Volume planning should be done upfront and a company should spend enough effort to do it well. The typical X-type shape of product structure flow within the semi-process industry, having a large number of components and end-products but a small number of intermediates, has an advantage for volume planning. A two-stage hybrid production model is still dominant in the semi-process industry. The first production stage is process-like, using a lot of raw materials, having large production batches and costly set-ups, and produces a small number of intermediate products. The second stage is flow-shop oriented and transforms the intermediate product into many distinct end-products. Volume planning should be done on the intermediate product level, which is typically the smallest segment of the product structure. Within this two-level scheduling approach, the first level generates a volume plan on the intermediate product level. The second scheduling level decides on the finished end-products coming out of the intermediate material flow. Furthermore, the product pareto rule is valid in most companies, stating that 20% of the stock keeping units (SKU's) correspond with 80% of the production volume. On transferring this to the volume planning on the intermediate product level, a company can establish a volume plan for a limited number of intermediate products and cope with the major part of the production volume. Agfa, the company involved in this research project, is a multinational producing imaging systems (graphical film, printing plates, X-ray film). At the intermediate product level Agfa uses cyclical scheduling. The benefits of a repetitive cyclical production plan are numerous. The predictability of the schedule allows synchronisation between different production stages. The technique used for establishing this repetitive nominal schedule, on the intermediate product level, is based on solving the economic lotsizing and scheduling problem (ELSP). The resulting cyclical volume plan is then used as the target volume plan for operational use, which can then use a fair share logic policy for lotsizing the end-products. This investigation will focus on the problem of determining end-products quantities fulfilling market demand, using the intermediate product volume plan as an input constraint. These end-product mix decisions will be governed by a tuned fair share algorithm. This paper examines the possibilities of migrating the fair share algorithm from a distribution environment towards a production environment. The results, of the fair share-based end-product planning, will be compared with the traditional end-product lotsizing, which uses the standard the EOQ model. Section 2 describes the semi-process production environment. Section 3 gives feedback on previous research. Section 4 illustrates the synchronised planning concept and the logic of the fair share algorithm. Section 5 lists the cyclical volume plan and relevant article data. Section 6 describes the experimental design and Section 7 brings the results of the simulation experiments, gradually tuning the fare share algorithm. This section ends with a comparison of results and estimates the benefits when using the proposed algorithm. Section 8 concludes the paper.

This investigation proves that the fair share algorithm, originating from a distribution planning environment, can be used within production planning. In order to achieve the necessary service level, the inbound flow of the product to become fair shared must be linked with dynamic market demand. By adding an aggregated stock control mechanism, decreasing or increasing the intermediate product flow depending on the total stock position, the service level for end-products remains stable at the target level of 95%. Additional tuning influences the end-products lotsizes. The model can be steered towards production lotsizes comparable with the standard EOQ model. This lotsize tuning has an effect on service level, which deteriorates when the installed minimum lotsizes are too high. The main benefit of the model integrating volume planning and mix decisions is the ability to reduce demand amplifications and prohibit market demand nervousness (amplified by traditional lotsizing) to enter into the upstream operations. This allows a major reduction in required safety stock at the intermediate product level. The simulation results demonstrate that the combination of a cyclical volume plan with the tuned fair share algorithm allows a significant 20% reduction in total stock value and a 7.3% reduction of operational costs (set-up and inventory holding costs) keeping the service level intact.