Lot size

Applicable Regulations Assume that a cream is to be filled into a tube that has 20 g printed on it. The lot size is 3000 units. The filling equipment s repeatability is known to be = 0.75 g ( 3.75%). Two somewhat simplified regulations will be investigated that epitomize the statistical and the minimal Individual fill weight approaches ... 

In contrast to variable testing (comparison of measured values or analytical values), attribute testing means testing of product or process quality (nonconformity test, good-bad test) by samples. Important parameters are the sample size n (the number of units within the random sample) as well as the acceptance criterion naccept, both of which are determined according to the lot size, N, and the proportion of defective items, p, within the lot, namely by the related distribution function or by operational characteristics. 

Disolve in hexane, seeded at 40°C slowly cook over 3 days to 15°C. Lot size 1 kg. 

Disolve in hexane, chill rapidly to 15°C, and seed, hold at 15°C for 3 days dry without heat. Lot size 12 kg. 

Once the lot size and inspection level are known, Table 3.2 can be used to identify the appropriate sampling plan. For example, if the lot size is 4000 and inspection level II is required, then L is the appropriate code letter. The code letter relates to the number of items (samples) from the lot that needs to be examined, as shown in Table 3.2. 

Next to batch production, where exact quantities of a product have to be produced many times over, it is minimum lot sizes that deserve particular consideration. This is usually the case when products are manufactured in large campaigns. Here, products are usually manufactured in a continuous process, with different production processes being combined within the framework of the process chain. When linking the individual production stages to each other it is important to also consider offset times. These can for example include the transportation and analysis time between two production stages. 

This more detailed model is necessary for target stock calculations where productions may overlap, the lengths of quants differ significantly and quants have multiple predecessors and successors (see Figure 4.14). Calculating lot sizes with for example the formula of Andler yields completely different results and the sum of changeover costs and stock costs are much higher. 

The demands are given as orders which are partially movable or have a fixed assignment to a resource with dearly defined setup, production and deaning times. There are also anonymous demands that were calculated from forecasts. The target inventory is a soft constraint that is used to model dynamic safety stocks. Most quants must fulfill integer batch sizes and often minimum lot sizes. 

In the beginning there is a general loop to decide if more lot sizing procedures should be applied to the existing quant network to meet the constraint of the minimum batch sizes of products. Then the quant network is examined, free usable stocks and free quantities of quants are made available. The material balances of any quant are calculated and decisions are taken whether quants require further explosions of their BOM. Structures for a fast cycle checking, sorting of existing quants and quant links and forecast intervals are built up. A recalculation of the due dates for all quants - also the ones of orders - can be done if specified by the user. 

At first the demands caused by target inventories are not considered. Because of the given minimum lot sizes or batch sizes the target inventories may already be met. After that additional quants may be generated if the target inventories are not yet met. 

Typically, orders are simpler to explode than anonymous demands, because for an anonymous demand it might be required to define a distribution of the forecast quantities over the forecast interval only one quant, quants with equal quantities, due dates at the beginning or end or equally distributed. At this time it can be defined for each product if lot sizes, batch sizes, minimum quantities, maximum quantities of quants should be considered. The quantities are broken into predefined equal parts and then assembled until they meet the mentioned constraints. 

The static lot sizing has several positive aspects. Big quant networks are transformed into smaller ones thus making faster calculations possible still fulfilling all constraints. The objective function can be reduced to contain only the changeover costs and the stock costs with the aim to find a trade off between these two costs (see Figure 4.17). 

Fig, 4.17 Static lot sizing for a batch product. The plan is a just-in-time production. According to the due date every batch is planned with minimum costs. Setups are indicated with a red arrow to the right. The stock costs of 45,216 Euro are a result of the different batch sizes of the product itself and its successor product. Therefore not every batch can be planned just-in-time. The changeover costs are 4,182,935 Euro. The sum of both costs is 4,228,151 Euro. The lower part of Figure 4.17 shows the result of... 

This article gives a short introduction to methods and tools based upon stochastic models that are applicable in supply chain management in order to give the reader a flavor of the potential of such methods. Typical terms we will deal with are service level, lot size, and production capacity. 

Consider two products A and B with the same demand of 20 units per time period, the same buffer size of 60 units, and the same production speed and set up time. The only difference is that product A is only sold in single units, but product B has 80% of orders of 1 unit and 20% of orders of 10 units. It is intuitively clear that product B will have a lower service level because is has a larger variance of the demand. It is not immediately clear that both products have different optimal lot sizes. The optimal lot size, i.e., the lot size resulting in maximal service, is 20 units for product A which results in a /3-service level of 98.6% (Figure 6.8). The optimal lot size for product B is 15 units which results in a not particularly good /3-service level of 90.6%. In order to achieve a /S-service level of 98.6% one would need a buffer of size 165 units, with a corresponding optimal lot size of 33. 

Optimal Lot Size and Service Level Resulting from Buffer Size... 

Optimal Lot Size A - - - Optimal Lot Size B 8 Service Level A - - - 6 Service Level B ... 

The problem of splitting the total production into lots or campaigns can be solved by a multiproduct extension of the old and well known Andler or Harris formula [7], which is for one product only. This extension copes with several products on the same production train and various side conditions, and minimizes the lot sizes. It can be shown that lot sizes should be proportional to the square-root of demand, as far as side conditions allow. The demand as well as the lot size can be measured in weight or value. It is important to realize that unnecessarily high lot sizes not only generate inventory cost but also negatively affect the production of more urgently needed products. 

Figure 6.10 shows the data flow of the software tool BayAPS PP for optimal capacity assignment for given stochastic demands. Transaction data about demand and inventories is typically imported from SAP R/3 as indicated, production capacity master data and side conditions are stored in the software tool. Forecasts can be taken from a forecast tool or from SAP R/3. The output ofthe tool is a list ofpriorities of products and their lot sizes, which are optimal based on the presently available information. Only the next production orders are realized before the computation is repeated, and the subsequently scheduled production is only a prediction. 

All lot sizes have to be divisible by the content of a single batch size in the production. 

The software tool performs an optimal calculation of lot sizes incorporating uncertain demand from forecasts or history as well as up-to-date inventory and open order data. The effort for the regular user is negligible because of the interface to SAP R/3. Various technical constraints can be included. Specific training to use the software is not necessary because it looks like the familiar Excel format to the... 

Third, processing times may require special modeling in chemical industry. While in discrete manufacturing processing times for a certain lot are usually dependent on the lot size, i.e., the number of units to be produced, this is often not true in the chemical industry. Here, processing times are often constant, irrespective of whether a reactor is filled to 70% or 90% of its capacity. This is often referred to as batch production [5], On the other hand, the quality of the material produced may depend on resource utilization. Certain reactions may not even be feasible, if a minimum bound of the procured material is not exceeded. This implies additional restrictions regarding the resource utilization level on the planning situation. 

Finally, an important characteristic identified in chemical production processes are time-consuming and costly setup operations. Thus, the representation of time is a critical issue in the modeling of chemical production processes. Three fundamental deficiencies of the representation result if continuous processes are modeled by standard bucket-oriented lot-sizing models. These are the carry-over of setup states... 

After having motivated the importance of coupling the production of adjacent periods via setup carry-over, now the lot size itself will be focused on. In the chemical industry, production quantities are often constrained such that a lower and/or upper bound is imposed on a continuous production run or that production has to be... 

Minimal bounds on the production quantity are most often process dependent. Typically, a minimal campaign length is required if for example a critical mass is necessary to initiate a chemical reaction. The same is valid for maximal bounds on the production quantity. The rationale here is that a cleaning operation may be required every time a certain amount has been produced. Finally, batch size restrictions often arise in the chemical industry, if for example the batch size is determined by a reactor load or, as discussed above, the processing time for a certain production step is independent of the amount of material processed. In these scenarios, when working with model formulations using a discrete time scale, it is important that the model formulation takes into account that lot sizes may comprise of production in several adjacent periods. 

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