### Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory

Workers that spend many hours into the sanitaryware factories find difficult to explain to others departments, how the scrap and rework impact in the flow, however this knowledge is important in position as planners or bookkeeper, figures as scrap, lead time or inventories are important for them. Due to the complexity of the process and different plant layouts, in this job, only will be modeling a process of several stages in series with scrap, where the rework items are treated in a parallel line, so the number of parts decreases downstream due to the scrap. We believe that will be easy to translate this model to others organizations. At the end, you have a numerical example.

### 1. – DEFINITION OF VARIABLES

A temporal periodicity is assumed, in which, time is divided into segments. Each segment is called n.

**Capacity**: For all i = 1…. M in space time n, Bni is defined as the amount of net pieces that the workshop i can produce in period n.

**Orders received**: Dni is defined as the number of orders received at the workshop i at time n.

**Inventory: **defined I_{n}^{i}, i= 1,..M, as inventory at the start of each workshop at the beginning of time n. With the following conditions:

i= 2,. . .M I_{n}^{i}* ^{≥}* 0

i=1 if I_{n}^{i}* ^{≥}* 0 positive inventory

-I_{n}^{i} delays or pending

**Production**: is defined as P_{n}^{i }, i=1,. . .M as the workshop i production in period n. This production has been defined by a policy that took into account the capacity B_{n}^{i} and inventory I_{n}^{i+1}.

The process would work this way:

At the beginning of period n+1 the inventory in 1 is:

I_{n+1}^{1} = I_{n}^{1} – D_{n}^{1} + P_{n}^{1}

**Production** Pn1 is seen as demand for the Workshop 2, which generates demand for the workshop 3. So the whole process is determined by external demand.

**Demand** Dn1 , n∈Z and process Bni , n∈Z are independent, stochastic, with the possibility of autocorrelation.

Also E _{D}_{n}_{1}** ** < min _{B}_{n}** _{i}** ; i = 1, . . .M

**2.-FLOW**

**2.1. – SERIAL FLOW**

The main flow for the production cycle could be divided in: Casting, punching, first finishing, green drying, green finishing, white drying, glazing, trademark application, glazed drying, firing, packing.

We could say that the pieces are borned by filling a batch of molds with slip, but during the thickness phase, hardness and handling of the pieces out of the molds, we can have losses or scrap; “s”.

Definition of variables:

Si: waste or scrap of workshop i

si: so much per one of scrap of workshop i

So, each workshop has to process the processed parts in “m” minus all scrap pieces upstream.

For a number of produced pieces in m, the production in workshop i, will be:

And the first pass yield will be: number of units coming out divided by the number of units going into of workshop:

**2.2. – PARALLEL PROCESS**

We can have rework in some phases; these pieces are disaggregated and treated on one parallel line.

Definition of variables:

Rwp: pieces sent to rework (generated by workshop p)

Rwp’: pieces sent to rework generated by workshop p’

rwp: so much per one of rework workshop p:

rwp’: so much per one of rework workshop p’

Although we could have rework in each phase, for clarity, we are going to focus in one very usual; the firing process in sanitary ware manufacturing, so we give to p the number 2.

In workshop number 2, after the process, inspection disaggregates the pieces in three parts:

The good ones: for workshop 1.

To repair or rework: defined as Rw pieces, they have small defects that current technology is able to repair with reasonable costs. They will be sent to workshop 2’.

Waste or scrap s2: With the current techniques is not profitable (or impossible) to repair the piece and have the physical and chemical characteristics or appearance in order to be marketed within the established quality parameters. The piece will be destroyed, but usually their remains can be used as raw materials.

The pieces to repair go to workshop 2’, where the processed pieces are inspected and they will be newly disaggregated in:

The good ones: to workshop 1.

To repair Rw2’: Sent again to workshop 2’.

Waste s2’: to be destroyed

If the workshop m produces P^{m} units, the process 2 has to process:

From the process 2 the pieces will go to the conditioning workshop 1:

The processed pieces minus the disaggregated ones to rework or to waste:

The pieces from the process 2 disaggregated to the process 2’ will be: the processed by 2 minus the ones sent to conditioning, minus the scrap. They are defined as the process pieces multiplied by the percentage of rework.

The good pieces from process 2’ will be: the disaggregated to rework from 2 minus the scrap from the second fire.

But 2’ produces rework too, whose percentage average is identified as rw2’, and scrap named s2’. This rework pieces from 2’ produces rework and waste and so on.

The total pieces reprocessed by 2’ are:

Where Rw2’would be:

For a number of pieces P^{m }processed in m, the total pieces reprocessed by 2’ are:

And the pieces generated at the conditioning workshop 1 by 2’ will be, rework from 2 minus scrap from 2’

Knowing the proportions can be summarized as:

table[/caption]

**Conclusion:** We know the challenges of using the real inventory as a benchmark for planning with waste and rework. To properly assess the inventory at any given time, we define a new concept, adjusted inventory, which is the inventory minus downstream piece losses. Based on this new concept, we have redefined two classical terms: Rotation: Parts supplied by the system to the warehouse divided by the sum of the adjusted inventories. Lead time: adjusted total inventory divided by the net production. The temporal influence on the flow of parallel processing has been quantified: the number of pieces that go out in each cycle is an exponential function in which, the mantissa and exponent depend on the system performance and the number of cycles, respectively. This article is one small extract of my thesis doctoral “Planning and inventory management in a manufacturing environment with waste and stochastic reprocessing” managed by Dr. Javier Conde. Department of Management. Faculty of Economics and Business Administration. U.N.E.D,Madrid, Spain. You can contact me at [email protected]

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