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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 Ini, i= 1,..M, as inventory at the start of each workshop at the beginning of time n. With the following conditions:

i= 2,. . .M           IniFormulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 1  0

i=1        if           IniFormulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 1  0 positive inventory

 -Ini  delays or pending

Production: is defined as Pni , 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 Bni and inventory Ini+1.

The process would work this way:

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

In+11 = In1 – Dn1 + Pn1

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∈ZFormulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 3  and process Bni , n∈ZFormulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 4  are independent, stochastic, with the possibility of autocorrelation.

Also E Dn1 Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 5  < min BniFormulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 6  ; 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

serial flow
serial flow

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:

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 7

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

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 8

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.

parallel process
parallel process

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 Pm units, the process 2 has to process:

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 9

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:

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 10

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.

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 11

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:

 Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 12

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 13

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 14

Where Rw2’would be:                                                              

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 15

For a number of pieces Pm processed in m, the total pieces reprocessed by 2’ are:

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 16

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:

Formulas To Calculate Scrap, Rework And Inventories In sanitaryware Factory 17

                         table 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]

José María Berges Asín

José María Berges Asín

José María Berges Asín lives in Spain and has 27 years of experience in an international sanitary ware company, mainly in production area. His training is: Industrial Engineering, E.M.B.A. and PhD Business administration.

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