An Unreliable Supply Chain Model With Inspection, Reworking and Scrapping

act:An Unreliable Supply Chain Model:
We present an operational assembly-oriented SCSAlthough incorporating a quality control process into
with in process quality control policy using an openan unreliable SCM can ensure the quality of the
queuing network approach. A nonlinearoutputs, the trade-off is the inevitable decrease in
profit-maximization formulation model is presented,the throughput of the SCM due to the presence of
and an enumerative algorithm to solve this problem isthe quality control process. One of the reasons being
provided. For small scale, the approach can obtainthat the quality control process can in fact, increase
efficient approximation solutions. But, for largethe total processing time of parts and the units of
problems, will need more computing time because ofscrapping. Since the in-process quality control system
the increased number of alternative policies neededwill dynamically affect the performance measures we
to be evaluated.discuss in the previous section, we have to use a
Key words:systematic approach to analyzing these effects.
Supply Chain Management, Quality Control process,Therefore, in this section, we construct a
Formulation.profit-maximization model that seeks a near-optimal
Introduction:(i.e., only a heuristic solution algorithm is proposed
We propose an analytically-based queuing networkhere) quality control policy for an unreliable SCM.
model for an unreliable supply chain with inspection,Relevant revenue and cost parameters are defined
reworking and scrapping【1】. Theas follows.
present Supply Chain Model consists of severalREVK: the revenue for a type-k part
supplying cells【2】. The mainCIKl: the cost of inspecting a type-k part in the
components in each cell are assembly machines,it’s lth visitation p cell,
robots, and an inspection station【3】.CWK: the waiting cost of a type k part
In the assembly-oriented supplying cell, the defectiveCSKl: the cost of scrapping a type-k part in its lth
parts which are detected by the inspection stationvisitation cell, with CSkl ＜ CSK,l+1 ,i=1,
can be dis-assembled (i.e., reworked) if the defects2,…,zk-1
are made in the supplying process of the currentCRkl: the cost of reworking a type-k part in the its
cell【4】, then they can be processedlth visitation, and
just like the original input material from the immediateCPkl: the cost of processing a type-k part in the its
preceding cell【5】, On the otherlth visitation cell.
hand, if defects of parts are caused by theLet r kj (the inspection rate for type-k parts in cell J)
processing from one of the preceding cells, the partsbe decision variables, we now show a
will be scrapped【6】.profit-maximizing model that incorporate the quality
Assumptions:control into an unreliable FMS.
The main assumptions are as follows:MAXIMIZE (1)whereand (2)for all k and j .
1. After going through a particular cell for processing,(3)
the part will not return to that cell again.In this model, the profit is accounted on per unit time
2. The local buffer is of infinite size.basis and J k represents the total return of type-k
3. The processing capacity of each cell is largeparts produced by the SCS. Equation (2) computes
enough to handle the input, i.e., the aggregatethe profit generated by type-k, which is the total
processing time (including the working time, reworkingrevenue (the 1st term) minus inspection costs (the
time and inspection time for all part types) multiplied2nd and 3rd terms), waiting costs (the 4th and 5the
by the aggregate arrival rate of all part type shouldterms), post-sales failure costs (the 6th term),
be less than one.scrapping costs (the 7th term), and reworking costs
4. The working time, reworking time and inspection(the last term). The above model is a complex
time of parts are mutually independent.nonlinear optimization problem which becomes more
5. The working time and reworking time belong to acumbersome when we attempt to incorporate the
general distribution.results of the queuing network model into it. In the
6. For each part type, the visitation sequence in thenext section, we use a numerical example to
Supply Chain is fixed and given.demonstrate the effect of the quality control policy
7. A part may go through the working area,on a two-step and two-digit search procedure is
reworking area and inspection many times, but theproposed as follows:
processing time in these three processes does notSTEP1: Search for the optimal inspection rates in the
change in each visit.range of 0 and 1 with increment of 0.1. denoting the
Assumptions 1 and 6 are practical situations in thesolutions by r* kj .
supply chain-oriented system because the works ofSTEP2: Search for the optimal inspection rates in the
supply chain rarely go back to the stations whichrange of r *kj -0.05 and r* kj +0.05 with increment
were visited before unless they need to beof 0.01.
reworked, and also because the routing of an supplyA Numerical Example:
chain system for a specified task is difficult toConsider a SCS with three cells where each cell
change. The assumption of infinite local size iscontains two operating areas, one for working (which
adopted by many researchers to simplify the solutionalso contain an inspection station) and the other for
procedure, to ensure that we reach the steady staterework two types of parts are processed in the
of the queuing system, assumption 3 is needed.SCS. Three separate cases are examined to illustrate
Assumptions 4 and 7 are required to aggregate thethe effect of the quality control function on system
working time, reworking time and inspection time.characteristics: (1) The SCS is completely reliable (2)
An Unreliable Supply Chain Model with Inspection,the SCS is unreliable and there is no quality control,
Reworking and Scrapping:and (3) the SCS is unreliable and has quality control;
Let us define the functions of an unreliable Supply20 percent of the processed parts are inspected.
Chain Model (SCM) cell and the movements of partsConclusion:
in the cell, and derive preliminary results to the entireIn the paper we have obtained the operational
SCM. The supplying cell that we consider consists ofcharacteristics of an assembly-oriented SCS with in
a working area, a working area, and an inspectionprocess quality control policy use an open queuing
station. A part will leave the cell if it passes or skipsnetwork approach. A nonlinear profit-maximization
inspection. If defects are detected, two possibilitiesformulation was presented, and an enumerative
arise: if the defect was due to the processing in thealgorithm to solve this problem was provided. For
current cell, the unit is routed to the reworking areasmall scale problem, the approach can be used to
and then circulated back to the working area forobtain efficient approximation solutions. However, for
processing. Otherwise, it will be scrapped. Inspectionlarge-scale problems, the proposed search procedure
is assumed to be 100% reliable and all defectivewill require more computing time because of the
items can be examined to determine if they are fromincreased number of alternative policies must be
the current cell or from one of the preceding cells.evaluated.
The Supply Chain Systems:References:
The Supply Chain systems (SCS) we consider consist【1】Anonymous. “Supply
of several supplying cells with processing, inspectionDisruptions May Linger as Quakeaftershock.”
and reworking functions in each cell. Parts of differentSeptember 22,1999.
types will flow through the SCS following specified【2】Bowers, M.R., and A. Agarwal.
routes that visit various cells in the system. As“Lower In-Porcess Inventories and Better
described earlier, a part leaves a cell if it passes orOn-Time Performance at Tanner Companies,
skips inspection. On the other hand, when aInc.” Interfaces 25(1995), pp. 30-43.
defective part is detected, the part will be reworked【3】Federgruen, A., and A. Heching.
and circuited back to the working area of the cell if“Combined Pricing and Inventory Control
the defects are made in the current cell. However, ifunder Uncertainty.” Operations Research
the defects are found to be made in one of the47(1999), pp. 454-75.
preceding cells, the parts will be scrapped from the【4】Fisher, M. L. “What Is the
cell without reworking. This section is further dividedRight Supply Chain for Your Product?”
into two subsections. In the first section we obtain,Harvard Business Review, March-April 1997, pp.
for each part type, the expected number of parts105-17.
that will be reworked and scrapped in each of their【5】-- --. “Rethinking
visitation cells, the expected number of undetectedDistribution: Adaptive Channels.” Harvard
defective parts, the total flow to the next cell in theBusiness Review, July-August 1986, pp.112-20.
visitation sequence, and finally, the average outgoing【6】Stephen Harley,
quality of each part type and of the SCS as a whole.“Transportation: The Cornerstone of Global
In the second action we examine the waiting timeSupply Chain Management”, Proceeding of
spent by each part in the system due to working,CLM Annual Meeting Council of Logistics Management,
reworking and inspection.1996, pp. 635-641.