I.INTRODUCTION
Two types of production systems are basically identified in the literature to
reflect the product market environment; make to order (MTO), make to stock (MTS)
production systems. In this study make to order, make stock and hybrid systems in the
literature will be reviewed comprehensively and a related model will be proposed as a
future research topic.
Make to stock companies generally product in batches and carry finished goods
inventories for most of the items. The advantage is that customer delivery times are
minimized as expense of inventory holding costs. Typically, companies producing
standard items with accurate demand forecasts prefer make to stock production
systems. Production begins before demand is known precisely.
In cases where exact needs of customers are difficult to anticipate and there
exists large number of product configurations, the companies work in make to order
environment. Typically no finished goods inventory are held, customer orders are
backlogged and due dates for each item are negotiated with customers. Jet engine
manufacturing can be given as an example; jet engines are produced only in response
to a customer order.
A system that lies in between is assemble to order system. There exist large
number end items assembled from relatively small set of standard subassemblies.
Since there exists large number of end items, it is difficult to forecast demand of end
items. Modules are assembled to stock and final assembly is performed only when a
customer order arrives. This system achieves a compromise between inventory
holding cost, product flexibility and delivery time.
In push systems, production decisions are based on long term forecasts where as
in pull systems production is demand driven. Build to order, and build to stock
systems are methods to combine push and pull systems within a single supply chain.
In the build to order system, an intermediate generic subassembly is built to stock, and
then they are customized to final products on demand. However in the build to stock
system, finished products are also built to stock.
In this research, hybrid models combining MTO and MTS systems will be
examined in detail. The models related to combined systems mostly focus on
determining which items should be made to order, or to stock; establishing a good
inventory policy for make to stock items and evaluating the performance of the
system. System performance is usually measured with, inventory level and waiting
time distributions, as well as average setup costs, inventory holding and backlogging
costs.
Traditionally it has been viewed that MTO systems and MTS systems as distinct
systems; however it should be noticed that a system with diverse product line and
customer base can only be modeled with an appropriate combination of these two
systems. So modeling an appropriate combination of these two systems is important.
Many models in the literature focus to model the queuing system of the items and try
to evaluate the performance of these queues.
The models in the literature can be roughly classified according to the
assumptions related to setups and number of servers. Many of them assume no setup
time and cost between changeovers and a single server queuing discipline. However
in this study, models assuming no setup between changeovers from MTO and MTS
items and single server queue systems are reviewed in priority.
II. LITERATURE REVIEW
Make to stock and make to order systems have been analysed since 1960’s.Popp
(1965) presented simple cost comparisons of making the item, make to stock versus
making it to order. He modelled a simple single-item stochastic inventory model with
zero lead-time.
One of the first models about combined make to order, make to stock systems is
proposed by Williams’ (1984). He assumes that low demand items make to order and
high demand items are make to stock, however this is not a strong assumption and
most of the current models do not have such an assumption. Rajagopolan (2002)
demonstrated that this may not be a good strategy. Williams assumes a (Q, r) policy
for MTS items. Priority is given to order or batch with the largest waiting time.
Federgruen and Katalan (1999) analyzed a hybrid system where a make to order
item is added to the production of make to stock items. They mainly focus whether to
interrupt production of make to stock items when an order is faced. Under absolute
priority rule, priority is given to MTO items. Preemption may or may not be allowed
or not. Under postponable priority rules make to order items are inserted into the
production schedule of the MTS items, but only when the facilities would switch
between MTS items. They also showed how for each option, a variety of performance
measures (inventory and waiting time distributions, average and setup, holding and
backup costs) can be evaluated and optimized efficiently by analytical methods.
Rajagopolan (2002) focuses to decide whether an item is MTS or MTO and
what type of inventory policy to use for the items made to stock. He models the
system as single server M/G/1 queue, on first come first served base. When demand
occurs for a MTO item, the demand is satisfied in that period. (Q, r) inventory model
is used for MTS items. The congestion effect, negative effect of an item to other items
is modeled. If an item is made to order, there maybe more setups and higher capacity
utilization, resulting higher stock levels for MTS items.
A nonlinear integer model with objective function minimizing inventory costs
and with a constraint of satisfying MTO items within a specified lead-time is solved
by a heuristic method.
Sox et al. (1997) considers a combined system where a similar problem where
demand for MTO items are to be satisfied within a certain time window. They don’t
consider set up times, lot sizing and congestion effects mentioned in Rajagopolan
(2002).Many papers deal to model the queuing system of the MTO and MTS items
focus on the queue time performance. Karmarkar et al. (1987) uses the size of queue
as decision variable a model the size of which is a decision variable. Queue time or
lead time performance measures are considered and finished goods inventories are not
modelled.
Carr and Duenyas (2000) focuses to model how a firm should to accept or reject
an additional order and which type of product to produce next. The firm is
contractually obliged to meet demand of MTS items and quantity of orders to commit
when signing is also determined by the model. Unit profits of MTO items are
assumed to be higher; however large shortage penalties exist for MTS items. The
assumption that firm has the chance of rejecting the orders and unit profits are
different, make this paper distinct. Basically a strategy to find what proportion of
production capacity the firm should dedicate to MTS items and how the company
decides or rejects to accept new orders are tried to be found.
They characterized the structure of optimal policies in the context of multiclass
M/M/1 queue, where the classes are MTO and MTS items. The objective is to find a
policy maximizing the average profit per unit time over infinite horizon. The relevant
costs are inventory costs for MTS and MTO items and the penalties incurred when
MTO demand is not satisfied. In this model a proxy holding cost is also considered as
proportional with the time MTO item is processed. Carr and Duenyas (2000) model
the system as a Markov decision process, where the states are number of MTS items
in the stock (n1) and number of units of MTO items in process (n2).Then this analysis
works to establish a dynamic decision mechanism to accept or reject the order by
looking at the current state of the system.
They showed that optimal average profit per unit increases as service rate or
arrival rate of MTO items, or revenue generated by unit MTO item increases.
However it will decrease as penalty costs or holding costs increase or arrival rate of
MTS items increase.
Lee (1996) considers the case where delay of product differentiation is possible
and proposes to build to order and build to stock cases. For the build to order system
there exists generic processes up to a time t (t<T where T is the time of producing a
batch). Inventory of generic work in processes (units processed up to time t) is hold
and they are further processed when an order comes. First come first served discipline
is used.
The intermediate inventory stock is managed with a periodic review order up to
–S inventory system with review period is one time unit. The response time to all
customer orders arriving at a particular time unit is used as a performance measure.
He showed that for the cases where derivative of inventory holding cost with respect
to time is small, total inventory cost would decrease.
III.PROPOSED SYSTEM
A production system producing many MTO items and a single MTS item is
considered. Up to time t, there exists a generic production processes for both make to
order and make to stock items. At this time point t, intermediate inventory of generic
work in process is held. Moreover for the make to stock item, finished goods
inventory will be also held. For simplification of the model it is assumed that make to
order items has absolute priority and preemption is also allowed. So generic work in
process items can be processed, as a make to stock item whenever there exists no
make to order item waiting to be processed.
There exists two dependent systems to be considered; processing of make to
order items can be modeled as in the build to order model of Lee when absolute
priority and preemption is considered. Intermediate inventory stockpile can be
modeled as standard periodic up to S policy. The S level can be determined by
minimizing inventory holding cost with the constraint of expected customer response
time should be less than a. For the make to stock item, when the system is considered
independently, two echelon inventory models can be solved by satisfying a minimum
level fill rate. If there is no setup cost for ordering, base stock (Sj) policy is optimal
for each level j. If the echelon inventory position Pjt<Sj; an amount of Sj-Pjt will be
ordered from upstream.
Figure 1 illustrates the proposed system.
t
Intermediate Stock


T-t
MTO
MTS
Figure I.Proposed Sytem
However the complexity is that both systems cannot be considered as
independent systems. Whenever an order exists for MTO items, MTO system cannot
fully use the intermediate level stockpile, so there should be compensation to finished
goods inventory for the MTS for this case.
IV.THE MODEL
The assumptions can be stated as follows:
 It is possible to delay production differentiation up to point t. Manufacturing
lead time(T) is fixed.
 Single product case is considered, for this product units produced are
classified as MTO or MTS after point t.
 Demand for MTO and MTS items follows Poisson distribution with means
1, 2 respectively.
 MTO items have absolute priority and preemption is allowed.
 No inventory is held for MTO items.
 No fixed ordering cost exists.
 Unit holding cost rate for end items are higher than intermediate stock in
process. (h2>h1).
Two performance measures are considered for this system; expected number of
backlogged units for MTS items and expected customer response time to all products
for MTO items. The objective function is minimizing inventory-holding costs by
satisfying minimum levels for these performance measures. In the model production
differentiation up to point t is fixed, however as a future extent variable case can be
considered.
Notation can be summarized as :
T: Manufacturing lead-time
t: Point of differentation (fixed for this case)
1:Mean arrival rate for MTO items
2:Mean arrival rate for MTO items
S1: Base stock level at intermediate stockpile
S2: Base stock level for MTS items
Y: Customer response time
h1: Unit holding cost rate for intermediate work in process items
h2: Unit holding cost rate for end items
b: performance level for allowed number of backlogged units
y: performance level for allowed number for customer response time
P (x/ T): probability of having a demand of x in the period T.
 (S 2 | 2 ) : Expected number of backorders for MTS items.
: Effective lead-time
The proposed model is:
min h1S1  h 2S2
subject to
 ( S 2 | 2 )  b
E (Y )  y
 ( S 2 | 2 ) 
x 
 (x  S
x  S 2 1
2
) p ( x | 2 )
  T  t   ( S1 )t
t 1
E (Y )  T  t   P ( D (t  r )  S1 )
r 1
or
t 1

E (Y )  T  t    p ( x | 1 (t  r ))
r 0 x  S1
(S1) is the fill rate at the intermediate inventory stockpile and the crucial part in
this model to find this value. Effective lead-time for the MTS items is a function of
the fill rate for the intermediate level stockpile, which is a function of the number of
customer orders for the MTO items. So fill rate at MTS items is a function of stock
level at the intermediate level stockpile, as well as customer orders for MTO items.
V.INSIGHTS ABOUT MODEL & CONCLUSION
The proposed system is a combination of a pull and push system. By the
applied system customer respond times for MTO will decrease since a generic
inventory exists to be processed. The customer lead-time will be shortened. Secondly
inventory holding costs will be less for MTS items when considered with the case
where only finished goods inventory is held. Since unit holding cost of generic
inventory stockpile will be less than finished goods inventory.
To enhance quick response firms usually prefer make to stock production
systems and to offer large variety firms usually prefer make to order production
systems. However environments with a diverse product line and customer base can be
only best served with a combination of these two extreme philosophies.
In this research a comprehensive literature survey about hybrid systems is made
and an alternative combined system was proposed. The proposed system utilizes and
combines idea of delaying production differentiation point and a multiechelon
inventory system for MTS item. The system proposed is an alternative to achieve a
compromise between inventory holding cost, product flexibility and respond time to
customer orders.
As a future work, a model for finding the effective lead time for MTS item as a
function of the MTO system can be modelled. Different priority rules among MTO
items and MTS item, and effect of the priority rules on the overall system
performance can be examined.Moreover effect of change in point of differentiation on
the system performance can be examined.
VI.REFERENCES
Carr, S., I. Duenyas. 1998. Optimal admission control and sequencing
in a make-to-stock/make-to-order production system.
Federgruen, A., Z. Katalan. The impact of adding a make-to-order
item to a make-to-stock system. Management Sci. 45(7) 980–994.
Karmarkar, U. S., S. Kekre, S. Kekre. 1985. Lotsizing in multi-item
multi-machine job shops. IIE Trans. 17(3) 290–297.
Lee H.L. 1996. Effective inventory and service management thorough product and
process design. Oper. Res. 44(2). 151-158.
Popp,W. 1965. Simple and combined inventory policies, production
to stock or to order? Management Sci. 11(9) 868–873.
Rajagopalan,S. 2002 Make to Order or Make to Stock: Model and Application.
Management Sci. 48(2) 241–256.
Sox, C. R., L. J. Thomas, J. O. McClain. 1997. Coordinating production
and inventory to improve service. Management Sci. 43(9) 1189–1197.
Williams, T. M. 1984. Special products and uncertainty in production/
inventory systems. Eur. J. Oper. Res. 15 46–54.