TERM PROJECT
DEMAND VARIABILITY IN SUPPLY
CHAINS
By
Eren Anlar
Introduction
This paper considers supply chain demand variability. It consists of concepts and
related literature review. Finally, a related research area is proposed. The proposition
consists of the assumptions, the model and the solution methodology.
Concepts
Scheduled ordering: the retailers may order only every T periods, and their order
quantities must equal an integer multiple of a fixed batch size, Qr.
Synchronized ordering occurs when all N retailers order in the same periods, every T
periods.
Balanced ordering occurs when equal number of retailers order per period.
Flexible Quantity Strategy: Increasing T and decreasing Qr. This enables the retailer
to have more flexibility to choose the order quantity, but less flexibility in the timing
of orders.
Literature Review
Eppen and Schrage (1981) study a two-echelon model in which the supplier receives
inventory at fixed intervals. Deuermeyer and Schwarz (1981) and Svoronos and
Zipkin (1988) provide techniques to approximate average costs in a continuous
review model with Poisson demand. Both of them assume no restrictions on when the
retailers may order.
Shapiro and Byrnes (1992) empirically examine demand variance in the medical
supply industry and observe that final demand exhibits little fluctuation, but that
orders from hospitals exhibit dramatic variability. Their results suggest that reducing
the supplier’s demand variance may benefit a supply chain. Axsater (1993) provides
exact methods to approximate average costs in a continuous review model with
Poisson demand under the assumption that no restrictions on when retailers may
order. Song (1994) showed, for a particular definition of demand variability, that the
buffer cost will increase with increasing variability. Lee et al. (1996) assume
synchronized ordering, and retailer orders are always filled either by the supplier or an
outside. Therefore, the supplier’s actions do not impact the retailers, nor do the
retailers’ actions influence the supplier’s demand variance. Cachon and Lariviere
(1996) studied shortage gaming. Chen and Samroengraja (1996) obtain exact results
for a model in which retailers implement base stock policies at fixed intervals and
only one retailer orders at a time. Their work provides exact results with batch
ordering. Fisher and Raman (1996) consider a Quick Response system, an apparel
industry initiative intended to cut manufacturing and distribution lead times through a
variety of means, particularly the cost of excess inventory that must be sold below
cost at the end of the season and of lost sales due to inventory stockouts. They showed
that Quick Response could reduce stockout and markdown costs by reducing lead
time sufficiently to allow a portion of production to be committed after some initial
demand has been observed. Drezner et al. (1996) and Chen et al. (1997) studied
demand updating. Lee et al. (1997) identified the four causes of the bullwhip effect
(i.e. the name given to the common observation that demand variance propagates up a
supply chain): synchronized ordering (all retailers order in the same periods), shortage
gaming (retailers inflate their orders to receive a better allocation), demand updating
(the supplier is unaware of true retailer demand and so must rationally assume a
higher variance), and price fluctuations (retailers purchase more than their short term
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needs to take advantage of temporary price discounts). Chen and Zheng (1997)
provide exact methods to approximate average costs in a continuous review model
with Poisson demand by assuming no restrictions on when retailers may order. Cohen
and Baganha (1998) considered supply chain demand variance, but they do not
consider strategies for reducing the variance of the retailers’ orders. Aviv and
Federgruen (1998) consider both synchronized and balanced alignments and find that
balanced ordering generally has lower costs. Their model has heterogeneous retailers
and a supplier capacity constraint. Cachon (1999) considers five variables that
influence the supplier’s demand variance. Two of them are structural: consumer
demand variability and the number of retailers. The other three are policy parameters:
the retailers’ batch size, the retailers’ order interval length, and the alignment of the
retailers’ order intervals. Kelle et al. (1999) conclude that negative effect of high
variability and uncertainty can be decreased by small frequent orders. These orders
are economical for the partners in the supply chain if the ordering costs are small
relative to the inventory holding cost. Ridder et al. (1999) considers a Newsvendor
problem and concludes that reduction of the demand uncertainty in stochastic
production and inventory systems is economically favorable for most demand
distributions. However, for some demand distributions a reduction of the demand
uncertainty will not result in the desired cost reduction. Federgruen and Zipkin
(1984), Jackson (1988), Jackson and Muckstadt (1989), McGavin et al. (1993),
Nahmias and Smith (1994) and Graves (1996) allow shipments to retailers at
intermediate times between replenishments to the supplier, allowing the supplier to
hold some stock. Their models assume synchronized ordering and unit ordering. They
conclude that the variability of supplier demand has no impact, since the supplier is
concerned only with the total amount of inventory needed at the start of each interval.
Research Analysis
The research area is consideration of a supply chain demand variability in a model
with one supplier and N retailers and with various demand distributions. Demand
distributions that are considered are: Lognormal, Weibull and Beta.
This section describes the proposed research area in detail. The specific questions to
be analyzed are below:
1) Effect of switching from synchronized order intervals to balanced order
intervals on holding and backorder costs.
2) Effect of increasing T on the variability of a single retailer’s order process.
3) Effect of increasing T on average % increase in holding and backorder costs
(relative to T=1).
4) Effect of Flexible Quantity Strategy on holding and backorder costs.
5) Effect of Flexible Quantity Strategy on holding and backorder costs when the
supplier is required to provide a high (above 90%) fill rate.
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Notation
N = number of retailers
p
Dr  consumer demand over p periods
hr = cost per unit of retailer inventory per period
hs = cost per unit of retailer inventory per period
pr = cost per retailer backorder per period
C = average supply chain costs per period = N (hr EI r   pr EBr   hs Qr EI s 
For each location I, the following are defined after demand occurs (event 1) but
before orders are submitted (event 2): on-hand inventory, Ii; backorders, Bi; on hand
inventory, OIi; and inventory position, IPi= Ii - Bi + OIi. On-order inventory is
inventory ordered but not received.
IPi* = inventory position just after the firms order (event 2)
OPi* = on-order inventory just after firms order (event 2)
Assumptions

 p 
1) There exists a finite d such that Pr  Dr  d  =1.


2) The supplier randomly shuffles the retailers’ orders for that period.
3) T  N
4) m* is an integer
5) Holding costs for on-route inventory are ignored.
Model
One supplier distributes a single product to N identical retailers. The retailers
implement scheduled ordering policies. The sequence of events within each period:
1) Demand is realized
2) Firms submit orders to their inventory sources
3) Shipments are released
4) Costs are assessed
5) Shipments are received
Consumer demand is non-negative, stationary, discrete, and independent across
periods. The retailers can order in review periods, which occur every T periods.
Retailers follow a scheduled ordering policy: In any review period when IPr  Rr, a
retailer orders a sufficient integer multiple of Qr units to raise IPr above Rr. Batch size
is Qr. The supplier follows an (Rs, nQs) policy, which is analogous to retailers’ policy,
except the supplier may order in any period. Since the supplier’s demand equals an
integer number of batches, all supplier variables are measured in batches of inventory.
The supplier’s orders are always received in Ls periods. Inventory shipped from the
supplier in period t arrives at a retailer in period t + Lr. Unfilled demands are
backordered, and all backorders are eventually filled.
Since the supplier may receive orders from several retailers within a period, the
supplier must allocate inventory among retailers. The supplier shuffles the retailers’
orders for that period without giving preference to any retailer. The orders are then
placed in an order queue. Orders are filled from this queue on a first-in-first –out
basis. Then the supplier partially ships a retailer order. Balanced orders are possible
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only when N is an integer multiple of T. m* = N/T, therefore, m* retailers order each
period.
Expectation of the proposed model
If we were to change from synchronized order intervals to balanced order intervals,
the supply chain holding cost and backorder cost will decrease. The existence of
consumer demand makes the supplier to carry safety stock to guarantee reliable
deliveries. If balanced orders are implemented, the supplier’s demand variance will
decline as T is increased and the average % increase in holding and backorder costs
relative to T =1, will be significant. Hence, lengthening the retailers’ order intervals
reduces the supplier’s demand variability but increases supply chain holding and
backorder costs. Also, it will reduce the retailer’s ordering frequency, leading to a
reduction in ordering costs.
Generally, a flexible quantity strategy will reduce supply chain costs when there are
few retailers and low consumer demand variability. However, if either consumer
demand variability or the number of retailers were to increase this strategy will lose
its effectiveness. Reducing the supplier’s demand variance through a flexible quantity
strategy is most effective when the supplier is required to offer a high fill rate.
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