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8/6/2019 Tamlin Suppy Chain Disruptions
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Capacity Investments in Supply Chains: Sharing the Gain Rather Than Sharing the Pain
Brian Tomlin
Manufacturing & Service Operations Management Vol. 5, No. 4, Fall 2003, pp. 317333
The supply chain risk investigated in this paper is demand uncertainty. The problem setting is one
supplier, one manufacturer, one time period. His modeling has similarity to the newsvendor problem.
The supplier and the manufacturer decides on capacity at the beginning of the period, the manufacturerorders from supplier and produces after observing the demand. There is no extra cost of lost sales, only
loss of possible profit. The article is interested in the capacity of the supplier and trying to use price
contract to coordinate the supply chain. The supplier's capacity is restricting because the supplier wouldnot install capacity more than the manufacturer's capacity, as there is zero probability of the supplier
selling to manufacturer more than the manufacturer's capacity.
The result is, the manufacturer's optimal contract is a quantity-premium price only schedule, that is, theaverage wholesale price per unit increases in the order size. This is opposite of trying to get discount at
ordering larger amounts. The manufacturer promises higher margin for larger order so that the supplier
would install more capacity. The higher average payment is dubbed as sharing the gain. Simplepiecewise linear (one or two breakpoints) quantity-premium schedules are shown to be highly efficient.
There is an extension for comparing firm-commitment (if order is less than a level, the difference is
compensated) to single-break-point quantity-premium contracts. If wholesale price is higher than alimit than quantity-premium is always better for higher capacity, if price is lower than the desired
capacity plays a role. If higher capacity is desired, firm-commitment is better, there is a threshold value
of capacity.
8/6/2019 Tamlin Suppy Chain Disruptions
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Process Flexibility in Supply Chains
Stephen C. Graves Brian T. Tomlin
Management Science Vol. 49, No. 7, July 2003, pp. 907919
The supply chain risk investigated in this paper is demand uncertainty. There is a multistage, multi-
product supply-chain. The problem is to satisfy the uncertain demand with available capacity. There is
no failure, the capacity of nodes in the supply chain are fixed and known. Nodes in the supply chaincan have flexibility in meeting the demand for more than one of the end products. They want to
compare different supply chain designs with different production flexibilities in terms of how much of
the uncertain demand of end products can be met with the given design. They define inefficiencies forsuch flexible supply-chains as floating bottlenecks and stage-spanning bottlenecks. These bottlenecks
cause unused capacity and unmet demand. They develop a metric g and show in simulations that higher
value of g protect against inefficiencies.
8/6/2019 Tamlin Suppy Chain Disruptions
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On the Value of Mix Flexibility and Dual Sourcing in Unreliable Newsvendor Networks
Brian Tomlin, Yimin Wang
Manufacturing & Service Operations Management Vol. 7, No. 1, Winter 2005, pp. 3757
There is one company, one or many resources, many (two) products and one period. The problem is to
meet the unknown demand with resources that has some probability of failure. The company invests in
resource capacity at the beginning of the period. Production planning is made after demand andresource failures are observed. The result is flexible networks are good for demand uncertainty but
dedicated resources are better if there is a higher failure rate or the company is risk averse.
Four configurations are compared: 1) SD: single-source dedicated network, two products each are
produced at separate source. 2) SF: single-source flexible network, two products both produced in the
same source 3) DD: dual-source dedicated network. Each product has two facilities 4) DF dual source
flexible network. Each product has a dedicated facility and there is third flexible facility that canproduce both products. Flexibility is good for meeting uncertain demand, dual sourcing is good for
meeting demand when there is source failure probability.
The firms investment problem is formulated as a two-stage stochastic program. In the second stage,
after demands and investments have been realized, the firm allocates production to maximize the
contribution. Capacity investment has a linear cost. The risk neutral firm maximizes profit which is theexpected value of sales minus investment and production costs. The loss averse firm uses a weight
higher than one for loss instances in calculating expected profit. The firm interested in the downside
uses mean of a percentage of the left tail of the wealth distribution to calculate the expected profit.
The flexibility premium is defined as the relative difference in the marginal total costs at which the firm
is indifferent between SD and SF networks. Higher than zero implies firm is willing to pay a higher
price for flexibility and lower than zero implies the firm requires a lower price for flexibility to bepreferred. They show that the SF network is preferred to the SD network for all reliabilities and for all
demand distributions in the case of a risk-neutral firm facing equal resource reliabilities and costs.
(indifferent if there is perfect correlation between demands.) When firm is not risk-neutral theflexibility premium value goes down and can be negative for higher failure risks. The downside of the
single facility breaking down can be higher than the upside of flexible production in meeting uncertain
demand.
Numerical study is performed to compare all four (SD, SF, DD, DF) networks. Experiment design
factors are correlation of demand signals, relative contribution margin of products, source reliability
probabilities and degree of risk aversion including risk-neutral. Source failures are independent andidentical. A full factorial design of 7599=2,835 instances were solved for each of the four
networks. For each instance 200 demand couples are generated to calculate expected profit for each
instance.
The result of the numerical study, as expected, finds that the desirability of a dual-sourcing network
(DD versus SD or DF versus SF) increases as supply-chain reliability decreases. They further reportthat flexible sourcing is more preferable as demands become more negatively correlated, or the spread
in contribution margins increases, or the number of products increases. The dedicated sourcing is more
preferable when resource investments become less reliable or firm becomes more concerned about thedownside risk.
8/6/2019 Tamlin Suppy Chain Disruptions
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On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption
Risks
Brian Tomlin
Management Science Vol. 52, No. 5, May 2006, pp. 639657
In this article there is a single product and a single firm with two suppliers, one reliable and one
unreliable. Unreliable supplier fails from time to time such that it supplies nothing. There is infinite-horizon and full backlogging of unmet demand.
The aim is to show the value of having a plan for the possibility of a supplier's failure. In generalcompanies do not plan for supplier failure so by default choose the acceptance strategy, which is
optimal only if the failure happens with a very low probability and the supplier's time to recover is
short. In the real life examples given, companies that do something after a supplier disruption, ended
up being more successful than other companies which were affected by the same calamity and justwaited for the supplier to recover.
Actions taken by companies for a supplier failure can be categorized as mitigation or contingencytactic. Mitigation tactics are those in which the firm takes some action in advance of a disruption (and
so incurs the cost of the action regardless of whether a disruption occurs). Contingency tactics are those
in which a firm takes an action only in the event a disruption occurs. The contingency tactic in thearticle is paying the reliable supplier to increase capacity in case of failure.
An example of contingency tactics, which is not modeled but mentioned, is demand management.Demand management is switching customer demand to a substitute. Another strategy is financial
mitigation. Financial mitigation is being compensated by insurance or something similar for losses due
to the disruption.
Contingency tactic of using another source needs a readily available reliable source with volume
flexibility. The firm balances the replenishment cost of the backlogged demand to carrying inventory
and rerouting orders. Capacity of the unreliable supplier, the flexibility of the reliable supplier, the riskaverse or neutral nature of the firm, the probability of the supplier being up and the expected length of
down time of the supplier are elements that impacts the selection of the best tactic.
In conclusion firms has to be ready for downtime of their suppliers. Using inventory mitigation is
not an attractive strategy in an environment of rare but long disruptions, as significant quantities of
inventory need to be carried for extended periods without a disruption. So it may best for the firm to
plan for an alternative supplier in case the current supplier goes down for some reason and is not likelyto resume production anytime soon. Advance notice of an upcoming disruption, to be discussed in later
articles, would change the strategies and decrease the cost of tackling the problem.
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On the Value of a Threat Advisory System for Managing Supply Chain Disruptions
Brian T. Tomlin, Lawrence V. Snyder
Working paper Current version: April 26, 2007
This article is about the value of information about the failure risk of the supplier. The article assumes
that the firm can observe and calculate the failure risk fully and in the risk is regularly updated. The
benefit of the risk system is the cost reduction that comes from changing inventory level and use of anadditional supplier when necessary. They conclude that there is a value to a system that analyzes and
updates risk in suppliers. The value is calculated by comparing the cost if the firm employs a single
strategy disregarding the changes in risk and the adaptive inventory level and supplier policy thatchanges with changing risk and recovery probabilities.
They assume that the supplier has multiple threat levels with different failure probabilities that can be
observed and identified. The change between threat levels is a Markov process independent of timepassed since last recovery. After a failure, the recovery probability in the next period depends on the
time passed since the failure, the state from which failure occurred and the threat level of the supplier
after the recovery. There is full backlogging of unmet demand. When model has finite number ofperiods the ending inventory is salvaged.
The value of the threat advisory is significantly influenced by the structure of the disruption riskprocess and the supplier capacity. The structure of the disruption risk process consists of the relative
disruption risk in different threat levels and the nature of transitions between threat levels. When there
is an alternative supplier available, in the finite horizon, the product life-cycle may affect the strategychosen.
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The power of flexibility for mitigating supply chain risks
Christopher Tang, Brian Tomlin
Int. J. Production Economics 116 (2008) 1227
The article models five different instances to show that investing in flexibility gives back in significant
savings. They report that firms are reluctant to invest in flexibility because reliable data and accurate
cost-and-benefit analysis are hard to obtain. They conclude that with the examples they have showneven when data is inaccurate firms are better off by investing in some flexibility rather than doing
nothing to prepare for a possible disruption. The cost of investment for flexibility is not discussed.
They do not consider rare events that may disturb a supply chain. They model a different strategy to
deal with each risk, so 5 in total. For each strategy, they plot the various degrees of the flexibilities
versus the percentage gain over no flexibility. They show in every model that gain from flexibility is an
increasing concave function. So they conclude even a low degree of flexibility would bring significantbenefit and be better than not planning for a possible disturbance.
Here are the models considered in the rest of the paper:
Model 1. The risk is supplier's cost is random. The strategy is to use have more than one supplier and
order all from the cheapest. The number of suppliers ranges from one to five. The price of each supplieris IID. The percentage cost reduction of multiple suppliers compared to one supplier is a concave
increasing function.
Model 2. The risk is the demand is random. The strategy is to have a flexible amount supply contract
rather than fixed amount contract. The firm places the order before the demand happens. After the
demand I realized, the firm has percentage flexibility in changing the amount of the order up or down.
For different values of flexibilities, the percentage profit gain over fixed order profit is a concaveincreasing function.
Model 3. The risk is the capacity of the plants. The flexibility is the ability of plants to produce morethan one product. Demand for each product is equal and constant. The model has four products and
four plants. The numerical example shows margin improvement in sales, ability to meet the demands,
for 2 flexible system. Expected profit for 2,3 and 4 flexible plant system is same. So they say it is aconcave increasing function in flexibility.
Model 4. The risk is the uncertain demand. The flexibility is postponement of product differentiation.
There are 2 products. Production takes T periods for both. Both products begin as a generic product anddifferentiates at time 'tau'. It takes T-'tau' periods to transform the generic product into 2 different end
products. The model has infinite-horizon and full backlogging of unmet demand. Percentage savings in
safety stock over no postponement is plotted for two different demand models. Savings in IID(independent and identically distributed) demand is linear and RW (random walk) demand is concave
and increasing with increase in postponement 'tau'.
Model 5. The risk is the uncertain demand. There are two substitutable products. Flexibility is the
timing of the pricing decision on the products. As more time passes demand is less uncertain. Demand
shock terms are additive and follows auto-regressive process of order one (AR(1)). The plot ofpercentage increase in expected profit via t postponement over zero postponement is increasing and
concave in t.
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Disruption-Management Strategies for Short Life-Cycle Products
Brian Tomlin
Naval Research Logistics, June 2009, 56 (4), 318-347.
There are two risks, supplier may fail and the demand is uncertain. There are three methods considered
for mitigating these risks, supplier diversification, contingent sourcing and demand switching. These
three methods are investigated in all possible combinations resulting in twelve strategies. There is oneperiod, a newsvendor type setting. Cases of a single product and two products are investigated.
There is a cost of ordering per unit, so the firm pays something even when the supplier fails to shipgoods. There is no cost of having a supplier diversification. Both suppliers are same in every aspect,
like cost and risk of failure. The contingent source has a higher marginal cost and perfect reliability.
There is no fixed cost to retain a contingent source. Switching demand has an extra cost and there is a
limited fraction of customers who are willing to switch. The firm is modeled both as risk-neutral andrisk-averse. For the risk averse firm the utility is equal to profit when there is a profit and when there is
a loss the firm's utility is a multiple of the loss, where multiplier is bigger than one.
For the single product, obviously, there is no demand switching. So there is a total of four possible
strategy combinations. When the firm uses only a contingent supplier, the initial order amount is same
as when the firm uses no strategy. The contingent source is only used in case of the supplier's failure. Incase of supplier diversification, the firm uses two identical suppliers. The optimal ordering amount is
same for both suppliers. The total initial order is either equal to when there is a single supplier or more.
The firm orders more and makes inventory hedging when the contingent source is unavailable or veryexpensive compared to regular suppliers. If the firm is risk-averse, the firm may choose a strategy
where the contingent source is used even when the regular supplier delivers. This strategy happens
when the firm is very risk-averse and the supplier reliability is low. The article concludes single product
case with some numerical results to compare single-tactic strategies, use of dual-sources and contingentsource. For the risk neutral firm, the benefit of using a single tactic is less than 1% when supplier
reliability is higher than 97%, (the base case reliability is 98.5%).
For the two product firm, if there is no demand switching, the risk-neutral firm acts equivalent to one
product case. If there is no demand switching, the risk-averse firm prefers dedicated sourcing to single
common sourcing, where risk-neutral firm is indifferent between them. When there is demandswitching some results about strategies is given by assuming deterministic equal demand for both
products. Optimal single-tactic under different conditions (base, risk averse, negative correlation, high
product substitutability) is investigated (demand covariance versus supplier reliability) by numerical
studies. Another numerical study is made to compare two-tactic strategies for risk-neutral firm. If eithersupply or demand risk is negligible, two-tactic strategy does not add value over single tactic. Best two-
tactic strategy delivered on average about 90% value of the three-tactic strategy.
Three extensions to the model are: alternative dual sourcing strategies, contingent capacity reservation
and non-identical suppliers. The alternative dual sourcing compares sourcing for two products and
more than one suppliers. The regular model uses two suppliers which supply both products. Theextension defined as shared dual source is three suppliers where one supplies both products, the others
are dedicated suppliers. The extension defined as dedicated dual source has four suppliers where each
product has two dedicated suppliers. The ability to switch demand makes these extensions moreprofitable than base case. If the firm has to reserve capacity at the contingent supplier for a cost, using
contingent supplier becomes less desirable. If the firm uses contingent supplier, for the risk-neutral firm
the initial order may differ and the contingent source may be used even if the supplier does not fail.
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The article concludes that depending on the conditions a firm is in, the strategy that is best for a firm
differs. Thus same strategy may not be best for every firm. If the firm is risk-averse, implementation of
some form of strategy is more important.
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Impact of Supply Learning When Suppliers Are Unreliable
Brian Tomlin
Manufacturing & Service Operations Management, Spring 2009, Vol. 11, No. 2, pp. 192-209
There are two risks, supplier failure and unknown demand. The supplier's failure rate is not known for
sure and the firm updates the probability over time. Supplier uncertainty is modeled as both all or
nothing and percentage yield. There is a cost of ordering that is linear to the order amount that is paideven if the supplier fails. There is a minimum order amount. Supplier lead times are assumed to be
zero. Demand no filled in a period is lost and incurs a cost of \pi per unit.
In the first model there are two suppliers. First supplier's failure rate is known. The failure rate of the
second supplier is assumed to follow a Beta family distribution. A Beta distribution easily updates after
a Bernoulli trial. There are T time periods, inventory cannot be carried from one period to the next and
unfilled sales are lost. The model minimizes cost. Because of equivalence of expectation, after thedecision to whether or not to source from supplier two, the amount of order is independent of
uncertainty on the second supplier's failure rate. If it is not optimal to order from second supplier in a
period then for the rest of the periods it will not optimal to order from the second supplier. Closed formsolution do not exist in general to which estimated values of the distribution that the second supplier
becomes unprofitable. Second supplier can be more attractive or stay attractive by having a lower
ordering cost and or lower minimum order amount.
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To Wait or Not to Wait: Optimal Ordering Under Lead Time Uncertainty and Forecast Updating
Yimin Wang, Brian Tomlin
Naval Research Logistics, 2009, Vol 56, pp. 766-779
Managing Disruption Risk: The Interplay Between Operations and Insurance
Lingxiu Dong, Brian Tomlin
Working Paper
Mitigating Supply Risk: Dual Sourcing or Process Improvement
Yimin Wang, Wendell Gilland, Brian TomlinManufacturing & Service Operations Management, Summer 2010, Vol. 12, No. 3, pp. 489-510
Regulatory Trade Risk and Supply Chain Strategy
Yimin Wang, Wendell Gilland, Brian TomlinProduction and Operations Management, Forthcoming.