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.

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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.

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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.

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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.