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Convex Analysisの二,三の進展について

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The Theory of Industrial Organization

Perspectives in supply chain risk management

We study a single-product setting in which a firm can source from two suppliers, one that is unreliable and another that is reliable but more expensive. Suppliers are capacity constrained, but the reliable supplier may possess volume flexibility. We prove that in the special case in which the reliable supplier has no flexibility and the unreliable supplier has infinite capacity, a risk-neutral firm will pursue a single disruption-management strategy: mitigation by carrying inventory, mitigation by single-sourcing from the reliable supplier, or passive acceptance. We find that a suppliers percentage uptime and the nature of the disruptions (frequent but short versus rare but long) are key determinants of the optimal strategy. For a given percentage uptime, sourcing mitigation is increasingly favored over inventory mitigation as disruptions become less frequent but longer. Further, we show that a mixed mitigation strategy (partial sourcing from the reliable supplier and carrying inventory) can be optimal if the unreliable supplier has finite capacity or if the firm is risk averse.

Contingent rerouting is a possible tactic if the reliable supplier can ramp up its processing capacity, that is, if it has volume flexibility. We find that contingent rerouting is often a component of the optimal disruption-management strategy, and that it can significantly reduce the firms costs. For a given percentage uptime, mitigation rather than contingent rerouting tends to be optimal if disruptions are rare.

https://pubsonline.informs.org/doi/suppl/10.1287/mnsc.1060.0515/suppl_file/mnsc.1060.0515-sm-tomlin_companion_5_06.pdf

On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks

This survey reviews the forty-year history of research on transportation revenue management (also known as yield management). We cover developments in forecasting, overbooking, seat inventory control, and pricing, as they relate to revenue management, and suggest future research directions. The survey includes a glossary of revenue management terminology and a bibliography of over 190 references.

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Revenue Management: Research Overview and Prospects

We investigate a production planning problem in a periodic review environment with variable production capacity, random yields, and uncertain demand. The implications of random yields and variable capacity for lot sizing previously have been explored separately, but not jointly. Many production environments are likely to be subject to both types of uncertainties. To minimize the total discounted expected costs production, holding, and shortage costs, we formulate the problem as a stochastic dynamic program. For the finite-horizon problem, we prove that the objective function is quasi-convex and that the structure of the optimal policy is characterized by a single critical point for the initial stock level at each period. That is, if the initial stock is greater than this critical point, the optimal planned production is zero; otherwise, it is greater than zero. Expressions for solving the critical point and the optimal planned production are obtained. We further show that the solution for the finite-horizon problem converges to that of the infinite-horizon problem.

Periodic review production models with variable capacity, random yield, and uncertain demand

This paper extends recent results of Baker et al. Baker, K. R., M. J. Magazine, H. L. W. Nuttle. 1986. The effect of commonality on safety stocks in a simple inventory model. Management Sci.32 982-988. in understanding the impact of component commonality on stocking levels under service level constraints. A model is formulated for an arbitrary number of products with general joint demand distribution. The results obtained are not all intuitive. While utilizing commonality is beneficial, nothing general can be said about the resulting change in the components' stock levels. When the cost structure is of a particular simple form, though, some interesting general patterns do emerge. We also discuss the case of using a service-level measure where rationing of common components might be required, and characterize the implied rationing rule.

Component Commonality with Service Level Requirements

We study a joint lot sizing and inspection policy under an EOQ model where a random proportion of units are defective. Those unitscan be discovered only through costly inspections. The problem is thus bivariate: both lot size and fraction to inspect are to be chosen. We first analyze a model in which the only penalty for uninspected defectives is financial, and then consider a model where defective units cannot be used and thus must be replaced by non-defective ones.

Joint lot sizing and inspection policy in an EOQ model with random yield

A periodic-review production model with variable yield (uncertain supply) and uncertain demand is formulated and investigated. First, we provide a complete analysis of the final (single) period problem. The order point turns out to be unaffected by the yield distribution, but the expected yield corresponding to optimal lot size generally does not equal the difference between the order point and initial stock. We then explore properties of the two-period problem, the solution of which is generally non-myopic. Finally, the solution structure of the n-period problem is reported.

Periodic Review Production Models With Variable Yield And Uncertain Demand

We explore analytically cardinal effects of the extent of demand randomness on optimal inventory levels and the associated expected costs. To model changes in demand randomness, we make extensive use of a mean-preserving transformation commonly used in probabilistic microeconomics, as well as the notion of risk-pooling aggregating independent demands. For the single period news vendor model, the order quantity and associated costs are shown to depend on the randomness parameter in a simple and highly interpretable manner. We show by a simple example that in some situations risk pooling might neither reduce inventories, nor move them closer to the mean or median demand. The managerial relevance of such analyses is discussed.

Yigal Gerchak

Papers

Periodic review production models with variable capacity, random yield, and uncertain demand

Component Commonality with Service Level Requirements

Joint lot sizing and inspection policy in an EOQ model with random yield

Periodic Review Production Models With Variable Yield And Uncertain Demand

On the effect of demand randomness on inventories and costs