Supply chain scheduling
The book is a volume out of a series. The authors are both from USA and the present book is the overview and detailed description of more than 20 years scientific work on this topic. The volume is organized in an introductory part and two main parts, in the introduction all the main concepts and basics of scheduling used are presented (including a five-component description scheme for scheduling problems in supply chains). The first part is for centralized scheduling problems, where a single decision maker tries to balance the parts of the supply chain -- here mainly production and distribution. The second part is for decentralized problems, where concurring decision makers are involved, sometimes cooperating, sometimes concurring with each other. What is the main concept of the book? It concentrates on all scheduling driven problems arising in the area of supply chains, all decisions are concrete planning issues. The book does not discuss management problems on a strategic level, but always on a specific planning level (for a certain time horizon). Once the book deals with the topic of pricing, all other problems do not use methods like marketing or forecast, it is assumed that for the problems a set of data is present or will be present in the process of planning the customer supplies. Also the aspect of vehicle routing (or similar typical delivery problems) is not included in the book -- to concentrate on scheduling, not on delivering optimally. So the book may be interesting for managers, but also for mathematicians and management scientists, all who want to see the scheduling behind the decisions. In the introducing chapters, an overview of typical supply chains is given and the solution methods for typical scheduling problems are described: Some well-known polynomial solutions are stated, like SPT (shortest processing time rule), or EDD (earliest due date rule) for scheduling with due dates. Most of the scheduling problems arising from supply chains are hard to solve (which means they are NP-hard problems), here heuristic algorithms ore dynamic programming or branch-and-bound are introduced. For the decentralized problems the main solution ideas come from game theory. Since it is essential for the whole book, I want to describe the ``Five-field-model-representation'' used in the book, an extension from the ``Three-field-model-representation'' for classical production scheduling problems: Classical: Machine environment | process constraints | objective function; for example: 1 | no constraints, all \(n\) processing times known at the beginning | mean completion time -- this problem was one of the first scheduling (sequencing problems) and it is solved with the SPT sequence in \(O (n*\log n)\). 5-Field: machine environment | process constraints | delivery characteristics | number of customers | objective function; for example: 1 | | \(V (1,1)\) iid | \(n\) | \(Dmax\) means there is one machine for production, no constraints for the jobs, one vehicle (\(V(1,1)\) with capacity for 1 job) and iid (immediate individual delivery, which means a completed job is delivered immediately, individually is given by the vehicle capacity), there are \(n\) customers and the objective is \(Dmax\) (the maximal delivery time over all customers). In Part I, the centralized supply chain problems are analyzed in four chapters, offline problems (all processing times are known in advance), online problems (jobs arrive dynamically during the planning time horizon), pricing problems (here the product prices are variable and can be optimally assigned by the planner), subcontracting problems (here parts of the production may be given to subcontractors). All four chapters deal with scheduling methods for the specific problems, some algorithms, NP-hardness proofs and solution ideas are given, additionally typical numerical examples are presented to give an insight in the structural problems for solving them. Part II deals with decentralized problems in three chapters, general issues in planning with conflicting objectives, cooperative games (the conflicting parties are willing to cooperate) and non-cooperative games (the conflicting parties act unfriendly and are not willing to cooperate). The main problem solving idea comes from the game theory and so-called Nash-equilibrium is taken into account. Methods for incentives are presented to reach a better total cost solution by incentives given to the party which schedule must be deteriorated. For non-cooperative games the typical worst-case scenarios and best playing strategies are shown on specific examples. Conclusion: The book presents an impressive overview of the scheduling theory and practice applied to supply chain models (which are present everywhere!), an extensive reference is given for all the work done in scheduling over more than 60 years (the most conceptions are developed later -- in the past 20 years). It is detailed and presents illustrating numerical examples, it contains several algorithms and NP-hardness proofs, each chapter has a concluding part with further research ideas.
scientific article; zbMATH DE number 7451850