New PDF release: Capacity and Inventory Planning for Make-to-Order Production
By Klaus Altendorfer
The booklet offers diverse types for the simultaneous optimization challenge of means funding and paintings unencumber rule parameterization. the final bills are minimized both together with backorder bills or contemplating a provider point constraint. The on hand literature is prolonged with the combination of a dispensed purchaser required lead time as well as the particular call for distribution. additionally, an endogenous creation lead time is brought. diversified types for make-to-order construction platforms with one or a number of serial processing phases are built. means funding is associated with the processing charges of the machines or to the variety of the machines. effects are equations for carrier point, tardiness, and FGI lead time in one of these construction process. For targeted instances with M/M/1 and M/M/s queues particular suggestions of the optimization difficulties or optimality stipulations bearing on potential funding and paintings free up rule parameterization are provided.
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Additional resources for Capacity and Inventory Planning for Make-to-Order Production Systems: The Impact of a Customer Required Lead Time Distribution
0) for Eq. 12) delivers the expected FGI value of 0. This means in both extreme cases for the utilization there is no FGI in pieces available. The comparison to the limit ρ ! 0 of the FGI lead time shows, that even with the maximum expected FGI lead time at utilization 0 there is no expected FGI in pieces available. The reason for that is that at utilization zero, the input rate has to be zero and for that reason no products are produced. 13) Derivation see Appendix. 13) can only be solved numerically.
1 shows that the service level approaches 0 independently of the distribution parameter β of customer required lead time. For ρ ! e. λ ! 0) the service level reaches a value below 100 % ð1 À β=ðμ þ βÞÞ depending on the relation between processing rate μ and the parameter of the customer required lead time distribution β. The result for ρ ! 0 can intuitively be argued by the fact that each order needs a certain time to be processed which depends on μ and its on-time probability is at ρ ! 0 exactly equal to the probability that the processing time is shorter than the customer required lead time.
Note that in the case of ρ ! 0 with μ ! 1 it clearly follows that η ! 1. Weighting the expected FGI lead time values from Eq. 7) 1 1 À β kþβ Derivation see Appendix. For the limit ρ ! 1 the expected value of FGI lead time approaches 0. From service level equal to 0 at ρ ! 1 it is intuitively clear that nothing can be in the FGI when the utilization reaches 100 %. For ρ ! e. λ ! 0) a certain maximum expected value of FGI lead time can be calculated as μ=ðβðμ þ βÞÞ. This value decreases in β which means the maximum expected FGI lead time value increases when the expected customer required lead time increases.
Capacity and Inventory Planning for Make-to-Order Production Systems: The Impact of a Customer Required Lead Time Distribution by Klaus Altendorfer