On the optimal control of manufacturing and remanufacturing activities with a single shared server

We consider a single-product make-to-stock manufacturing–remanufacturing system. Returned products require remanufacturing before they can be sold. The manufacturing and remanufacturing operations are executed by the same single server, where switching from one activity to another does not involve time or cost and can be done at an arbitrary moment in time. Customer demand can be fulfilled by either newly manufactured or remanufactured products. The times for manufacturing and remanufacturing a product are exponentially distributed. Demand and used products arrive via mutually independent Poisson processes. Disposal of products is not allowed and all used products that are returned have to be accepted. Using Markov decision processes, we investigate the optimal manufacture–remanufacture policy that minimizes holding, backorder, manufacturing and remanufacturing costs per unit of time over an infinite horizon. For a subset of system parameter values we are able to completely characterize the optimal continuous-review dynamic preemptive policy. We provide an efficient algorithm based on quasi-birth–death processes to compute the optimal policy parameter values. For other sets of system parameter values, we present some structural properties and insights related to the optimal policy and the performance of some simple threshold policies.     

Optimal core acquisition and remanufacturing policies under uncertain core quality fractions

Cores acquired by a remanufacturer are typically highly variable in quality. Even if the expected fractions of the various quality levels are known, then the exact fractions when acquiring cores are still uncertain. Our model incorporates this uncertainty in determining optimal acquisition decisions by considering multiple quality classes and a multinomial quality distribution for an acquired lot. We derive optimal acquisition and remanufacturing policies for both deterministic and uncertain demand. For deterministic demand, we derive a simple closed-form expression for the total expected cost. In a numerical experiment, we highlight the effect of uncertainty in quality fractions on the optimal number of acquired cores and show that the cost error of ignoring uncertainty can be significant. For uncertain demand, we derive optimal newsboy-type solutions for the optimal remanufacture-up-to levels and an approximate expression for the total expected cost given the number of acquired cores. In a further numerical experiment, we explore the effects of demand uncertainty on the optimal acquisition and remanufacturing decisions, and on the total expected cost.     

Theoretical study on the optical activity of spiro[3.3]hepta-1,5-diene

The spectroscopic and chiroptical properties of the title compound 1 has been predicted and interpreted by a quantum mechanical approach using the CNDO-CI modification of Del Bene and Jaffé. The calculated rotational strength of the longest wavelength transitions according to the method of Hug and Wagnière suggests left-handed chirality for levorotatory 1. The assignment is in agreement with previous work. In addition, the same computational method has been employed for spiro[4.4]nona-1,6-diene (2) and spiro[4.4]nonatetraene (3).     

The pseudorotation of cycloheptane—I

The pseudorotation of cycloheptane is described by means of the Fourier expansion of the endocyclic torsion angle ω_i = A sin φ_j + B sin 3φ_j + C sin 5φ_j + D sin 7φ_j; φ_j = Δ/2 + 2πj/7; j = 0, 1,...,6; i = 2j + 4, mod 7 and Δ being a phase angle.The topography of the pseudorotational itineries for the chair/twist-chair and the boat/twist-boat families is discussed. X-ray diffraction data concerning the geometry of 7-membered rings occurring in fused ring compounds are analysed by means of the proposed relationship. The least squares procedure for evaluation of the parameters A, B, C and D is given in an appendix.The calcium salt of cycloheptane car?ylic acid, (C₇H₁₃·COO)₂Ca·5H₂O in solid state, displays disorder closely related to pseudorotation. Preliminary X-ray diffraction data of this structure (to be published elsewhere) are given.     

On the hard core equation of state for nematics

An equation of state is proposed for a system of rods interacting only through hard core repulsions. A quantitative comparison is made with recently proposed equations of state based upon the scaled-particle and Percus-Yevick theory.     

Control of a production-inventory system with returns under imperfect advance return information

We consider a production-inventory system with product returns that are announced in advance by the customers. Demands and announcements of returns occur according to independent Poisson processes. An announced return is either actually returned or cancelled after a random return lead time. We consider both lost sale and backorder situations. Using a Markov decision formulation, the optimal production policy, with respect to the discounted cost over an infinite horizon, is characterized for situations with and without advance return information. We give insights in the potential value of this information. Also some attention is paid to combining advance return and advance demand information. Further applications of the model as well as topics for further research are indicated.