Dynamic demand lot-sizing rules for incremental quantity discounts

Numerous studies have developed and compared lot-sizing procedures for finite-horizon dynamic demand, material requirements planning (MRP), environments when either no purchase discounts exist or for the case of all-units quantity discounts. This paper examines lot-sizing rules when product price schedules follow incremental quantity discounts. The optimal (non-discount) procedure and some traditional heuristic procedures are modified to incorporate incremental quantity discounts. We further modify two heuristics with a ‘look-ahead enhancement’ that performs very well under experimentation. Numerical tests revealed the overall best-performing heuristic in this study to be a modified ‘least-unit cost’ method with a look-ahead enhancement. That procedure produced an average cost penalty vs optimal of 0.26%.     

Computing mountain passes and transition states

The mountain-pass theorem guarantees the existence of a critical point on a path that connects two points separated by a sufficiently high barrier. We propose the elastic string algorithm for computing mountain passes in finite-dimensional problems and analyze the convergence properties and numerical performance of this algorithm for benchmark problems in chemistry and discretizations of infinite-dimensional variational problems. We show that any limit point of the elastic string algorithm is a path that crosses a critical point at which the Hessian matrix is not positive definite.This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

Purchasing decisions under stochastic prices: Approximate solutions for order time, order quantity and supplier selection

This paper analyzes purchasing strategies for retailers regarding the best timing and amount of purchases when operating under combined timing and quantity flexibility contracts in an environment of uncertain prices. To decrease the computational complexity and make the procedure adaptable to the case of multiple suppliers, we introduce, analyze, and compare a ??time strategy?? and a ??target strategy?? and then develop a hybrid ??adaptive target strategy?? to facilitate and improve the purchasing decision for the case of option contracts with generally rising prices. The adaptive target strategy is simpler and more intuitive than the traditional binomial lattice method, while the risk of failing to meet a target profit can also easily be calculated. We then extend the solution procedure to maximize expected profits in an environment of selecting among multiple suppliers with potentially different price processes, and we further provide risk analysis to help determine a good estimate for the number of option contracts from different suppliers to generate in order to create adequate risk protection. Numerical analysis demonstrates how the number of candidate suppliers impacts the expected profit and the risk. Monte Carlo simulation results demonstrate that the developed solution procedures provide satisfying outcomes and that the calculation is fast, even for multiple-dimension and multiple-supplier cases.     

Use of Adsorbents for Recovery of Acetic Acid from Aqueous Solutions Part II—Factors Governing Selectivity

Measurements have been made of uptake of acetic acid and water from low-pH aqueous solution onto polymeric adsorbents and activated carbons. In additon to composite isotherms, isotherms were obtained for acetic acid and water individually by use of gas-chromatographic and Karl Fisher techniques for analyses of both bulk solution and the material taken up by the adsorbent. While capacities for acetic acid are determined by the surface area and the chemical nature of the adsorbent, selectivity is governed by the pore volume and the wetting and swelling tendencies of the sorbent, with the latter being particularly important for polymers. Activated carbons and pyrolyzed polymers give better selectivity than do common polymeric adsorbents.

Measurements of pore volume by immersion in various liquids were compared with pore volumes computed from nitrogen adsorption-desorption measurements and from mercury-intrusion porosimetry. The nitrogen adsorption-desorption results were interpreted to obtain micropore and mesopore volumes. The results from the different methods agree well, if allowance is made for lack of full wetting and for swelling tendencies. Higher selectivity for acetic acid over water is obtained for adsorbents having a large percentage of the pore volume as micropores.

Measurements of competitive adsorption of acetic acid and methyl ethyl ketone from aqueous solution onto different carbons and pyrolyzed polymers showed that a higher surface density of active hydrogen sites, as measured by reaction with LiAlH₄, leads to an improved selectivity for the carboxylic acid.     

Coordinating contracts for supply chains that market with mail-in rebates and retailer promotions

Marketing promotions are pervasive in industry, yet too often they are introduced without regard to their potential impact on the whole supply chain. This paper considers a cooperative business environment where a manufacturer and a retailer work interactively in determining their independent sales promotional actions. We use a newsvendor-modelling framework to study coordinating issues when the manufacturer provides mail-in rebates directly to consumers while the retailer exerts promotional effort to further spur consumer demand. We find that quantity discount contracts in conjunction with buy-back achieve supply chain coordination. Successful coordination can result in significant supply chain improvement, which leads the retailer to order more units and exert higher promotional effort level. With numerical examples, we provide additional insights on the conditions for the manufacturer to offer rebates.     

Die Untersuchung von Eisengallustinten

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