A characterization of optimal base-stock levels for a continuous-stage serial supply chain

In this paper, we present a continuous model to optimize multi-echelon inventory management decisions under stochastic demand. Observing that in such continuous system it is never optimal to let orders cross, we decompose the general problem into a set of single-unit sub-problems that can be solved in a sequential fashion. When shipping and inventory holding costs are linear in the stage, we show that it is optimal to move the unit associated with the k-th next customer if and only if the inventory unit is held in an echelon located within a given interval. This optimal policy can be interpreted as an echelon base-stock policy such that the base-stock is initially increasing and then decreasing in the stage. We also characterize the optimal policy when costs are piecewise-constant. Finally, we study the sensitivity of the optimal base-stock levels to the cost structures.multi-echelon; optimal control; unit-tracking decomposition;

Optimal expediting decisions in a continuous-stage serial supply chain

In this paper, we analyze expediting decisions in a continuous-time, continuous-stage serial supply chain facing a Poisson demand process. For each unit in the chain, one must decide at which speed it should be moved downstream, given the state of the system, so as to minimize total supply chain costs. We decompose the problem into a set of one-dimensional subproblems that can be easily solved and characterize the optimal expediting policy: under quite general assumptions, the optimal speed of a given unit accelerates upstream, and then slows down downstream. We finally provide a case study where we estimate the benefits of expediting compared to a fixed transportation speed and show them to be significant.lead-time management; optimal control; unit-tracking decomposition;

Inventory control in production-inventory systems with random yield and rework: The unit-tracking approach

This paper considers a single-stage make-to-stock production–inventory system under random demand and random yield, where defective units are reworked. We examine how to set cost-minimizing production/order quantities in such imperfect systems, which is challenging because a random yield implies an uncertain arrival time of outstanding units and the possibility of them crossing each other in the pipeline. To determine the order/production quantity in each period, we extend the unit-tracking/decomposition approach, taking into account the possibility of order-crossing, which is new to the literature and relevant to other planning problems. The extended unit-tracking/decomposition approach allows us to determine the optimal base-stock level and to formulate the exact and an approximate expression of the per-period cost of a base-stock policy. The same approach is also used to develop a state-dependent ordering policy. The numerical study reveals that our state-dependent policy can reduce inventory-related costs compared to the base-stock policy by up to 6% and compared to an existing approach from the literature by up to 4.5%. From a managerial perspective, the most interesting finding is that a high mean production yield does not necessarily lead to lower expected inventory-related costs. This counterintuitive finding, which can be observed for the most commonly used yield model, is driven by an increased probability that all the units in a batch are either of good or unacceptable quality

The human secretome

The proteins secreted by human cells (collectively referred to as the secretome) are important not only for the basic understanding of human biology but also for the identification of potential targets for future diagnostics and therapies. Here, we present a comprehensive analysis of proteins predicted to be secreted in human cells, which provides information about their final localization in the human body, including the proteins actively secreted to peripheral blood. The analysis suggests that a large number of the proteins of the secretome are not secreted out of the cell, but instead are retained intracellularly, whereas another large group of proteins were identified that are predicted to be retained locally at the tissue of expression and not secreted into the blood. Proteins detected in the human blood by mass spectrometry-based proteomics and antibody-based immuno-assays are also presented with estimates of their concentrations in the blood. The results are presented in an updated version 19 of the Human Protein Atlas in which each gene encoding a secretome protein is annotated to provide an open-access knowledge resource of the human secretome, including body-wide expression data, spatial localization data down to the single-cell and subcellular levels, and data about the presence of proteins that are detectable in the blood

On Determination of Inventory Cost Parameters

Efficient inventory control depends on correct values of inventory cost parameters, such as holding costs, shortage/stockout costs and ordering/setup costs. However, there exists surprisingly little research concerning the size of these parameters or how they should be determined. This thesis is devoted to increasing our knowledge of these matters. The research is presented in the form of five scientific papers, A-D, preceded by a summarizing introduction. The introduction also contains a review of how cost parameters are determined today, and an extended discussion pertaining to the capital cost of holding inventory ? how it ought to be determined and the reasonable values for this cost. Methodologically, the research belongs to the field of applied mathematical modeling and operations research. Papers A, B and D draw from results in financial theory, and in these papers three sources of financial risk associated with holding inventory are investigated, namely stochastic demand (in A and D), stochastic per unit replenishment cost (in A and B) and stochastic ordering cost (in A). Paper C presents a more accurate method for determining the holding cost by employing an Activity Based Costing approach. In Paper E we focus on a two-level distribution system and investigate how the different system parameters influence the induced shortage/stockout cost at the higher echelon that is used to coordinate the system. The conclusions of Papers A, B and D are that the financial risks associated with stochastic demand and setup cost have little influence on the optimal policy, and thus on the inventory cost parameters. In the case of stochastic demand, a minor improvement could be obtained by adjusting the order point. On the other hand, the financial risk associated with stochastic per unit replenishment cost does have a large influence on the optimal policy. We demonstrate that a good estimate of the optimal policy can be obtained through traditional heuristics if the capital cost of holding inventory is computed as the current replenishment cost times a capital cost rate that is the sum of the risk free interest rate and the rate at which the risk adjusted replenishment cost is expected to decrease. The size of the capital cost rate is discussed in Section 7 in the introduction. Empirical data indicate that on average it is fairly low, around 2.5%, and that it can be negative. These results contradict the common hypothesis that the capital cost makes up the main part of the holding cost. The method for determining the holding cost presented in Paper C does not rely on the assumption that the capital cost constitutes the main part of the holding cost. Numerical tests show that substantial cost savings can be made (>20%) when using this method as compared to a more traditional method where the holding cost is computed as a percentage of the product value. The contributions of Paper E include insights into how the induced shortage/stockout cost is influenced by the system parameters. It also contains the determination of simple closed form estimates for this cost. Having a good simple estimate offers a practical means to achieve coordinated control in decentralized systems

The capital cost of holding inventory - A real options approach

This thesis is based on three scientific papers dealing with costs and financial risks associated with keeping stock. Reasonable cost parameters are important to implement an effective inventory control system, which in turn is one of the key activities in logistics management. All three papers consider a single-level inventory system. Single-period, multi-period as well as continuous review systems are investigated. The models are analyzed in a real options framework. Stochastic demand is treated in Paper A and C, stochastic purchase price per unit in Papers A and B and stochastic set-up cost in Appendix 4. The parameters are varied one at a time and they are assumed to follow stochastic processes normally used in financial literature. Both the lognormal Wiener process and the Ornstein-Uhlenbeck process are used. The optimal policy is derived through a backward-pass dynamic programming approach. The expected net present value of the inventory costs associated with the optimal policy is then used to evaluate the cost efficiency of policies based on simple adjustments of well-known heuristics, such as the EOQ-formula. The thesis shows that the financial risk associated with a stochastic set-up cost typically can be neglected when the inventory control parameters are determined. This holds for stochastic demand, too, although a minor improvement could be achieved by a simple adjustment of the order point. It is also shown that autocorrelated demand has very little effect on the optimal inventory policy. The systematic risk of the unit purchase price has a significant effect on the optimal inventory control parameters. It is shown that an excellent approximation is attained if the expected rate of relative decrease in risk adjusted purchase price, i.e., the risk premium, is added to the capital cost rate. The results show that if this rate varies over time, a good policy is to use the average price change over a period of about 1/3 to 2/3 of the order cycle when estimating the risk premium. It can be concluded that one can obtain a close to optimal inventory control system by using well-known heuristics with just minor adjustments of the capital holding cost