多种变质性物品的经济批量问题

本文考虑了多种变质性物品在同一台设备上生产的最优基本生产周期问题。本文采用了基本周期法,给出了问题的数学模型,分析了模型最优解的存在性,并给出了求解该模型的算法和算例,从算例的结果说明基本周期法比公共周期法解决经济批量问题更优。     

Tutorial on constructing a red blood cell inventory management system with two demand rates

Many countries face the situation where demand for blood products is growing faster than donor recruitment, so the efficient management of available blood supplies is of great economic and social importance. Historically, blood models dealt with two main issues—expiration of blood products with a limited shelf life vs. minimizing blood inventory shortages. Advances in blood storage technologies have resulted in extended shelf lives for some blood products, as well as the ability to use substitute, synthetic blood products at an additional cost. Moreover, prior models do not support multiple demand levels and priorities, where demand for non-urgent blood products can be restricted in event of low inventory levels. The work described in this paper revisits a queuing model and using level crossing techniques, determines an optimal policy to support modeling trade-offs between the following criteria: multiple demand levels (emergency and discretionary), service levels, costs, as well as the traditional objectives of minimizing shortages and expiration (matching supply and demand). Using simulation, the model was compared with current control techniques and demonstrated to be effective using real data obtained from Canadian Blood Services.     

New models and algorithms for the cyclic inventory routing problem

This is a summary of the author’s PhD thesis supervised by El-Houssaine Aghezzaf and defended on 4 December 2006 at the Universiteit Gent. The thesis is written in English and is electronically available from http://ir18.ugent.be/birger.raa/. This work studies the problem of finding optimal three-way cost trade-offs between vehicle fleet costs, distribution costs and holding costs in the cyclic replenishment of a set of customers with constant demand rates from a single depot.      

Effects of imperfect products on lot sizing with work in process inventory

The economic production quantity (EPQ) is one of the most widely known inventory control models that can be regarded as the generalized form of the Economic Order Quantity. However, the model is built on an unrealistic assumption that all the produced items need to be of perfect quality. Also, the introduction of work in process, WIP, as part of the inventory has been of lesser concern in developing inventory models. This paper attempts to develop the economic production quantity considering work in process inventory and manufacturing imperfect products that may be either reworkable or non-reworkable. The non-reworkable imperfect products are sold at a reduced price. This paper introduces a new model for this problem.     

Stochastic leadtimes in a one-warehouse,N-retailer inventory system with the warehouse not carrying stock

This study extends upon a multi-echelon inventory model developed by Graves, introducing in the one-warehouse, N-retailer case—as Graves suggested—stochastic leadtimes between the warehouse and the retail sites in place of the original deterministic leadtimes. Effects of stochastic leadtimes on required base stock levels at the retail sites in the case where the warehouse carries no stock (e.g., serves as a cross-dock point) were investigated analytically. Two alternative treatments of stochastic leadtime distributions were considered. Using as a baseline Graves’ computational study under deterministic leadtimes, results of the current study suggest that it may be better to use the deterministic model with an accurately estimated mean leadtime than a stochastic model with a poorly estimated mean leadtime.     

Optimal integrated production and inventory control of an assemble-to-order system with multiple non-unitary demand classes

We study a pure assemble-to-order system subject to multiple demand classes where customer orders arrive according to a compound Poisson process. The finished product is assembled from m different components that are produced on m distinct production facilities in a make-to-stock fashion. We show that the optimal production policy of each component is a state-dependent base-stock policy and the optimal inventory allocation policy is a multi-level state-dependent rationing policy. Using numerical experimentation, we first study the system behavior as a function of order size variability and order size. We show that the optimal average cost rate is more sensitive to order size variability than to order size. We also compare the optimal policy to the first-come first-serve policy and show that there is great benefit to inventory rationing. We also propose two simple heuristics and show that these can effectively mimic the optimal policy which is generally much more difficult to determine and, especially, to implement.     

Fleet routing position-based model for inventory pickup under production shutdown

This paper addresses the problem of collecting inventory of production at various plants having limited storage capacity, violation of which forces plant shutdowns. The production at plants is continuous (with known rates) and a fleet of vehicles need to be scheduled to transport the commodity from plants to a central storage or depot, possibly making multiple pickups at a given plant to avoid shutdown. One operational objective is to achieve the highest possible rate of product retrieval at the depot, relative to the total travel time of the fleet. This problem is a variant (and generalization) of the inventory routing problem. The motivating application for this paper is barge scheduling for oil pickup from off-shore oil-producing platforms with limited holding capacity, where shutdowns are prohibitively expensive. We develop a new model that is fundamentally different from standard node-arc or path formulations in the literature. The proposed model is based on assigning a unique position to each vehicle visit at a node in a chronological sequence of vehicle-nodal visits. This approach leads to substantial flexibility in modeling multiple visits to a node using multiple vehicles, while controlling the number of binary decision variables. Consequently, our position-based model solves larger model instances significantly more efficiently than the node-arc counterpart. Computational experience of the proposed model with the off-shore barge scheduling application is reported.     

Block seriation problems: A unified approach. Reply to the problem of H. Garcia and J. M. Proth (Applied Stochastic Models and Data Analysis, 1, (1), 25–34 (1985))

In their article, entitled ‘Group technology in production management, the short horizon planning level’, H. Garcia and J. M. Proth have stated the following problem: starting from a (0, 1) binary matrix of size (N x M), how to divide into independent subsets the rows of this matrix simultaneously with a one-to-one corresponding partition of the columns, maximizing the presence of 1s in the intersecting blocks with a joint minimization of the presence of 0s outside of these blocks. The authors have proposed an efficient and very fast heuristic algorithm in comparison with the existing methods of a fast-growing literature on the subject. The only drawback of this algorithm is its dependence on the initial partition. In this paper, we try to improve this algorithm slightly, first in rewriting the objective function in a linear form and secondly in giving computational improvements related to this linear formulation.     

Production lot sizing with process deterioration and machine breakdown

The paper presents a generalized economic manufacturing quantity model for an unreliable production system in which the production facility may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time (when it starts producing defective items) and may ultimately break down afterwards. If a machine breakdown occurs during a production run, then corrective repair is done; otherwise, preventive repair is performed at the end of the production run to enhance the system reliability. The proposed model is formulated assuming that the time to machine breakdown, corrective and preventive repair times follow arbitrary probability distributions. However, the criteria for the existence and uniqueness of the optimal production time are derived under general breakdown and uniform repair time (corrective and preventive) distributions. The optimal production run time is determined numerically and the joint effect of process deterioration, machine breakdowns and repairs (corrective and preventive) on the optimal decisions is investigated for a numerical example.     

Optimal transportation policies for production/inventory systems with an unreliable and a reliable carrier

In this paper, we consider a periodic-review make-to-order production/inventory system with two outbound transportation carriers: One carrier is reliable, the other carrier is less reliable but more economical. The objective is to find the optimal shipping policy that minimizes the total discounted transportation, inventory, and customer waiting costs. Under several scenarios, we characterize the optimal policy and present the structural properties for the optimal control parameters and the key performance measures. Our results provide managerial insights on how a manufacturer can effectively manage its transportation carriers and product shipment. We also discuss several possible extensions of the model.     

Modeling lotsizing and scheduling problems with sequence dependent setups

Several production environments require simultaneous planing of sizing and scheduling of sequences of production lots. Integration of sequencing decisions in lotsizing and scheduling problems has received an increased attention from the research community due to its inherent applicability to real world problems. A two-dimensional classification framework is proposed to survey and classify the main modeling approaches to integrate sequencing decisions in discrete time lotsizing and scheduling models. The Asymmetric Traveling Salesman Problem can be an important source of ideas to develop more efficient models and methods to this problem. Following this research line, we also present a new formulation for the problem using commodity flow based subtour elimination constraints. Computational experiments are conducted to assess the performance of the various models, in terms of running times and upper bounds, when solving real-word size instances.     

Joint pricing and inventory control with a Markovian demand model

We consider the joint pricing and inventory control problem for a single product over a finite horizon and with periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s, S, p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing through numerical examples. The results indicate that it is more beneficial to implement dynamic pricing in a Markovian demand environment with a high fixed ordering cost or with high demand variability.     

A controlled M / G / 1 workload process with an application to perishable inventory systems

We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload . The result is used to obtain the overflow distribution of this controlled workload process; we derive and , where T is the duration of the first cycle. W(t) can be linked to a certain perishable inventory model, and we use our results to determine the distribution of the duration of an empty period.D. Perry was supported by a Mercator Fellowship of the Deutsche Forschungsgemeinschaft.     

A non-stationary periodic review production–inventory model with uncertain production capacity and uncertain demand

In this paper we consider a nonstationary periodic review dynamic production–inventory model with uncertain production capacity and uncertain demand. The maximum production capacity varies stochastically. It is known that order up-to (or base-stock, critical number) policies are optimal for both finite horizon problems and infinite horizon problems. We obtain upper and lower bounds of the optimal order up-to levels, and show that for an infinite horizon problem the upper and the lower bounds of the optimal order up-to levels for the finite horizon counterparts converge as the planning horizons considered get longer. Furthermore, under mild conditions the differences between the upper and the lower bounds converge exponentially to zero.     

基于生长价值跟踪的生鲜农产品采收销售模型

生鲜农产品的生长增值性对于提升渠道价值具有重要贡献。为此,将影响生鲜农产品需求的成熟度进行数学刻画并引入增值性变质库存模型,针对生鲜农产品育成育肥后定时采收销售和达到临界成熟后适时采收销售两种情形建立了农户利润模型,求解出了最优采收销售时间。研究得出,农户适时采收销售获得的利润更大;产品达到临界成熟后,农户无需再付出生产努力。     

Combined pricing and inventory control with multiple unreliable suppliers

We study a general finite horizon, periodic review combined inventory and pricing model with N suppliers and T periods, where both the demands and the supply mechanisms are random. The random supply mechanisms are of a general type that includes most structures encountered in practice. Demands are price dependent according to general, stochastic demand functions. We characterize the optimal combined pricing and ordering policies to all N suppliers. The general results pertain to general independent supply mechanisms. Under random capacities—one of the special random supply mechanisms—they also extend to suppliers that are positively dependent on each other.     

Inventory with service time and transfer of customers and/inventory

An inventory system with two parallel service facilities is considered. A certain number of customers are transferred from longer to shorter queue whenever their difference reaches a prescribed quantity. Along with this customer transfer, a certain quantity of inventory is also transferred, depending on availability. Further, if one of the queues has customers, but has no inventoried items whereas the other has at least one inventoried item to spare, then exactly one item is taken to the former and service begins thereby enhancing the efficiency of the system. Stability of the system is analysed. Several performance measures that helps in efficient design of such systems, are computed. Some numerical results are provided.     

Managing an integrated production inventory system with information on the production and demand status and multiple non-unitary demand classes

In this paper, we study a system consisting of a manufacturer or supplier serving several retailers or clients. The manufacturer produces a standard product in a make-to-stock fashion in anticipation of orders emanating from n retailers with different contractual agreements hence ranked/prioritized according to their importance. Orders from the retailers are non-unitary and have sizes that follow a discrete distribution. The total production time is assumed to follow a k₀-Erlang distribution. Order inter-arrival time for class l demand is assumed to follow a k_l-Erlang distribution. Work-in-process as well as the finished product incur a, per unit per unit of time, carrying cost. Unsatisfied units from an order from a particular demand class are assumed lost and incur a class specific lost sale cost. The objective is to determine the optimal production and inventory allocation policies so as to minimize the expected total (discounted or average) cost. We formulate the problem as a Markov decision process and show that the optimal production policy is of the base-stock type with base-stock levels non-decreasing in the demand stages. We also show that the optimal inventory allocation policy is a rationing policy with rationing levels non-decreasing in the demand stages. We also study several important special cases and provide, through numerical experiments, managerial insights including the effect of the different sources of variability on the operating cost and the benefits of such contracts as Vendor Managed Inventory or Collaborative Planning, Forecasting, and Replenishment. Also, we show that a heuristic that ignores the dependence of the base-stock and rationing levels on the demands stages can perform very poorly compared to the optimal policy.