备货型商品在三种销售价格下的利润函数（I）

本文考虑的是备货型商品的生产与优化管理。商品的生产过程是随机可控的。需求过程是一个根据销售价格高低来控制的随机过程。本文主要研究是这样一个系统的利润函数。     

On the tradeoff between optimal order-base-stock levels and demand lead-times

We investigate the tradeoff between finished-goods inventory and advance demand information for a model of a single-stage make-to-stock supplier who uses an order-base-stock replenishment policy to meet customer orders that arrive a fixed demand lead-time in advance of their due-dates. We show that if the replenishment orders arrive in the order that they are placed, then the tradeoff between the optimal order-base-stock level and the demand lead-time is “exhaustive”, in the sense that the optimal order-base-stock level drops all the way to zero if the demand lead-time is sufficiently long. We then provide a sufficient condition under which this tradeoff is linear. We verify that this condition is satisfied for the case where the supply process is modeled as an M/M/1 queue. We also show that the tradeoff between the optimal order-base-stock level and the demand lead-time is linear for the case where the supply process is modeled as an M/D/1 queue. More specifically, for this case, we show that the optimal order-base-stock level decreases by one unit if the demand lead-time increases by an amount equal to the supplier’s constant processing time. Finally, we show that the tradeoff between the optimal order-base-stock level and the demand lead-time is exhaustive but not linear in the case where the supply process is modeled as an M/D/∞ queue. We illustrate these results with a numerical example.     

Optimal control of a production-inventory system with customer impatience

We consider the control of a production-inventory system with impatient customers. We show that the optimal policy can be described using two thresholds: a production base-stock level that determines when production takes place and an admission threshold that determines when orders should be accepted. We describe an algorithm for computing the performance of the system for any choice of base-stock level and admission threshold. In a numerical study, we compare the performance of the optimal policy against several other policies.     

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.     

Quality and pricing decisions in production/inventory systems

In this article, we consider the impact of finite production capacity on the optimal quality and pricing decisions of a make-to-stock manufacturer. Products are differentiated along a quality index; depending on the price and quality levels of the products offered, customers decide to either buy a given product, or not to buy at all. We show that, assuming fixed exogenous lead times and normally distributed product demands, the optimal solution has a simple structure (this is referred to as the load-independent system). Using numerical experiments, we show that with limited production capacity (which implies load-dependent lead times) the manufacturer may have an incentive to limit the quality offered to customers, and to decrease market coverage, especially in settings where higher product quality leads to higher congestion in production. Our findings reveal that the simple solution assuming load-independent lead times is suboptimal, resulting in a profit loss; yet, this profit loss can be mitigated by constraining the system utilization when deciding on quality and price levels. Our results highlight the importance of the relationship between marketing decisions and load-dependent production lead times.     

An agent-based model of supply chains with dynamic structures

This paper proposes a common agent-based model for the simulation of MTS and MTO supply chains with dynamic structures. Based on the model, scholars can model supply chains easily. Basic characters of supply chains are proposed in the model. Agents, who are used to simulate the members of supply chains, produce appropriate products by intelligent choices. The relationships among agents are connected by their products. Different agents’ attributes are presented by their knowledge and actions of agents are introduced in the paper. Experiments are produced to show the availability of the agent-based model. The model should be available as a toolkit for the studying of dynamic supply chains.     

The impact of production time variability on make-to-stock queue performance

In this paper, we exploit the distributional Little’s law to obtain the steady-state distribution of the number of customers in a GI/G/1 make-to-stock queueing system. Non-exponential service times in make-to-stock queue modeling are usually avoided or at best, considered in approximations due to difficulties in developing an exact method. By providing a numerical solution of the GI/G/1 make-to-stock queue, we observed the impact of production time variability on optimal inventory control policies. The numerical results prove the degree of errors in the results if an exponential service time distribution were assumed instead of the actual distribution.     

IPA Derivatives for Make-to-Stock Production-Inventory Systems With Backorders Under the (R,r) Policy

This paper addresses Infinitesimal Perturbation Analysis (IPA) in the class of Make-to Stock (MTS) production-inventory systems with backorders under the continuous-review (R,r) policy, where R is the stock-up-to level and r is the reorder point. A system from this class is traditionally modeled as a discrete system with discrete demand arrivals at the inventory facility and discrete replenishment orders placed at the production facility. Here, however, we map an underlying discrete MTS system to a Stochastic Fluid Model (SFM) counterpart in which stochastic fluid-flow rate processes with piecewise constant sample paths replace the corresponding traditional discrete demand arrival and replenishment stochastic processes, under very mild regularity assumptions. The paper then analyzes the SFM counterpart and derives closed-form IPA derivative formulas of the time-averaged inventory level and time-averaged backorder level with respect to the policy parameters, R and r, and shows them to be unbiased. The obtained formulas are comprehensive in the sense that they are computed for any initial inventory state and any time horizon, and are simple and fast to compute. These properties hold the promise of utilizing IPA derivatives as an ingredient of offline design algorithms and online management and control algorithms of the class of systems under study.      

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.     

Queueing analysis on a single-station make-to-stock/make-to-order inventory-production system

We consider a one-station production system that produces standard products for ordinary demands and custom products for specific demands. In this system, the workstation has two manufacturing modes. In mode 1, it produces standard products and, in mode 2, it produces custom products by performing the additional alternating works on one existing finished standard product. Base-stock control policy is applied to control the production of standard products. The fill rate of the ordinary demand and the on-time-delivery-rate of the specific demand are considered as the measures of the qualities of service. By assuming an Markovian system, qualities of service under base-stock policy are obtained; furthermore, the optimal base-stock level can be obtained numerically under the requirements on the qualities of services.