Optimal control policies for an inventory system with commitment lead time (original) (raw)
Related papers
Inventory Management with Advance Demand Information and Flexible Delivery
Management Science, 2008
This paper considers inventory models with advance demand information and flexible delivery. Customers place their orders in advance, and delivery is flexible in the sense that early shipment is allowed. Specifically, an order placed at time t by a customer with demand leadtime T should be fulfilled by period t + T ; failure to fulfill it within the time window [t, t + T ] is penalized. We consider two situations: (1) customer demand leadtimes are homogeneous and demand arriving in period t is a scalar dt to be satisfied within T periods. We show that state-dependent (s, S) policies are optimal, where the state represents advance demands outside the supply leadtime horizon. We find that increasing the demand leadtime is more beneficial than decreasing the supply leadtime.
2008
Our aim in this paper is to investigate how variability and uncertainty in advance demand information (ADI) affects the performance of a make-to-stock supplier. To this end, we develop a model of a supplier who receives orders for one item at a time from customers that may belong to one of two classes. Each customer in the first class requests immediate delivery, and hence provides no ADI at all. Each customer in the second class makes a cancelable reservation in advance of his requested due date, and hence provides uncertain ADI. We assume that the supplier uses an order base stock replenishment policy with a release lead time. According to this policy, each customer order triggers the potential placement of a replenishment order by the supplier at a time that is determined by offsetting the demand due date by a fixed planned supply lead time. The replenishment order is actually placed only if there have been fewer cancellations that replenishment orders in the past; otherwise, it is skipped. We investigate via simulation the impact of important ADI related parameters on the optimal decision variables and performance of the replenishment policy, for four different variations of the model. In each variation, the replenishment (or supply) process is represented by a different queueing system. The systems that we consider are the M/M/1, M/D/1, M/M/∞, and M/D/∞ queues, respectively.
A produce-to-stock system with advance demand information and secondary customers
Naval Research Logistics, 2007
We consider a manufacturer (i.e., a capacitated supplier) that produces to stock and has two classes of customers. The primary customer places orders at regular intervals of time for a random quantity, while the secondary customers request a single item at random times. At a predetermined time the manufacturer receives advance demand information regarding the order size of the primary customer. If the manufacturer is not able to fill the primary customer's demand, there is a penalty. On the other hand, serving the secondary customers results in additional profit; however, the manufacturer can refuse to serve the secondary customers in order to reserve inventory for the primary customer. We characterize the manufacturer's optimal production and stock reservation policies that maximize the manufacturer's discounted profit and the average profit per unit time. We show that these policies are threshold-type policies, and these thresholds are monotone with respect to the primary customer's order size. Using a numerical study we provide insights into how the value of information is affected by the relative demand size of the primary and secondary customers.
An integrated inventory model with controllable lead time and distribution-free demand
Applied Stochastic Models in Business and Industry, 2010
The impact of lead time reduction on an integrated periodic review inventory system comprising a single vendor and multiple buyers with a step crashing cost function and service-level constraints is studied. The probability distribution of demand during the protection period for each buyer is unknown, but the mean and the variance are given. Each production lot of the vendor can be delivered in a number of shipments to all buyers. A minimax distribution-free procedure with Lagrange multipliers is applied to determining the lead time, the common shipment cycle time, the target levels of replenishments and the number of shipments per production cycle so that the expected total system cost is minimized. Numerical experiments along with sensitivity analysis were performed to illustrate the effects of parameters on the decision and the total system cost. AN INTEGRATED INVENTORY MODEL 417 lost sales. Moon and Choi [4] pointed out that Ouyang et al. [3] made a mistake by including both the service-level constraint (SLC) and the shortage cost into the model in which both were used redundantly to determine the appropriate level of safety stocks. Hariga [5] developed a stochastic setup cost reduction model with lead time, lot size and setup cost interaction. Chuang et al. [6]
Modelling imperfect advance demand information and analysis of optimal inventory policies
European Journal of Operational Research, 2007
We consider an inventory control problem where it is possible to collect some imperfect information on future demand. We refer to such information as imperfect Advance Demand Information (ADI), which may occur in different forms of applications. A simple example is a company that uses sales representatives to market its products, in which case the collection of sales representatives' information as to the number of customers interested in a product can generate an indication about the future sales of that product, hence it constitutes imperfect ADI. Other applications include internet retailing, Vendor Managed Inventory (VMI) applications and Collaborative Planning, Forecasting, and Replenishment (CPFR) environments. We develop a model that incorporates imperfect ADI with ordering decisions. Under our system settings, we show that the optimal policy is of order-up-to type, where the order level is a function of imperfect ADI. We also provide some characterizations of the optimal solution. We develop an expression for the expected cost benefits of imperfect ADI for the myopic problem. Our analytical and empirical findings reveal the conditions under which imperfect ADI is more valuable.
The value of early order commitment in a two-level supply chain
European Journal of Operational Research, 2007
One approach to supply chain coordination is early order commitment, whereby a retailer commits to purchase a fixedorder quantity at a fixed delivery time before demand uncertainty is resolved. In this paper, we develop an analytical model to quantify the cost savings of an early order commitment in a two-level supply chain where demand is serially correlated. A decision rule is derived to determine whether early order commitment will benefit the supply chain, and accordingly to determine the optimal timing for early commitment. Our results indicate that the supply chain would experience greater savings from early order commitment when -(a) the inventory item receives less value-added activities at the retailer site; (b) the manufacturing lead time is short; (c) demand correlation over time is positive but weak; or (d) the delivery lead time is long (if a condition exists). We also propose a rebate scheme for the supply chain partners to share the gains of practicing early order commitment.
The Value of Advance Demand Information in Production/Inventory Systems
Annals of Operations Research, 2000
Advance demand information, when used effectively, improves the performance of production/inventory systems. In this paper, we investigate the value of advance demand information in production/inventory systems. For a single-stage make-to-stock queue, we assess the value of using advance demand information under a variety of assumptions on the cost of obtaining advance demand information, and the delivery timing requirements. This analysis enables us to identify conditions under which advance demand information may bring significant benefits.
Time-based service constraints for inventory systems with commitment lead time
OR Spectrum
We consider a firm which targets a certain level of customer responsiveness with a minimum operational cost. The firm employs a preorder strategy, in which customers place their orders before their actual need based on a predefined time window called commitment lead time and, in turn, they receive a bonus. The firm aims to determine the optimal control policy, which consists of the optimal commitment lead time and the optimal base-stock level, such that the total operational cost is minimized subject to a time-based service level target. We formulate two time-based service criteria to measure the firm's responsiveness in terms of average customer waiting time and individual customer waiting time in two constraint optimization models called ACO and CCO, respectively. We derive the exact probability distribution of customer waiting time, and we propose exact and heuristic optimization algorithms to solve the ACO and CCO models. We show that the commitment lead time not only increases the firm's responsiveness level but also decreases the customers' maximum waiting time. We find that when the firm targets a high level of responsiveness, the value of commitment lead time is more highlighted. We study multiple interesting extensions with two customer classes, random replenishment lead times and a combined model with two time-based service level targets.
Investigating Reservation Policies of Advance Orders in the Presence of Heterogeneous Demand
SSRN Electronic Journal, 2000
We consider an inventory system, operated by a base stock policy and serving two customer classes. One customer class, Class 1, does not provide any advance demand information at all, while the other, Class 2, does. In order to reward a customer of Class 2 for providing advance order information, it may be sensible to make reservations for the order in the inventory system, thereby preventing later arriving orders from getting access to the inventory before this particular order. We propose various reservation policies and study their impact on the performance of the inventory system.
Optimal Inventory Control with Advance Supply Information
Economic and Business Review
It has been shown in numerous situations that sharing information between the companies leads to improved performance of the supply chain. We study a positive lead time periodic-review inventory system of a retailer facing stochastic demand from his customer and stochastic limited supply capacity of the manufacturer supplying the products to him. The consequence of stochastic supply capacity is that the orders might not be delivered in full, and the exact size of the replenishment might not be known to the retailer. The manufacturer is willing to share the so-called advance supply information (ASI) about the actual replenishment of the retailer's pipeline order with the retailer. ASI is provided at a certain time after the orders have been placed and the retailer can now use this information to decrease the uncertainty of the supply, and thus improve its inventory policy. For this model, we develop a dynamic programming formulation, and characterize the optimal ordering policy as a state-dependent base-stock policy. In addition, we show some properties of the base-stock level. While the optimal policy is highly complex, we obtain some additional insights by comparing it to the state-dependent myopic inventory policy. We conduct the numerical analysis to estimate the influence of the system parameters on the value of ASI. While we show that the interaction between the parameters is relatively complex, the general insight is that due to increasing marginal returns, the majority of the benefits are gained only in the case of ull, or close to full, ASI visibility.