Look-back policies for two-stage,pull-type production/inventory systems

We consider a two-stage, pull-type production/inventory system with a known service mechanism at the first stage. Set-ups and start-ups are involved in the operation of the second stage. We develop a production control policy for the second stage, within the class of (R, r) continuous-review policies, that minimizes the long run average total cost. We use a semi-Markov decision model to obtain an optimal policy for the operation of the second stage. The structure of the optimal policy suggests the use of a suboptimal look-back policy that delays the set-up at the second stage if the buffer lacks sufficient raw material. The performance of the system and the average total cost under the suboptimal policy can be obtained approximately using a decomposition algorithm. We show examples justifying the use of this suboptimal policy.This research is supported by the NSF Grant No. NSF-NCR-9110105, NSF Grant No. NSF-DDM-9014868 and by the North Atlantic Treaty Organization Grant No. NATO-CRG-900580.     

An evaluation of inventory and transportation policies of a regional blood distribution system

Blood is a valuable but perishable community resource. Regional blood centers coordinate the blood drawing and inventory policies of the hospital blood banks in a region for more efficient use of the resource. This study used a simulation model to analyze the costs and effects of several different operational policies for a regional blood center. Simulated experiments were carried out in four areas: (1) increasing the amount of blood available, (2) changing the number of delivery vehicles, (3) comparing two types of inventory consignment policies (shipping blood to hospitals with a recall privilege and frequent redistribution of blood amongst regional hospitals) to a direct-sale, no-redistribution policy, and (4) examining the effect of sending fresher blood supplies as inventories to hospitals with lower probabilities of transfusion. The results of the third experiment are presented in detail. It was found that periodic redistribution of the regional inventory yielded lower expiration rates and lower shortage rates. The results of the other three experiments are presented briefly.     

Cost allocation in inventory transportation systems

In this paper, we deal with the cost allocation problem arising in an inventory transportation system with a single item and multiple agents that place joint orders using an EOQ policy. In our problem, the fixed-order cost of each agent is the sum of a first component (common to all agents) plus a second component which depends on the distance from the agent to the supplier. We assume that agents are located on a line route, in the sense that if any subgroup of agents places a joint order, its fixed cost is the sum of the first component plus the second component of the agent in the group at maximal distance from the supplier. For these inventory transportation systems, we introduce and characterize a rule which allows us to allocate the costs generated by the joint order. This rule has the same flavor as the Shapley value, but requires less computational effort. We show that our rule has good properties from the point of view of stability.     

Optimal inventory policies with two modes of freight transportation

Theoretical inventory models with constant demand rate and two transportation modes are analyzed in this paper. The transportation options are truckloads with fixed costs, a package delivery carrier with a constant cost per unit, or using a combination of both modes simultaneously. Exact algorithms for computing the optimal policies are derived for single stage models over both an infinite and a finite planning horizon.     

Rationing policies for some inventory systems

This paper considers inventory systems which maintain stocks to meet various demand classes with different priorities. We use the concept of a support level control policy. That is rationing is accomplished by maintaining a support level, say K, such that when on hand stock reaches K, all low priority demands are backordered. We develop four analytical and simulation models to improve the existing models. Firstly, multiple support levels are used instead of using a single support level. Secondly, a simulation model with a more realistic assumption on the demand process has been provided. Thirdly, a single period deterministic cost minimisation model has been developed analytically. Finally, we address a continuous review (Q, r) model with a compound Poisson process.     

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.     

Constraint programming for stochastic inventory systems under shortage cost

One of the most important policies adopted in inventory control is the replenishment cycle policy. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a constraint programming approach able to compute optimal replenishment cycle policy parameters under non-stationary stochastic demand, ordering, holding and shortage costs. We show how in our model it is possible to exploit the convexity of the cost-function during the search to dynamically compute bounds and perform cost-based filtering. Our computational experience show the effectiveness of our approach. Furthermore, we use the optimal solutions to analyze the quality of the solutions provided by an existing approximate mixed integer programming approach that exploits a piecewise linear approximation for the cost function.     

Determining near optimal base-stock levels in two-stage general inventory systems

This paper proposes an easily implementable, scalable decomposition heuristic for determining near optimal base stocks in two-level general inventory systems. In this heuristic, the general system is decomposed into assembly systems—one for each end product. For these assembly systems, the base-stock levels are calculated separately, taking into account risk-pooling effects for the common components. Our numerical analyses yield two main insights: First, the base-stock levels determined by the heuristic are close-to-optimal. Second, considerable improvements can be obtained compared to common-sense heuristics.     

Uniform distribution of inventory positions in two-echelon periodic review systems with batch-ordering policies and interdependent demands

We consider a two-level inventory system in which there are one supplier and multiple retailers. The retailers face stochastic, interdependent customer demands. Each location employs a periodic-review (R,nQ), or lot-size reorder point, inventory policy. We show that each location's inventory positions are stationary and the stationary distribution is uniform and independent of any other's.     

A comparison of outbound dispatch policies for integrated inventory and transportation decisions

This paper investigates the impact of alternative outbound dispatch policies on integrated stock replenishment and transportation decisions. The logistics literature reports that two different types of such policies are popular in current practice. These are time-based and quantity-based dispatch policies. Considering the case of stochastic demand, the paper presents analytical and numerical results showing that the cost savings obtained through quantity-based policies can be substantial. However, under a quantity-based policy, a specific delivery time cannot be quoted when the customer places an order. Hence, the paper also investigates the cost and customer waiting time implications of hybrid policies and demonstrates that hybrid policies are superior to time-based policies in terms of the resulting costs. Furthermore, although hybrid policies are not superior to quantity-based policies in terms of the resulting costs, they are superior in terms of a service measure which is quantified by the long-run average cumulative waiting time.     

Stability analysis of constrained inventory systems with transportation delay

Stability is a fundamental design property of inventory systems. However, the often exploited linearity assumptions in the current literature create a major gap between theory and practice. In this paper the stability of a constrained production and inventory system with a Forbidden Returns constraint (that is, a non-negative order rate) is studied via a piecewise linear model, an eigenvalue analysis and a simulation investigation. The APVIOBPCS (Automatic Pipeline, Variable Inventory and Order Based Production Control System) and EPVIOBPCS (Estimated Pipeline, Variable Inventory and Order Based Production Control System) replenishment policies are adopted. Surprisingly, all kinds of non-linear dynamical behaviours of systems can be observed in these simple models. Exact expressions of the asymptotic stability boundaries and Lyapunovian stability boundaries are derived when actual and perceived transportation lead-time is 1 and 2 periods long respectively. Asymptotically stable regions in the non-linear Forbidden Return systems are identical to the stable regions in its unconstrained counterpart. However, regions of bounded fluctuations that continue forever, including both periodicity and chaos, exist in the parametrical plane outside the asymptotically stable region. Simulation shows a complex and delicate structure in these regions. The results suggest that accurate lead-time information is essential to eliminate inventory drift and instability and that ordering policies have to be designed properly in accordance with the actual lead-time to avoid these fluctuations and divergence.     

Impacts of two-stage deterioration on an integrated inventory model under trade credit and variable capacity utilization

The joint economic lot sizing problem (JELP) model provides a global view to facilitate the development of a production-inventory policy for an integrated system. However, when a deteriorating item is involved, previous studies have neglected the following two important issues: (1) the deterioration quantity increases the demand for the supplier's capacity, which consequently requires the supplier to recalculate the corresponding average cost and reevaluate the capacity utilization, and (2) given the supplier's production rate, in-transit deterioration imposes restrictions on the delivery distance or in-transit time. Therefore, the existing integrated policies may lead to infeasible solutions for the distribution channel when a deterioration item is included. In view of these two issues, a generalized JELP model under delay in payments is formulated to investigate the integrated production-inventory policy for an item with two-stage deterioration (in-transit and retail deterioration) while incorporating both transportation time and capacity utilization. By developing the average cost functions of the supply chain members and employing several new definitions (e.g., variable capacity utilization), this paper provides a mechanism for measuring the influence of two-stage deterioration on the supplier's capacity utilization for the JELP. Three algorithms are proposed to obtain optimal decisions based on the theoretical results. This paper demonstrates that the supplier's variable capacity utilization is relevant to transportation time and two-stage deterioration, which can be applied to evaluate the feasibility of the integrated production-inventory policy for the deteriorating item. Furthermore, there is a maximum allowable value for the retailer's order cycle.     

Optimizing delivery lead time/inventory placement in a two-stage production/distribution system

In this paper we study a system composed of a supplier and buyer(s). We assume that the buyer faces random demand with a known distribution function. The supplier faces a known production lead time. The main objective of this study is to determine the optimal delivery lead time and the resulting location of the system inventory. In a system with a single-supplier and a single-buyer it is shown that system inventory should not be split between a buyer and supplier. Based on system parameters of shortage and holding costs, production lead times, and standard deviations of demand distributions, conditions indicating when the supplier or buyer(s) should keep the system inventory are derived. The impact of changes to these parameters on the location of system inventory is examined. For the case with multiple buyers, it is found that the supplier holds inventory for the buyers with the smallest standard deviations, while the buyers with the largest standard deviations hold their own inventory.     

Optimal ordering policies in inventory systems with random demand and random deal offerings

In this paper, we determine the optimal order policies for a firm facing random demand and random deal offerings. In a periodic review setting, a firm may first place an order at the regular price. Later in the period, if a price promotion is offered by the supplier (with a certain probability), the firm may decide to place another order. We consider two models in the paper. In the first model, the firm does not share the cost savings (due to the promotion offered by the supplier) with its own customers, i.e. its demand distribution remains fixed. In the second model, the cost savings are shared with the final customers. As a result, the demand distribution shifts to the right. For both the models, in a dynamic finite-horizon problem, the order policy structure is divided into three regions and is as follows. If the initial inventory level for the firm exceeds a certain threshold level, it is optimal not to order anything. If it is in the medium range, it is optimal to wait for the promotion and order only if it is offered. The order quantity when the promotion is offered has an ‘order up to’ policy structure. Finally, if the inventory level is below another threshold, it is optimal to place an order at the regular price, and to place a second order if the promotion is offered. The low initial inventory level makes it risky to just wait for the promotion to be offered. The sum of the order quantities in this case has an ‘order up to’ structure. Finally, we model the supplier's problem as a Stackelberg game and discuss the motivation for the supplier to offer a promotion for the case of uniform demand distribution for the firm. In the first model (when the firm does not share the cost savings with its customers), we show that it is rarely optimal for the supplier to offer a promotion. In the second model, the supplier may offer a promotion depending on the price elasticity of the product.     

A sample-path approach to the optimality of echelon order-up-to policies in serial inventory systems

We present a new proof of the optimality of echelon order-up-to policies in serial inventory systems, first proved by Clark and Scarf. Our proof is based on a sample-path analysis as opposed to the original proof based on dynamic programming induction.     

An efficient approach for dual sourcing inventory systems with Tailored Base-Surge policies

Nowadays most companies use dual sourcing strategies to manage supply chains. Recently, a practical policy called the Tailored Base-Surge (TBS) policy has been proposed to manage the system, and shown to perform well. We study a dual sourcing inventory system with i.i.d. demands and TBS policies. Using the techniques of MacLaurin series analysis, we develop an efficient method to calculate the moments of the inventory position, the bullwhip effect, and performance measures. Numerical experiments show that our method works well.     

Control policies for single-stage production systems with perishable inventory and customer impatience

We consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance.     

Linear programming based decomposition methods for inventory distribution systems

We consider an inventory distribution system consisting of one warehouse and multiple retailers. The retailers face random demand and are supplied by the warehouse. The warehouse replenishes its stock from an external supplier. The objective is to minimize the total expected replenishment, holding and backlogging cost over a finite planning horizon. The problem can be formulated as a dynamic program, but this dynamic program is difficult to solve due to its high dimensional state variable. It has been observed in the earlier literature that if the warehouse is allowed to ship negative quantities to the retailers, then the problem decomposes by the locations. One way to exploit this observation is to relax the constraints that ensure the nonnegativity of the shipments to the retailers by associating Lagrange multipliers with them, which naturally raises the question of how to choose a good set of Lagrange multipliers. In this paper, we propose efficient methods that choose a good set of Lagrange multipliers by solving linear programming approximations to the inventory distribution problem. Computational experiments indicate that the inventory replenishment policies obtained by our approach can outperform several standard benchmarks by significant margins.     

Strategic design of distribution systems with economies of scale in transportation

We formulate and analyze a strategic design model for multi-product multi-echelon distribution systems where there are significant economies of scale in the transportation movements. The key design decisions considered are: the number and locations of distribution centers (DC's) in the system, the number and locations of consolidation centers (CC's), the inventory levels of the various products to be held at the distribution centers, and the routing of shipments (through a consolidation center or direct) between plants and distribution centers. A heuristic solution method is developed that can efficiently find near-optimal solutions. The quality of solutions to a series of test problems is evaluated---by comparison to exact solutions created by enumeration in small tests, and by comparison to lower bounds developed for larger test problems. In the problems for which exact solutions are available, the heuristic solution is within 1% of optimal. The computational procedure appears to hold substantial promise for effective solution of large distribution system design problems.