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.     

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.     

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.     

Age-based vs. stock level control policies for a perishable inventory system

In this study, we investigate the impact of modified lotsize-reorder control policy for perishables which bases replenishment decisions on both the inventory level and the remaining lifetimes of items in stock. We derive the expressions for the key operating characteristics of a lost sales perishable inventory model, operating under the proposed age-based policy, and examine the sensitivity of the optimal policy parameters with respect to various system parameters. We compare the performance of the suggested policy to that of the classical (Q,r) type policy through a numerical study over a wide range of system parameters. Our findings indicate that the age-based policy is superior to the stock level policy for slow moving perishable inventory systems with high service levels.     

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.     

Evaluation of stock allocation policies in a divergent inventory system with shipment consolidation

In this paper we consider a one-warehouse N-retailer inventory system characterized by access to real-time point-of-sale data, and a time based dispatching and shipment consolidation policy at the warehouse. More precisely, inventory is reviewed continuously, while a consolidated shipment (for example, a truck) to all retailers is dispatched from the warehouse at regular time intervals. The focus is on investigating the cost benefits of using state-dependent myopic allocation policies instead of a simple FCFS (First-Come-First-Serve) rule to allocate shipped goods to the retailers. The analysis aims to shed some light on when, if ever, FCFS is a reasonable policy to use in this type of system? The FCFS allocations of items to retailers are determined by the sequence in which retailer orders (or equivalently customer demands) arrive to the warehouse. Applying the myopic policy enables the warehouse to postpone the allocation decision to the moment of shipment (from the warehouse) or the moments of delivery (to the different retailers), and to base it on the inventory information available at those times. The myopic allocation method we study is often used in the literature on periodic review systems.     

An alternative to safety stock policies for multi-level rolling schedule MRP problems

We study the impact of positive lead times on the multi-level lot-sizing problem in a rolling schedule environment. We show how stockout situations may arise even in a context of deterministic demand. We therefore develop a procedure to avoid such stockouts and we compare its performance through a simulation study to a safety stock strategy. Simulation results show the superiority of the proposed procedure.     

Retailer’s inventory policies for a one time only manufacturer trade deal of uncertain duration

This paper models a retailer’s response to temporary manufacturer’s trade deals characterized by a time interval of random length, but with the ending date known before its occurrence. Uncertainty is handled through a reordering point, which serves as a trigger mechanism for a new special order and is activated at the discount termination date. The model generates ordering policies, applicable to any probability distribution and is shown to yield well-known deterministic optimal policies as a limiting case.     

Managing inventory and production capacity in start-up firms

We consider the problem of managing inventory and production capacity in a start-up manufacturing firm with the objective of maximising the probability of the firm surviving as well as the more common objective of maximising profit. Using Markov decision process models, we characterise and compare the form of optimal policies under the two objectives. This analysis shows the importance of coordination in the management of inventory and production capacity. The analysis also reveals that a start-up firm seeking to maximise its chance of survival will often choose to keep production capacity significantly below the profit-maximising level for a considerable time. This insight helps us to explain the seemingly cautious policies adopted by a real start-up manufacturing firm.     

Optimal production and inventory rationing policies with selective-information sharing and two demand classes

This paper studies the impact of partner selection on the value of information sharing in a distribution system with one capacitated make-to-stock manufacturer and two retailers. When the high priority retailer with a higher shortfall cost is the sole partner, in the case that the low priority one places an order, the manufacturer allocates inventory more accurately according to more predictable orders from the high priority retailer. When only the low priority retailer shares information, the manufacturer is better informed about orders from this retailer, which shall trigger rationing decisions. Such intriguing differences in utilizing information from two prioritized retailers further induce different interactions between production and rationing policies and form two distinctive but closely related selective-information sharing systems. We characterize the manufacturer’s optimal production and rationing policies under both systems. Through a numerical study, we emphasize the effectiveness of partnering with the high priority retailer. When the manufacturer can establish information sharing links with only one retailer, such a choice usually brings more benefits despite differences in order sizes and/or demand rates of the two retailers. When a selective-information sharing system is the pilot run to full-information sharing, we find that the value of information throughout the implementation process often exhibits second-mover advantage and such a choice also helps the manufacturer create a more balanced return pattern. Finally, we illustrate that the cost-effectiveness of inventory rationing can be significant and optimally rationing inventory is the prerequisite for the superior of the selective-information sharing system with the high priority retailer.     

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.     

An inventory model for stock with advertising sensitive demand

K. S. Chaudhuri Department of Mathematics, Jadavpur University, Kolkata-700 032, West Bengal, India Corresponding author. Email: shib_sankar{at}yahoo.com Email: k_s_chaudhuri{at}yahoo.com The effect of advertising media and sales effort on future demandof merchandize is considered. In an oligopolistic marketingsystem, it is quite natural to boost sales by using advertisingand sales effort to earn more money from a business sector.Determination of demand and costs due to advertising and saleseffort is quite difficult. The approach in this paper is toconcentrate on investment for the purpose of advertising andincreasing sales effort in order to maximize profit. The paperextends an inventory model over finite and infinite time horizonswhere demand is influenced by the level of stock, advertisingmedia and sales effort. The associated profit maximization problemis solved by the ‘Euler–Lagrange method’.The model is illustrated with a numerical example.     

A lower bound on a class of coordinated inventory/production problems

A new lower bound is given for a class of coordinated multi-product inventory problems. The bound has considerable generality and so far shows promise to be good. This promise includes duplicating two recent excellent results from the literature.     

Optimal replenishment policies for deteriorating items with stock sensitive demand under two-level trade credit and limited capacity

Recently, Min et al. [18] established an inventory model for deteriorating items under stock-dependent demand and two-level trade credit and obtained the optimal replenishment policy. Their analysis imposed a terminal condition of zero ending-inventory. However, with a stock-dependent demand, it may be desirable to order large quantities, resulting in stock remaining at the end of the cycle, due to the potential profits resulting from the increased demand. As a result, to make the theory more applicable in practice, we extend their model to allow for: (1) an ending-inventory to be nonzero, (2) a maximum inventory ceiling to reflect the facts that too much stock leaves a negative impression on the buyer and the amount of shelf/display space is limited.     

Decision making on stock levels in cases of uncertain demand rate

Inventory control is a typical problem of decision making. In this paper a periodic replenishment of stock, the spare parts being of one kind, is discussed for some cases when the demand rate is uncertain. The first decision, before all others in the sequence, is done by assuming an a priori distribution of demand rate. In time, as the demand process goes on, corrections of parameters of the a priori distribution are made according to the accumulated knowledge about past demand. This Bayesian approach to decision making based on learning about the uncertain demand rate is known for the case when the demand rate is unknown but constant. It is shown that this same approach can be used in some cases when the demand rate is unknown and not constant. Results are given and used for inventory control.     

Evaluation of inventory policies with unidirectional substitutions

We propose evaluation approaches to multi-item base-stock inventory policies where unidirectional substitutions are allowed. The problems in the paper are in the context of spare parts management and we identify two substitution cases: substitution upon demand arrivals and substitution upon order deliveries. This leads us to three unidirectional substitution policies, for each of which we develop Markovian models. As the number of part types increases, computational effort required to solve the Markovian models increases rapidly. To reduce computation burden, an approximation approach based on the decomposition of multi-dimensional state transition is used for systems with two or more spare part types. Numerical studies show unidirectional substitution improves various system performance measures such as the average inventory level, the average backlogged demand, and the fill rate. The proposed decomposition approach reduces the computation required to compute the performance measures and the approximation errors seems to be quite small.     

Hospital service levels during drug shortages: Stocking and transshipment policies for pharmaceutical inventory

Journal of Global Optimization - In this study, we consider a health network that faces uncertain supply disruptions in the form of regional, nationwide, or worldwide drug shortages. Each hospital...     

Environmental safety stock: The impacts of regulatory and voluntary control policies on production planning,inventory control,and environmental performance

This paper analyzes the impacts of different pollution control policies on a firm’s decisions of production planning and inventory control. Based on a stochastic model with both demand and environmental uncertainties, we derive the optimal policies of production planning and inventory control under both regulatory and voluntary pollution control approaches, and investigate their operational and environmental effects. We establish that the conventional wisdom which suggests that reduction of environmental waste at the end of a production process also decreases the stock and throughput levels of a production system is not necessarily true. Rather, a regulatory environmental standard that limits the total amount of waste may induce the firm to raise its planned stock level, which would lead to a higher expected amount of environmental wastes before the standard is enforced as well as environmental risks at other stages of the production process. The additional planned stock level, which is termed “environmental safety stock,” can be reversed by using the voluntary control approach that provides the firm with the flexibility to occasionally exceed the environmental standard. We also conduct numerical experiments to analyze the effects of different values of model parameters under different control approaches. The analytical results provide new insights to the impacts of a firm’s production and inventory decisions on the natural environment as well as to the choices of pollution control approaches by decision makers in both the private and public sectors.     

A note on inventory policies for products with residual-life-dependent demand

We study inventory ordering policies for products that attract demand at a decreasing rate as they approach the end of their usable lifetime, for example, perishable items nearing expiration. We consider the “product freshness’’, or equivalently, the time until expiration (“residual life”) as a factor influencing the customer demand. In a profit-maximizing framework, we build on the Economic Order Quantity (EOQ) replenishment model and formulate the inventory ordering problem using a deterministic demand function that is concave decreasing in the the age of the product. We provide analytical results on the optimal ordering policy, including an explicit characterization of the decisions in the linear-demand case, and we develop an easy-to-implement adaptive heuristic policy for the general case. Numerical examples show that the optimal policy generates significant profit gains compared to the traditional cost-based policies and the adaptive heuristic policy performs highly satisfactorily in the tested instances.