Arnab Bisi

A Censored-Data Multiperiod Inventory Problem with Newsvendor Demand Distributions

We study the stochastic multiperiod inventory problem in which demand in excess of available inventory is lost and unobserved so that demand data are censored. A Bayesian scheme is employed to dynamically update the demand distribution for the problem with storable or perishable inventory and with exogenous or endogenous price. We show that the Weibull is the only newsvendor distribution for which the optimal solution can be expressed in scalable form. Moreover, for Weibull demand the cost function is not convex in general. Nevertheless, in all but the storable case, sufficient structure can be discerned so that the optimal solution can be easily computed. Specifically, for the perishable inventory case, the optimal policy can be found by solving simple recursions, whereas the perishable case with pricing requires solutions to more complex one-step look-ahead recursions. Interestingly, for the special case of exponential demand the cost function is convex, so that for the storable inventory case, the optimal policy can be found using simple one-step look-ahead recursions whereas for the perishable case the optimal policy can be expressed by exact closed-form formulas.

Wholesale-price contracts with postponed and fixed retail prices

Abstract We study the wholesale-price contract with retail price-postponement in a supply chain consisting of one manufacturer and one retailer. For additive and multiplicative demand models, we establish sufficient conditions for the unimodality of profit functions and derive unique optimal solutions. We also extend existing results on the fixed retail price case and a revenue management problem.

New structural properties of (s,S) policies for inventory models with lost sales

We revisit the classical inventory model for which (s,S) policies are optimal. We consider the finite and infinite horizon versions of the lost sales problem. New structural properties are developed for the optimal policy and cost function. These properties are then used to develop computational schemes for the lost sales problem with Erlang demands.

Yield management of workforce for IT service providers

Many IT service firms often suffer inadequate staffing and a possible subsequent profit loss. This may happen for a number of reasons: the high cost of timely adjusting a firms workforce capacity, the nature of IT projects, fluctuating market demand, etc. This paper proposes a strategic use of the emerging online market mechanism, known as e-lancing, for yield management of workforce for IT service providers. By dynamically controlling admissions of online and conventional orders, a service provider can reach customers in the online channel and increase profits. The proposed model considers an IT service firm, which receives IT project orders through two channels: a conventional procurement channel and an online spot market such as Elance Online. We employ Markov decision theory to obtain optimal admission control policies. The structures of the optimal policy, which is not of threshold type, are analyzed mathematically and examples are presented numerically. The base model and its extended models, which can serve as useful tools for demand control problems of IT service providers, capture the most important characteristic of IT projects, where if a project is admitted, it seizes a random number of workers simultaneously, then it releases the workers either individually or in a group. Highlights? This paper proposes a new approach that helps IT service firms improve workforce utilization. ? Our Markov Decision model dynamically admits orders from traditional and online channels. ? The model captures the most essential characteristics of IT projects. ? Our results include characteristics of optimal policies and simulation results.

A Periodic-Review Base-Stock Inventory System with Sales Rejection

We consider a system in which an order is placed every T periods to bring the inventory position up to the base stock S. We accept demand until the inventory position reaches a sales rejection threshold M. Our objective is to find the optimal values of S and M that minimize the long-run average cost per period. We establish the stationary distribution of our system and develop structural properties of the optimal solution that facilitate computation. In particular, we show that in an optimal solution, the optimal value of M is nonnegative under some reasonable conditions. Hence, in our model a mixture of backorders and lost sales may occur. Additionally, we compare our system against traditional systems in which demand during stockouts is either fully backordered or lost.

Average Cost Optimality for an Unreliable Two-Machine Flowshop with Limited Internal Buffer

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.

Average Cost Optimal Policy for a Stochastic Two-Machine Flowshop with Limited Work-in-Process

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.

Integrated Contract and Spot Market Procurement by a Risk-Averse Buying Firm

We study the problem of optimally integrating contractual and spot market procurement sources for a risk-averse buying firm that purchases a commodity product at a specified rate over time. The sources involve deterministic and stochastic price processes, respectively. The risk-averse firm is concerned about the magnitude and uncertainty of procurement expenses. The problem is of increasing significance with the emergence of electronic markets that facilitate procurement from competitive spot (open) market. Models are developed to determine the optimal procurement policy in continuous time across the two sources for specified price and risk aversion parameters. We examine cases when the contract price parameter is exogenously specified and when it is endogenously adjusted according to the procurement policy. We show that the optimal strategy prescribes simultaneous procurement from both contract and spot market sources. The applications of the model on illustrative datasets provide insights into the relative advantages of integrating the two sources of procurement over a “pure contract” or a “pure market” procurement source.

A centralized ordering and allocation system with backorders and strategic lost sales

This article considers a multi-retailer distribution system that is managed by a central decision maker who, at the start of each period, determines how much to order to replenish the system stock. The decision maker also determines how to allocate incoming pipeline inventory to maintain inventory balance among the retailers. It has been noted in the literature that balancing inventories can equalize service levels among retailers. To improve the efficacy of the allocation, this article allows some demand to be rejected to keep inventories in balance. Consequently, depending on the realized pattern of demand during the delivery lead time, the inventory is dynamically allocated to each of the retailers. For the model with two retailers, an exact representation of the infinite-horizon long-run average cost function is developed. This exact expression is used to develop conditions for the unique solution for the two-retailer case. The presented analysis holds for a wide class of continuously and discretely distributed demand.

A finite-horizon inventory system with partial backorders and inventory holdback

Abstract We consider a periodic-review base stock inventory system with partial backorders. At the beginning of each period t of a T period problem, an order of size q t is placed for delivery one period later. As the stochastic demand is realized, as much as possible of it is filled immediately from the inventory on-hand. If the realized demand exceeds the inventory on-hand, up to q t – k t units of excess demand are backordered to be filled from the pipeline inventory or future orders. The on-order quantity k t denotes the reservation quantity held back for use in subsequent periods. The case k t = q t yields the full lost sales model while the case k t = − ∞ yields the full backorder model.