Joseph M. Milner

Supply chain capacity and outsourcing decisions: the dynamic interplay of demand and supply uncertainty

We study the interplay of demand and supply uncertainty in capacity and outsourcing decisions in multi-stage supply chains. We consider a firms investment in two stages of a supply chain (Stage 1 models the “core” activities of the firm, while Stage 2 are the “non-core” activities). The firm invests in these two stages in order to maximize the multi-period, discounted profit. We consider how non-stationary stochastic demand affects the outsourcing decisions. We also consider how investment levels are affected by non-stationary stochastic supply when the market responds to the firms investments. We characterize the optimal capacity investment decisions Tor the single- and multi-period versions of our model and focus on how changes in supply and demand uncertainly affect the extent of outsourcing. We find that as the responsiveness of the market to investments made by the firm increases, the reliance on outsourcing generally increases. While greater supply and greater demand have the expected effect on investments, decreases in variability are not as straightforward. Greater supply uncertainty increases the need for vertical integration while greater demand uncertainty increases the reliance on outsourcing. In the multi-period model, we find that the nature of adjustments in capacity based on changes in demand or supply follows from the comparative statics of the single-period model, although whether outsourcing increases or decreases depends on the costs of adjusting capacity.

Order Quantity and Timing Flexibility in Supply Chains: The Role of Demand Characteristics

We study how differences in product demand characteristics affect the strategic value of different types of supply chain flexibility for accurate response. We propose a single-period inventory modelling framework with two ordering opportunities. The second order reflects updated demand information and potentially capitalizes on supply chain flexibility. We consider two complementary forms of flexibility: quantity flexibility in production and timing flexibility in scheduling. In this framework, we analyze the total inventory cost of a firm for alternate demand types. We model functional products through the standard assumption of independent demand over the period, fashion-driven innovative products through a Bayesian model, and innovative products with evolving demand through a Martingale process. The three demand processes exhibit very different behavior with respect to the value of the alternate forms of flexibility. We observe that quantity flexibility is of moderate value for functional goods and of high value for fashion-driven products for all lead times. Quantity flexibility is of low value for goods with evolving demand with long lead times but of high value for short lead times. Alternately, we observe timing flexibility is of highest value for functional goods, especially for cases of high holding cost, and is of lesser value for fashion-driven goods. It is of least value for goods with evolving demand. Both quantity and timing flexibility capabilities are required to significantly reduce the relevant supply chain costs for evolving-demand innovative goods when the lead times are long.

On the Complementary Value of Accurate Demand Information and Production and Supplier Flexibility

We study the value of information, production flexibility, and supplier flexibility for a good for which an initial and a subsequent order may be placed. We consider a Bayesian model of demand in which the unknown mean demand rate is assumed to have a prior, which is a mixture of two normal distributions corresponding to the demand forecast for an innovative (fashion) good. We develop three models of production flexibility: a static model requiring initial placement of both orders, a partially dynamic model requiring a fixing of the time that the second order will be made, and a fully dynamic model with no restrictions on ordering. Supplier flexibility is modeled through supply lead times. We observe that the magnitude of the savings from the static to the fully flexible model, corresponding to the sum of the values of information and production flexibility, reflects all sources of variability: differences between demand means of the prior mixture, variability within each prior, and variability about the observed mean. We observe that as the difference between high and low demand cases increases, the value of information increases, though for long lead times, production flexibility is required to take advantage of the updated information. Further, we observe that the greater the uncertainty within each prior distribution, the greater the value of information relative to the value of production flexibility, particularly for long lead times. However, the greater the uncertainty around the mean demand, which is the uncertainty that cannot be resolved through observation, the lower the value of information. Finally, we observe that the value of supply flexibility grows initially in a concave then convex manner as a function of the supply lead times.

Contingent Labor Contracting Under Demand and Supply Uncertainty

Firms increasingly use contingent labor to flexibly respond to demand in many environments. Labor supply agencies are growing to fill this need. As a result, firms and agencies are engaging in long-term contracts for labor supply. We develop mathematical models of the interaction between firms and labor supply agencies when demand and supply are uncertain. We consider two models of labor supply uncertainty, termed productivity and availability uncertainty, and study how each affects the nature of the contracts formed. These models reflect two major roles played by the labor supply agency. In the case of productivity uncertainty we find that it is possible to construct a contract that coordinates the firm and agency hiring in an optimal way. In contrast, we show that in environments characterized by availability uncertainty, optimal contracts are not possible. However, there is a large range of contract parameters for which both parties would benefit from a contract. We analyze these and discuss the trade-offs that should be considered in contract negotiation.

Using simulated annealing to select least-cost assembly sequences

Applies simulated annealing (SA) to find the probable least cost assembly sequence for a mechanical product from among the thousands of feasible sequences. The sequences are represented by the assembly sequence network introduced by De Fazio and Whitney (1987). Candidate sequences are selected one at a time by the SA algorithm and their cost is estimated by designing a minimum unit cost concept assembly system using a dynamic programming algorithm. Alternate sequences are selected by perturbing the path through the sequence network in a way similar to a genetic algorithm. This method differs from that normally used to select least cost sequences, in which an engineer edits the thousands of sequences using judgment and experience, and then obtains the costs of a few that survive editing. Here, the search for a least cost sequence is done without prior editing. In the examples studied, there appear to be a large number of sequences that are technically quite different but of similar cost.<<ETX>>

Staffing to Maximize Profit for Call Centers with Alternate Service-Level Agreements

To ensure quality from outsourced call centers, firms sign service-level agreements (SLAs). These define service measures such as what constitutes an acceptable delay or an acceptable abandonment rate. They may also dictate penalties for failing to meet agreed-upon targets. We introduce a period-based SLA that measures performance over a short duration such as a rush hour. We compare it to alternate SLAs that measure service by individual and over a long horizon. To measure the service levels for these SLAs, we develop several approximations. We approximate the probability an acceptable delay is met by generalizing the heavy-traffic quality and efficiency driven regime. We also provide a new approximation for the abandonment rate. Further, we prove a central limit theorem for the probability of meeting a service level measured by the percentage of customers acceptably served during a period. We demonstrate how an outsourced call center operating in an environment with uncertain demand and abandonment can determine its staffing policy to maximize the expected profit for these SLAs. Numerical experiments demonstrate a high degree of accuracy for the approximations and the resulting staffing levels. We indicate several salient features of the behavior of the period-based SLA.

Dynamic Pricing Through Discounts for Optimizing Multiple-Class Demand Fulfillment

In a multiple-customer-class model of demand fulfillment for a single item, we consider the use of dynamic price discounts to encourage backlogging of demand for customer classes denied immediate service. Customers are assumed to arrive over several stages in a period, and customer classes are distinguished by their contractual price and sensitivity to discounts. Through dynamic programming we determine the optimal discounts to offer, assuming a linear model for the sensitivity of customers to such inducements. We show that customers are served in class order, and allocation of inventory to demand is determined by considering the current number of customers backlogged, as well as the current inventory position. Through comparison to a naive supplier allocating inventory first come/first served with no discounting, we show that profits are primarily influenced by the allocation of capacity, and the use of price discounts primarily benefits the second-class customers overall fill rate. Heuristics for implementation of the solution in real-time settings are given.

Spreadsheet Model Helps to Assign Medical Residents at the University of Vermont's College of Medicine

This paper describes a spreadsheet model that MBA students enrolled in an MS course constructed to replace the manual method of assigning medical residents in radiology to on-call and emergency rotations at the University of Vermonts College of Medicine. Although it contains more than 10,000 variables, the model was easy to build and solve by practitioners who are “lightly educated” in OR/MS. Based on this groups work, we discuss an approach that end-user practitioners can take to create spreadsheet optimization models. We also provide several observations and argue that spreadsheet models can provide an alternative scheduling method for problems of a smaller scope. Despite the major advances in personnel-scheduling methodologies and software, manual scheduling is still the predominant method used for such smaller-scope problems.

Liking and Following and the Newsvendor: Operations and Marketing Policies Under Social Influence

We consider a monopolistic firm selling two substitutable products to a stream of sequential arrivals whose purchase decisions can be influenced by earlier purchases. Before demand realizes, the firm faces a newsvendor problem for the two products with economies of scale in production for each. When consumers are responsive to others’ decisions, social influence amplifies demand uncertainty, leading to a lower profit for the firm. We propose three solutions for the firm to better cope with or even benefit from social influence: influencer recruitment and a reduced product assortment either before demand realization (ex ante) or under production postponement (ex post). First, the firm can offer promotional incentives to recruit consumers as influencers. We reveal an operational benefit of influencer marketing that a very small fraction of such influencers is sufficient to diminish sales’ unpredictability. Second, as the potential substitutability between products increases due to social influence, the firm may leverage the increased substitutability and enjoy lower cost in production by reducing product assortment before demand realization. Last, under production postponement, the firm can take advantage of the way that social influence results in demand herding and reduce product varieties by reacting to preorder information. This paper was accepted by Martin Lariviere, operations management.

Now Playing: DVD Purchasing for a Multilocation Rental Firm

This paper studies the problem of purchasing and allocating copies of movies to multiple stores of a movie rental chain. A unique characteristic of this problem is the return process of rented movies. We formulate this problem for new movies as a newsvendor-like problem with multiple rental opportunities for each copy. We provide demand and return forecasts at the store-day level based on comparable movies. We estimate the parameters of various demand and return models using an iterative maximum-likelihood estimation and Bayesian estimation via Markov chain Monte Carlo simulation. Test results on data from a large movie rental firm reveal systematic underbuying of movies purchased through revenue-sharing contracts and overbuying of movies purchased through standard (nonrevenue-sharing) ones. For the movies considered, our model estimates an increase in the average profit per title for new movies by 15.5% and 2.5% for revenue sharing and standard titles, respectively. We discuss the implications of revenue sharing on the profitability of the rental firm.