Assembly and kitting operations, as well as jointly sold products, are rather basic yet intriguing A decentralized supply chains, where achieving coordination through appropriate incentives is very important, especially when demand is uncertain. We investigate two very distinct types of arrangements between an assembler/retailer and its suppliers. One scheme is a vendor‐managed inventory with revenue sharing, and the other a wholesale‐price driven contract. In the VMI case, each supplier faces strategic uncertainty as to the amounts of components, which need to be mated with its own, that other suppliers will deliver. We explore the resulting components' delivery quantities equilibrium in this decentralized supply chain and its implications for participants' and system's expected profits. We derive the revenue shares the assembler should select in order to maximize its own profits. We then explore a revenue‐plus‐surplus‐subsidy incentive scheme, where, in addition to a share of revenue, the assembler also provides a subsidy to component suppliers for their unsold components. We show that, by using this two‐parameter contract, the assembler can achieve channel coordination and increase the profits of all parties involved. We then explore a wholesale‐price‐driven scheme, both as a single lever and in combination with buybacks. The channel performance of a wholesale‐price‐only scheme is shown to degrade with the number of suppliers, which is not the case with a revenue‐share‐only contract.
This work provides a comprehensive analysis of a general periodic review production/inventory model with random (variable) yield. Existence of an order point whose value does not depend on yield being random is proved in the single period case without specifying the yield model and using a very general cost structure. When yield is a random multiple of lot size, the nonorder-up-to optimal policy is characterized for a finite-horizon model. The finite-horizon value functions are shown to converge to the solution of an infinite-horizon functional equation, and the infinite-horizon order point is shown to be no smaller than when yield is certain.
This work concerns the advance scheduling of elective surgery when the operating rooms' capacity utilization by emergency surgery, as well as by elective procedures, is uncertain. New requests for bookings of elective surgery arrive each day. Such procedures preferably would be performed as soon as possible, but admitting too many patients may result in exceeding a day's capacity, possibly necessitating turning away some emergency cases. So the problem facing the hospital at the start of each day is how many of the additional requests for elective surgery to assign for that day. We provide a stochastic dynamic programming model for this aggregate advance scheduling problem. The model has some novel mathematical features. We analyze it and characterize the nature of the optimal policy, which is not necessarily of a control-limit type. Plausible numerical examples which confirm our theoretical results and provide additional insights are reported.health care, hospitals, dynamic programming, applications, probability, stochastic model applications
We investigate a production planning problem in a periodic review environment with variable production capacity, random yields, and uncertain demand. The implications of random yields and variable capacity for lot sizing previously have been explored separately, but not jointly. Many production environments are likely to be subject to both types of uncertainties. To minimize the total discounted expected costs (production, holding, and shortage costs), we formulate the problem as a stochastic dynamic program. For the finite-horizon problem, we prove that the objective function is quasi-convex and that the structure of the optimal policy is characterized by a single critical point for the initial stock level at each period. That is, if the initial stock is greater than this critical point, the optimal planned production is zero; otherwise, it is greater than zero. Expressions for solving the critical point and the optimal planned production are obtained. We further show that the solution for the finite-horizon problem converges to that of the infinite-horizon problem.inventory and production policies, stochastic dynamic programming, periodic review models
Consider a manufacturer or wholesaler who supplies some item to retailers facing demand rates that depend on the shelf or display space that is devoted to that product by themselves and their competitors. The manufacturer, via the use of financial levers at her disposal, wishes to coordinate this decentralized chain while making a profit. We model the physical scenario as one of constant displayed inventory level (on which demand rate depends positively) and continuous replenishment. With a single retailer, we show that to coordinate the channel and make a profit the manufacturer needs to augment the wholesale price lever by another-an inventory holding costs subsidy offered to the retailer. When multiple retailers compete in that product's market, there are two ways to envision and model the demand and market split. One assumes that market demand depends on aggregate inventory displayed, and then splits according to individual display levels. The other "assigns" customers to retailers according to their display levels, and then assumes that purchases are a function of the display level at the retailer selected. We characterize retailers' Nash equilibria in these models, and we explore whether the manufacturer can coordinate such channels.Coordination, Shelf-Space-Dependent Demand, Retail Competition, Nash Equilibrium
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