Tarkan Tan

Capacity reservation and utilization for a manufacturer with uncertain capacity and demand

We consider an original equipment manufacturer (OEM) who has outsourced the production activities to a contract manufacturer (CM). The CM produces for multiple OEMs on the same capacitated production line. The CM requires that all OEMs reserve capacity slots before ordering and responds to these reservations by acceptance or partial rejection, based on allocation rules that are unknown to the OEM. Therefore, the allocated capacity for the OEM is not known in advance, also because the OEM has no information about the reservations of the other OEMs. Based on a real-life situation, we study this problem from the OEM’s perspective who faces stochastic demand and stochastic capacity allocation from the contract manufacturer. We model this problem as a single-item, periodic review inventory system, and we assume linear inventory holding, backorder, and reservation costs. We develop a stochastic dynamic programming model, and we characterize the optimal policy. We conduct a numerical study where we also consider the case that the capacity allocation is dependent on the demand distribution. The results show that the optimal reservation policy is little sensitive to the uncertainty of capacity allocation. In that case, the optimal reservation quantities hardly increase, but the optimal policy suggests increasing the utilization of the allocated capacity. Further, in comparison with a static policy, we show that a dynamic reservation policy is particularly useful when backorder cost and uncertainty are low. Moreover, we show that for the contract manufacturer, to achieve the desired behavior, charging little reservation costs is sufficient.

Modelling imperfect advance demand information and analysis of optimal inventory policies

We consider an inventory control problem where it is possible to collect some imperfect information on future demand. We refer to such information as imperfect Advance Demand Information (ADI), which may occur in different forms of applications. A simple example is a company that uses sales representatives to market its products, in which case the collection of sales representatives’ information as to the number of customers interested in a product can generate an indication about the future sales of that product, hence it constitutes imperfect ADI. Other applications include internet retailing, Vendor Managed Inventory (VMI) applications and Collaborative Planning, Forecasting, and Replenishment (CPFR) environments. We develop a model that incorporates imperfect ADI with ordering decisions. Under our system settings, we show that the optimal policy is of order-up-to type, where the order level is a function of imperfect ADI. We also provide some characterizations of the optimal solution. We develop an expression for the expected cost benefits of imperfect ADI for the myopic problem. Our analytical and empirical findings reveal the conditions under which imperfect ADI is more valuable. � 2006 Elsevier B.V. All rights reserved.

Double Counting in Supply Chain Carbon Footprinting

Carbon footprinting is a tool for firms to determine the total greenhouse gas GHG emissions associated with their supply chain or with a unit of final product or service. Carbon footprinting typically aims to identify where best to invest in emission reduction efforts, and/or to determine the proportion of total emissions that an individual firm is accountable for, whether financially and/or operationally. A major and underrecognized challenge in determining the appropriate allocation stems from the high degree to which GHG emissions are the result of joint efforts by multiple firms. We introduce a simple but general model of joint production of GHG emissions in general supply chains, decomposing the total footprint into processes, each of which can be influenced by any combination of firms. We analyze two main scenarios. In the first scenario, the social planner allocates emissions to individual firms and imposes a cost on them such as a carbon tax in proportion to the emissions allocated. In the second scenario, a carbon leader voluntarily agrees to offset all emissions in the entire supply chain and then contracts with individual firms to recoup part of the costs of those offsets. In both cases, we find that, to induce the optimal effort levels, the emissions need to be overallocated, even if the carbon tax is the true social cost of carbon. This is in contrast to the usual focus in the life-cycle assessment LCA and carbon footprinting literatures on avoiding double counting. Our work aims to lay the foundation for a framework to integrate the economics-and LCA-based perspectives on supply chain carbon footprinting.

Tactical capacity management under capacity flexibility

In many production systems a certain level of flexibility in the production capacity is either inherent or can be acquired. In that case, system costs may be decreased by managing the capacity and inventory in a joint fashion. In this paper we consider such a make-to-stock production environment with flexible capacity subject to periodic review under non-stationary stochastic demand, where we allow for positive fixed costs both for initiating production and for acquiring external capacity. Our focus is on tactical-level capacity management which refers to the determination of in-house production capacity while the operational-level integrated capacity and inventory management is executed in an optimal manner. We first develop a simple model to represent this relatively complicated problem. Then we elaborate on the characteristics of the general problem and provide the solution to some special cases. Finally, we develop several useful managerial insights as to the optimal capacity level, the effect of operating at a suboptimal capacity level and the value of utilizing flexible capacity.

The final order problem for repairable spare parts under condemnation

We consider a manufacturer of complex machines that offers service contracts to her customers, committing herself to repair failed spare parts throughout a fixed service period. The suppliers of spare parts often discontinue the production of some parts as technology advances and ask the manufacturer to place a final order. We address the problem of determining final orders for such spare parts. The parts that we consider are repairable, but they are subject to the risk of condemnation. We build a transient Markovian model to represent the problem for a repairable spare part with a certain repair probability and repair lead time and we present some approximations that allow for further real-life characteristics to be included. Furthermore, an approximate model that can be computed more efficiently is presented, and the sensitivity of the results obtained with respect to the problem parameters is discussed, helping us develop several managerial insights.

An exact solution procedure for multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse

We consider a multi-item two-echelon inventory system in which the central warehouse operates under a (Q,R) policy, and the local warehouses implement basestock policy. An exact solution procedure is proposed to find the inventory control policy parameters that minimize the system-wide inventory holding and fixed ordering cost subject to an aggregate mean response time constraint at each facility.

Optimal inventory policies with non-stationary supply disruptions and advance supply information

We consider the production/inventory problem of a manufacturer (or a retailer) under non-stationary and stochastic supply availability. Although supply availability is uncertain, the supplier would be able to predict her near future shortages - and hence supply disruption to (some of) her customers - based on factors such as her pipeline stock information, production schedule, seasonality, contractual obligations, and non-contractual preferences regarding other manufacturers. We consider the case where the information on the availability of supply for the near future, which we refer to as advance supply information (ASI), is provided by the supplier. The customer demand is deterministic but non-stationary over time, and the system costs consist of fixed ordering, holding and backorder costs. We consider an all-or-nothing type of supply availability structure and we show the optimality of a state-dependent (s,S) policy. For the case with no fixed ordering cost we prove various properties of the optimal order-up-to levels and provide a simple characterization of optimal order-up-to levels. For the model with fixed ordering cost, we propose a heuristic algorithm for finding a good ordering strategy. Finally, we numerically elaborate on the value of ASI and provide managerial insights.

Integrated capacity and inventory management with capacity acquisition lead times

We model a make-to-stock production system that utilizes permanent and contingent capacity to meet non-stationary stochastic demand, where a constant lead time is associated with the acquisition of contingent capacity. We determine the structure of the optimal solution concerning both the operational decisions of integrated inventory and flexible capacity management, and the tactical decision of determining the optimal permanent capacity level. Furthermore, we show that the inventory (either before or after production), the pipeline contingent capacity, the contingent capacity to be ordered, and the permanent capacity are economic substitutes. We also show that the stochastic demand variable and the optimal contingent capacity acquisition decisions are economic complements. Finally, we perform numerical experiments to evaluate the value of utilizing contingent capacity and to study the effects of capacity acquisition lead time, providing useful managerial insights.

Integrated workforce capacity and inventory management under labour supply uncertainty

In a manufacturing environment with volatile demand, inventory management can be coupled with dynamic capacity adjustments for handling the fluctuations more effectively. In this study, we consider the problem of integrated capacity and inventory management under non-stationary stochastic demand and capacity uncertainty. The capacity planning problem is investigated from the workforce planning perspective where the capacity can be temporarily increased by utilising contingent workers from an external labour supply agency. The contingent capacity received from the agency is subject to an uncertainty, but the supply of a certain number of workers can be guaranteed through contracts. There may also be uncertainty in the availability of the permanent and contracted workers due to factors such as absenteeism and fatigue. We formulate a dynamic programming model to make the optimal capacity decisions at a tactical level (permanent workforce size and contracted number of workers) as well as the operational level (number of workers to be requested from the external labour supply agency in each period), integrated with the optimal operational decision of how much to produce in each period. We analyse the characteristics of the optimal policies and we conduct an extensive numerical analysis that helps us provide several managerial insights.

Inventory Control in a Spare Parts Distribution System with Emergency Stocks and Pipeline Information

Motivated by collaboration with a global spare parts service provider, we consider a two-echelon inventory system with multiple local warehouses, a so-called support warehouse, and a central warehouse with ample capacity. In case of stock-outs, the local warehouses can receive emergency shipments from the support warehouse or the central warehouse at an extra cost. Our focus is on using information on orders in the replenishment pipeline, i.e., pipeline information, to achieve cost-efficient policies for requesting emergency shipments. We introduce a policy where the request for an emergency shipment is based on the time until an outstanding order will reach the stock point considered. The goal is to determine how long one should wait for stock in the replenishment pipeline before requesting an emergency shipment, and the cost effects of using pipeline information in this manner. The analysis utilizes results from queuing theory and provides a decomposition technique for optimizing the policy parameters that reduces the complex multiechelon problem to more manageable single-echelon problems. The performance of our policy indicates that there can be a significant benefit in using pipeline information.