Strategic safety stock placement in supply chain design with due-date based demand

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Abstract

We present a strategic safety stock placement model in supply chain design for assembly-type product with due-date based demand, where demand data are based on dates when company has to ship to customers rather than order receiving dates. We formulate multi-echelon stock placement by guaranteed-service model with demand propagation equations through backward explosion, where demand can be either stationary or nonstationary. The stock placement model is incorporated into network design problem and its optimization procedure is provided. We show effectiveness of the optimization procedure and other significant features of the model through numerical examples of a machinery product supply chain.

Introduction

In this paper, we present an optimization model for safety stock placement combined with supply chain network design for assembly-type supply chain. The objective of the model is to minimize total cost including processing and transit costs together with stock holding cost. The stock placement problem is formulated by a modified “guaranteed-service model” with due-date based demand, which can be either stationary or nonstationary.

Motivation of our study was raised by a machinery business unit of our company. In order to survive in tough competitive environment, the machinery business unit is always under pressure to achieve better capability to meet customer demand with leaner process. It has a global supply chain with component assembly sites in Asia and a final assembly sites in Europe and is considering relocation of some facilities for a new product. Since the lead-time from component assembly to final product shipment is long, the business unit also wants to examine cost effective stock placement along with the facility relocation. Although demand is supposed to vary over a year, it is not easy to change stock points frequently. Therefore they need to determine appropriate stock points strategically for the year.

The conventional guaranteed-service model is based on periodic-review base-stock policy, where it is implicitly assumed that demand data set is provided on an order-arrival date basis, i.e., the data set is a collection of order statistics based on dates when orders are received. This type of demand data is valid when we assume each order is allocated to available stock upon its receipt and it is allowed to be back-ordered, where due-date requirements from customers are treated less significant consequently. Typical industry that fits such a situation is consumer product business. On the other hand, in B to B business like the machinery product industry, customer requirements regarding due-date are more important. The machinery business unit needs to forecast future demand based on dates when it has to ship to customers rather than order receiving dates, and safety stocks are prepared for the future shipment in advance. Once demand forecast is established as a master plan, required quantity of product to be processed and to be held as stock at each stage in the supply is calculated by MRP procedure or so-called “backward explosion” from the most downstream stage toward the upstream ones. Actual operation at each stage is executed to fulfill the planned required quantity based on the demand forecast. Here we call this scheme “Make-to-Plan” operation.

In order to model under Make-to-Plan scheme, transit time between stages as well as processing time at a stage is needed to calculate required quantities with lead-time offsetting. However, all of the guaranteed-service model formulations in previous literature have no explicit definition of transit time from a stage to the succeeding stage. The lack of explicit transit time definition can be a limitation in safety stock placement with network design where there are multiple options for a supplier's location with different transit times. Especially when one would consider stock placement with network design problem which have various options for facility locations, explicit definition of transit time turns beneficial.

In this paper, we reformulate the guaranteed-service model for assembly-type supply chain with explicitly defined transit time and combine it with network design problem. We also provide an optimization procedure for the model, which circumvent unnecessary search of wasteful space with a simple threshold function. Although effectiveness of the threshold function depends on values of several parameters, it works well with the parameter values that ordinarily appear in actual situations.

In summary, major contribution of this paper includes the followings: (1) extension of guaranteed-service model to Make-to-Plan scheme with due-date based demand, which can be either stationary or nonstationary and (2) supply chain network design model combined with stock placement and its efficient optimization procedure.

The rest of the paper is organized as follows. In the next section, we review previous literature. In Section 3, we show the safety stock placement model for assembly-type supply chain under Make-to-Plan scheme and its optimization algorithms with dynamic programming, which is used in a sub-step of the optimization procedure for supply chain design. Section 4 presents the supply chain design model with stock placement and its optimization procedure. The procedure is examined by numerical examples of the machinery product supply chain and its effectiveness is discussed in Section 5. Finally, in Section 6, we conclude by summarizing contribution of the research and some issues for future research.

Section snippets

Literature review

We review related previous works in the context of two research streams; one is safety stock placement problem for multi-echelon supply chain and the other is supply chain network design problem with stock placement.

Safety stock placement model

Notation

    G: (N, A)

    network of supply chain consisting of nodes N and arcs A

    N

    set of nodes that describe functions in supply chain

    A

    set of links that describe product flow relations among nodes

    Ñn

    set of nodes on the path from node n to the end node of the supply chain including node n

    Pn

    processing time at node n

    Tm,n

    transit time from node m to node n

    Ln

    lead-time from shipping at node n to completion of process at the end node

    H

    planning horizon

    sn

    service time at node n

    rn

    receiving time at node n

    τn

    safety

Supply chain design model with stock placement

Notation (additional)

    znk

    binary variable for site location selection, which is 1 if the kth location option for node n is selected and 0 otherwise

    Onk

    the kth location option for node n

    Kn

    number of location options for node n

    Nn

    set of all the upstream nodes of node n including n

    Pnk

    processing time at node n with option k

    Tmh,nk

    transit time from node m with option h to node n with option k

    C1nk

    unit processing cost at node n with option k

    C2mh,nk

    unit transit cost from node m with option h to node n with k

Example

We demonstrate how our optimization procedure works using the machinery product supply chain as shown in Fig. 3. The large rounded rectangles are nodes each of which represents the annotated function and small boxes in each node are location options to execute that function. Sub-product assembled at each node is consumed by one unit per a final product, i.e., βn=1 for any n.

The machinery product business unit is considering relocation of facilities for node 2 (upper body assembly), node 3 (base

Conclusion

We developed the supply chain design model with stock placement under Make-to-Plan scheme by extending guaranteed-service model. Using the model, safety stock placement problem for B to B business, where customer due-date is important, can be covered. In the model, we set comprehensive objective function consisting of processing and transit cost and holding cost of pipeline, in-transit and safety stocks, which reflects volumes of work in process affected by safety stock placement. Also we

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