Modelling the Supply Chain Activities

The supply chain is conceptualised as a series of agents working autonomously to deliver goods to the end consumer. For simplicity the number of echelons within the supply chain is limited to three consisting of the retailer, wholesaler and manufacturer. The decision on when to order and how much to order is determined internally by each agent and each operates independently and strives to achieve the minimal operating cost possible. Depending on their position in the supply chain, each agent places an order to the upstream agent and the upstream agent delivers goods to the downstream agent. Essentially, the retailer experiences the demand from the end customer (market demand) and determines when and how much order

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to place to the wholesaler. In turn, the wholesaler works out when to order and how much to order from the manufacturer. The manufacturer then produces the product and delivers it to the wholesaler who in turn determines the quantity of goods to deliver to the retailer and supplies it. The sequence of activities involved in determining when to order and how much to order for each agent is shown below. Each agent makes their decision using key parameters (adapted from Lau et al., 2004) and these are shown in Table 3.1.

Parameter Notation Retailer Wholesaler Manufacturer

Market demand D *

Order quantity Q * *

Production quantity PQ *

Mean of Orders from downstream agent

μ * * *

Standard deviation of Orders σ * * *

Stock received by agent SR * *

Stock shipped by agent SS * * *

Stock from Production SFP *

On-hand inventory OH * * *

On-order/Pipeline inventory OO * * *

Backlog quantity BL * * *

Inventory position IP * * *

Transportation lead time L * *

Production lead time PL *

Production Capacity PC *

Re-order point ROP * * *

Order up to level OUT * * *

New order quantity NQ * *

New production quantity NPQ *

Unit shortage cost b * * *

Unit Holding cost h * * *

Unit ordering cost o * *

Unit production cost om *

Fixed ordering cost f * *

Production setup cost p *

Safety factor k * * *

Table 3.1 Key Modelling Parameters

The table shows the parameters of operation and their mathematical representation (notation). The use of ‘*’ is to indicate whether the parameters relate to a specific agent or not. For example Market demand (D) only relates to the Retailer and stock received by agent (SR) relates to the retailer and wholesaler only, while stock from production only refers to the manufacturer. To help distinguish between information

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relating to other agents when describing the activities of a particular agent, subscripts x, and y are used. Subscript ‘y’ represents information relating to the upstream agent while ‘x’ refers to such parameters relating to the downstream agent. The sequence of activities and mathematical model is described as follows.

Step 1: At the beginning of each operating day, an agent receives stock delivered by upstream agent

The stock sent by the upstream agent is received at the current period by the agent after the transportation lead time of the upstream agent. This stock is received at the start of business.

SRt= SSy,t-L (1)

For the manufacturer SSy is replaced with SFP which is stock received from

production after the production lead time.

i.e. SRt= SFPt-PL (2)

Step 2: Update inventory position

Once the stock is received, the state of the on-hand inventory and the on-order inventory is updated as follows:

OHt= OHt-1 + SRt (3)

OOt= OOt-1 - SRt (4)

Then the inventory position is updated as shown below:

IPt= OHt + OOt - BLt-1 (5)

Step 3: Decides if an order should be placed and what quantity to order

A decision to order is made when the inventory position is less than the re-order point and the quantity to order (Qt) at a given period, t, is governed by the ordering

option adopted by the agent. This is discussed in section 3.3.2.1. Step 4: Updates its on-order inventory

The order information above (if any) is passed to the upstream agent and the on- order inventory is updated.

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Step 5: Experiences order from downstream agent

The order information for that day is received from the adjacent customer (downstream agent) and this is added to the pending order previously placed to determine the new order quantity for that period. If the agent is the retailer, the adjacent customer is the end customer and the customer order is called market demand.

𝑁𝑄_𝑥,𝑡 = 𝑄_𝑥,𝑡+ 𝐵𝐿_𝑡−1 (7)

Step 6: Decides the quantity to deliver to fulfil order from downstream agent

Each agent tries to fulfil all demand/order placed by downstream customer. However whatever the agent is unable to fulfil is back ordered.

𝑆𝑆𝑡 = 𝑀𝑖𝑛(𝑁𝑄𝑥,𝑡, 𝑂𝐻𝑡) (8)

𝐵𝐿_𝑡= 𝑁𝑄_𝑥,𝑡 − 𝑆𝑆_𝑡 (9)

Step 7: Updates its on-hand inventory information

𝑂𝐻_𝑡 = 𝑀𝑎𝑥(𝑂𝐻 − 𝑆𝑆_𝑡, 0) (10)

Step 8: Computes mean and standard deviation of orders

The mean of orders and standard deviation of orders is computed using the moving average (MA) technique. For the retailer the mean of orders is represented as mean of demand instead.

Step 9: Computes the operating cost for the day

The operating cost this study is interested in are the holding cost, the backlog cost and the ordering cost. These are computed using eq. (11), (12) and (13) respectively.

𝐻𝐶_𝑡 = ℎ ∗ 𝑂𝐻_𝑡 (11)

𝐵𝐶_𝑡= 𝑏 ∗ 𝐵𝐿_𝑡 (12)

𝑂𝐶_𝑡 = 𝑝 ∗ 𝑀𝑎𝑥(𝑄_𝑡, 0) + 𝑜 ∗ 𝑄_𝑡 (13)

For the manufacturer, the fixed ordering cost is known as production set up cost (p) and the unit ordering cost is called the unit production cost (op). Each cost is computed at the end of the day and averaged over the effective simulation period

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only. Another performance measure used was the daily fill rate of each agent as shown in eq. (14). This is expressed as a percentage. The average fill rate is computed only over the effective simulation period by adding all the fulfilled orders and dividing it by the total orders placed by downstream agents within the total effective period.

𝐹𝑅_𝑡 = 𝑆𝑆_𝑡/𝑁𝑄_𝑥,𝑡 (14)