Reference no: EM132346672

Assignment - Future Furniture

In today's supply chains, complexity arises not only from dynamics but also from the sheer number of participating entities. The typical supply chain involves hundreds, if not thousands, of suppliers, multiple factories, numerous distribution centers, and customers spread across the globe. These supply chains are often analyzed in a static mode with constant demand, constant orders, and constant production. As a result, such optimization solutions fail to predict supply chain dynamics and the substantial swings that can occur in inventories, orders, and shipments. In order to understand and correct these problems, a dynamic view and model of the supply chain is required.

Description of the system -

Consider the two-stage supply chain for Future Furniture, a retailer in furniture. They want to serve their customers by having enough items available in stock and therefore place orders to their manufacturer at the beginning of every week. The retailer faces a fixed lead time L of 3 weeks, so that an order placed at the beginning of week t is received at the start of week t+L.

The retailer follows a simple periodic review policy to determine the number of units to order, in which the retailer reviews the inventory and compares the current inventory position IP_t (including units in store and units on order) with a desired target level of inventory S_t (also called order-up-to level). If the inventory position is lower than the target level, an order is placed. The order size O_t is such that it brings the inventory up to this target level, i.e. O_t = S_t - IP_t. The target level consists of the safety stock SS_t plus the expected demand of customers over the next L+1 weeks.

The demand in week t is represented by D_t, where the retailer uses a moving average technique to forecast the demand. In other words, each week, the retailer estimates the expected demand (denoted by D ^_t) as an average of the previous p observations of demand. The retailer estimates the standard deviation of demand (denoted by σ ^_t) in a similar manner:

D ^_t = (_i=t-p∑^t-1D_i)/p

and

σ ^_t² = (_i=t-p∑^t-1(D_i - D ^_t)²)/(p-1)

Both equations express the sample mean and sample variance that need to be calculated in every week based on the p most recent observations of demand. Then, since the estimates of the mean and standard deviation change every week, the target inventory level also will change in every week: S_t = SS_t + (L+1) × D ^_t.

Each week, the following happens: early on Monday morning, the ordered goods arrive. Then the retailer assesses the inventory position and, based on that, places an order at the manufacturer. Only then, he opens the store.

Customers who cannot be served directly, will wait until the desired good is available again and buy it then.

Furthermore, it is assumed in this simple model that the manufacturer can always deliver any order after the lead time L.

Level 1 - For a start, assume that the order rate from customers is constant at 20 units per week.

We first assume that the retailer aims at a desired inventory level of 2D ^_t after order arrivals, this is often called a 2-week coverage. The formula for the desired inventory level is SS_t + D ^_t hence two-week coverage can be achieved by setting the safety stock to SS_t = D ^_t. To be conservative in this determination, the retailer averages sales over a 5-week period, smoothing out any potentially misleading short-term fluctuations.

Question 1 -

a. Model the system in Excel by accounting for the relevant stocks and flows. Include also the desired inventory level SS_t + D ^_t. Assume that the initial inventory is 10 and that in the first three weeks' orders of size 30 arrive. Use a time horizon of 62 weeks (please use this timeline throughout the entire assignment!). Include a figure which illustrates the desired inventory level after order arrival as well as the actual inventory level at the beginning of every week. Also include the gap between these two numbers, where a positive number means that you have more inventory than desired. Add a picture where you show demand and orders over time.

b. Experiment with your model by changing the initial inventory and the initial order size (for the first 3 weeks). What do you observe?

c. Now set the initial inventory to 20 and the order sizes for the first three weeks to 20 as well. From week 11 on, the customer weekly order rate is increased by 20% to 24 units per week.

Include a figure which illustrates the desired inventory level after order arrival as well as the actual inventory level at the beginning of every week. Also include the gap between these two numbers, where a positive number means that you have more inventory than desired. Add a picture where you show demand and orders over time.

d. Explain why we observe this kind of behavior.

Question 2 -

The retailer wants to compare the previous replenishment policy with a more advanced policy where the order is composed of the recent order rate plus a term that is proportional to the difference between the actual inventory position and the order-up-to level. That means:

O_t = O_t-1 + β × (S_t - IP_t - O_t-1) = (1 - β) × O_t-1 + β × (S_t - IP_t)

where β is a constant in between 0 and 1. This type of policy is a key feature of supply chain management and is widely reflected in the real world. Note that when β = 1, this policy corresponds to the same policy as in Question 3.

Adjust your model in "Question 1" to incorporate this more advanced replenishment policy. Characterize the system behavior over time when β = 0.9, 0.6 and 0.1. Explain why we observe this kind of behavior.

The retailer wants to have a better understanding of the influence of several aspects in the supply chain on his ordering behavior.            

Question 3 -

The first aspect the retailer wants to study is the influence of the lead time.

a. Adjust your model of Question 2 to incorporate a lead time of 2.

b. Adjust your model of Question 2 to incorporate a lead time of 4.

c. Characterize the system behavior over time for β = 1.0, 0.9, 0.6 and 0.1. Explain the influence of the lead time on this supply chain of both (a) and (b).

Question 4 -

The second aspect he wants to study is the influence of the number of periods to use for the demand forecasting technique.

a. Adjust your model of Question 2 to incorporate a moving average forecast over a 3-week period.

b. Adjust your model of Question 2 to incorporate a moving average forecast over a 10-week period.

c. Characterize the system behavior over time for β = 1.0, 0.9, 0.6 and 0.1. Explain the influence of the moving average technique on this supply chain of both (a) and (b).

Question 5 -

The third aspect he wants to study is the influence of price fluctuations. So far, we have only considered an increase of the weekly order rate from customers by 20% in week 11, which was the result of a price decrease. The retailer wants to increase the price again, such that the order rate from customers drops again to the old level of 20 units per week.

a. Adjust your model of Question 2 to incorporate a decrease of the customer weekly order rate to 20 units in week 14.

b. Adjust your model of Question 4 to incorporate a decrease of the customer weekly order rate to 20 units in week 21.

c. Characterize the system behavior over time for β = 1.0, 0.9, 0.6 and 0.1. Explain the influence of price fluctuations on this supply chain of both (a) and (b).

Level 2 - So far we assumed that there was no randomness in the customer order rate. In practice, customer demand is stochastic. Assume that the weekly demand follows a normal distribution with an average of 20 units and a standard deviation of 4 units. Furthermore, demand is always rounded to the nearest integer number and demand cannot get negative (in that case the number should be rounded up to zero). There is no demand shock of 20% in week 11.

Furthermore, the retailer prefers a more sophisticated approach to determine the safety stock level now that demand is modeled as a stochastic variable. Since demand follows a normal distribution, he proposes the following:

SS_t = z × σ ^_t × √(L+1)

where σ ^_t is the sample standard deviation for week t over the last 5 weeks, as expressed before and the constant z is the safety factor. This safety factor is chosen from statistical tables to ensure that the probability of no stock outs during the replenishment cycle is equal to the specified level of service (this is called the cycle service level). In particular, for a 95% cycle service level, the z-value equals 1.96. Future Furniture feels comfortable with this service level to determine the safety stock level.

Note that the order-up-to level should be an integer number to be more realistic (this was allowed but not required in Level 1). In order to satisfy the service level, we always round it up. Furthermore, order sizes have to be rounded as well and cannot be negative.

Adjust your model of Question 2 and save it as "Level 2". To compute the demand forecast in week 1 until week 5, assume that the observed demand was 20 units in week -4 until week 0. Furthermore, assume that the orders placed in week -2 until week 0 equal 20 units and that the initial inventory is 20.

Now that we have random demand samples, we can calculate the variability faced by the manufacturer and compare it to the variability faced by the retailer. Let the variance of the customer demand seen by the retailer be Var(D) and the variance of the orders placed by the retailer to the manufacturer be Var(Q^R). The ratio between these two numbers is known as the bullwhip effect. That is, the bullwhip effect caused by the retailer is given by

BW^R = Var(Q^R)/Var(D)

Since we obtain the variance over a sample of random numbers, you always need to use the sample variance to compute the bullwhip effect.

Question 6 -

As mentioned in Question 1, we are using a 62 week time horizon. However, we have made some assumptions regarding the beginning of this time horizon. Add the computation of the bullwhip effect caused by the retailer during week 11 until week 62 to "Level 2", where you use 1,000 simulation replications to obtain simulation results.

a. Report the expected bullwhip effect, and the 95% confidence interval of the expected bullwhip effect over one year. Do this for β = 1.0, 0.9, 0.6 and 0.1.

b. What is the influence of the replenishment policy on the bullwhip effect?

Level 3 - In Level 2 we assumed that the demand distribution does not change over time. In reality there are often seasonal patterns that have an impact on the supply chain.

Adjust your model of Level 2 and save it as "Level 3", where the demand will be sampled from a normal distribution with an average μ_t that changes per week according to the following repetitive pattern:

week	1	2	3	4	5	6	7	8	9	10	11	12	13
μt	20	25	30	36	43	50	45	40	36	32	29	26	23

The standard deviation σ_t of the demand distribution in week t can be computed with the variance-to-mean (VTM) ratio which is

VTM= σ²/μ = 0.5

To compute the demand forecast in week 1 until week 5, assume that the observed demand was 36, 32, 29, 26 and 23 units in week -4 until week 0, respectively. Furthermore, assume that the orders placed in week -2 until week 0 equal 32, 29 and 26 units, respectively.

Question 7 -

Compute the bullwhip effect caused by the retailer during week 11 until week 62, where you use 1,000 simulation replications to obtain simulation results.

a. Report the expected bullwhip effect, and the 95% confidence interval of the expected bullwhip effect over one year. Do this for β = 1.0, 0.9, 0.6 and 0.1.

b. What is the influence of seasonality on the bullwhip effect when you compare your results to Question 6?

Level 4 - So far, we have only analyzed the bullwhip effect caused by the retailer. However, the manufacturer has a raw material supplier. The manufacturer uses the same inventory replenishment policy structure as the retailer. However, the lead time between the raw material supplier and the manufacturer is 2 weeks.

Question 8 -

Previously you incorporate the interaction between the retailer and the manufacturer. In this extended supply chain the manufacturer needs to make a demand forecast based on the observed order rate of the retailer. The manufacturer will also use a moving average technique over a 5-week period to forecast the demand mean and variance. This forecast is then used to determine the target inventory level. When you need any information what happened prior to week 1, we assume that the observed demand was 20 units per week and all orders were equal 20 units (similar to our assumptions in Level 2).

a. Compute the bullwhip effects caused by the retailer and by the manufacturer during week 11 until week 62, where you use 1,000 simulation replications to obtain simulation results. Report the expected bullwhip effects and the 95% confidence interval of the bullwhip effects over one year. Do this for β = 1.0, 0.9, 0.6 and 0.1.

b. What is the influence of having multiple parties in your supply chain on the bullwhip effect? Good luck!!!