BST838
SUPPLY CHAIN DYNAMICS
COURSEWORK
On Unsatisfied Demand Observations in Inventory Systems
Date given to students: 18 May 2021
Date for oral examination: 21-25 June 2021
Date for report submission: 16 July 2021, via TURNITIN
Word limit: 2000
1. Background
In Lecture 7, we will discuss two inventory models that describe customer behaviour when
shortage occurs, namely, backlog and lost sales. The backlog model refers to the situation where
all unsatisfied customers wait for the stock to be replenished, i.e., the customers are patient. The
lost sales model refers to the situation where any unsatisfied customer retracts the purchasing
intention and withdraws from the system, i.e., the customers are impatient. The backlog model
can be represented by a linear equation, thus it appears more frequently in the literature.
In lost sales systems, a new problem emerges - whether the business is able to observe the
demand that has been lost. In some cases, the business may be aware of the size of the actual
demand, when the customer raises an enquiry prior to making the actual order. This can be
frequently seen in business-to-business scenarios. However, this is not the case in the retail context.
Suppose you go to the grocery store to buy some milk but discover an empty shelf. It is safe to
guess that the likelihood is very low that you as a consumer report your true need to the store
owner. Instead, you may walk away to another store, or choose something else, juice or soya milk.
This is the case where the store owner loses track of the actual demand.
The case when the business cannot observe the lost demand is referred to as demand censoring
in the literature, i.e., the observable demand is censored by the available inventory. Conrad (1976)
provides a simple explanation of this problem. Then the literature focuses mainly on estimating
the true demand from the observed demand, and make better ordering decisions (see e.g. Godfrey
and Powell, 2001; Huh et al., 2011; Besbes and Muharremoglu, 2013). Rudi and Drake (2014)
investigated the decision behaviour in the newsvendor setting with demand censoring. However,
most of the above research deal with the newsvendor system, rather than the general inventory
system. The objective of this assignment is to establish a system dynamics model that includes
demand censoring, investigate the effect of demand censoring on inventory performance and discuss
the implications of your findings. In particular, you are expected to
• via simulation, systematically investigate the performance of the lost sales system given in
Section 2;
• conceptually and mathematically extend the lost sales model, to incorporate demand cen-
soring and compare the difference in system performance;
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• discuss ways to mitigate the negative impact of demand censoring.
2. The base model
The model is established for a single-product, periodic-review, one-echelon inventory system.
Without loss of generality, we assume that this echelon represents the retailer. The lost sales is
assumed, where the inventory is bounded by a non-negative constraint. The lead-time is assumed
to be constant and equal to one period. The retailer adopts an order-up-to policy.
The following notation should be used in this assignment:
dt Demand (consumption) in period t
ft Demand forecast for period t
ot Order quantity in period t
it Inventory level at the end of period t
ss Safety stock
The retailer uses the simple exponential smoothing method to generate demand forecasts,
ft = α · dt−1 + (1 − α) · ft−1 (1)
The order-up-to policy is as follows,
ot = ft + ss− it (2)
The inventory balance equation is
it = max(it−1 + ot−1 − dt, 0) (3)
The demand follows a normal distribution with the expectation of 100 and standard deviation
of σ (unspecified at this stage). The safety stock is set as ss = 100 throughout. The smoothing
coefficient is set as α = 0.8.
You need to justifiably choose your own measures for the performance of the inventory system.
They can be either cost based (e.g., holding cost and shortage cost) or unit based (e.g., average
inventory level, availability, bullwhip and NSAmp).
3. Your tasks
Based on the base model above, establish a spreadsheet simulation model and answer the
following question:
(Q1) How does σ affect the performance of the inventory system in the lost sales model?
From the information given in Section 1, answer the following question:
(Q2) How do you extend the model to include demand censoring?
Conduct the simulation analysis again based on the extended model. Analyze the simulation
results and answer the following question:
(Q3) How does the addition of demand censoring affect the answer to Q1?
Based on your answers of Q1-Q3, answer the following question:
(Q4) Change the safety stock value. What do you observe? How should you mitigate the impact
of demand censoring?
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4. Assessment
4.1. Oral examination
The oral examination will last for approximately 10 minutes for each student and will take up
30% of the assessment. You are asked to present the base model in the spreadsheet form (15%)
and the extended model in conceptual and mathematical forms (15%). Verbal feedback will be
given during the examination which may be incorporated in your written report. Make sure you
have the following materials ready when you attend the examination: an Excel file for the base
model simulation, and a Powerpoint file (no more than 5 slides) for the extended model. You
will receive notifications of the exact date and time for your individual examination prior to the
examination week.
4.2. Report
You are asked to submit a written report which constitutes 70% of the assessment. The
following parts should be included in the report.
• Simulation analysis (20%)
Answer Q1. You should support your answer with results in numerical and graphical forms
(e.g. tables and figures). All necessary tables and figures should be included in the report,
but not be copied from a direct screen shot in the spreadsheet.
• Model evaluation and extension (30%)
Answer Q2 and Q3. Proper justification of any assumption relaxation should be given
and evidence provided (10%). Reliable sources of evidence include, but are not limited
to, published academic literature, industrial reports and news pieces. The extended model
(10%) needs to be presented in both conceptual (i.e. causal loop diagram) and mathematical
(i.e. difference equations) forms. New variables and parameters need to be properly defined
before use. Simulation results should be presented clearly (10%).
• Mitigation (10%)
Answer Q4. The discussion in this section should be based on your findings in previous
analyses.
The report should also be written in fluent plain English (5%) and show clear organization
(5%). The word limit of the report is 2000 excluding figures, tables and references. Please name
your submission file by your student number only, e.g., “1234567.pdf” or “1234567.docx”.
4.3. Criteria
You will be judged on criteria in the file “rubric.docx”.
5. Alignment with learning objectives
The ILOs of this module, as stated in the module description, are listed as follows. After the
completion of the module, the students are expected to be able to
(ILO1) understand the role of system structure in dynamic behaviour
(ILO2) show a critical awareness of the role of modelling and simulation to demonstrate the ways
in which dynamic problems in supply chains may be solved
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(ILO3) evaluate and justify assumptions in model development based on trade-off between relevance
and solvability
(ILO4) demonstrate a capability in supply chain dynamics simulation and test various supply chain
re-design strategies
(ILO5) be fully conversant with the concepts of verification and validation and its role in ensuring
model fidelity
(ILO6) relate dynamic behaviour to supply chain performance such as total cycle-time, total costs
and customer service levels
Table 1 shows how these intended learning objectives are aligned with the tasks in this course-
work.
Task Learning Objectives
Q1 ILO1, ILO4, ILO6
Q2 ILO1, ILO3, ILO5
Q3 ILO1, ILO4, ILO6
Q4 ILO2, ILO6
Table 1: Alignment of learning objective
References
Besbes, O., Muharremoglu, A., 2013. On implications of demand censoring in the newsvendor
problem. Management Science 59 (6), 1407–1424.
Conrad, S., 1976. Sales data and the estimation of demand. Journal of the Operational Research
Society 27 (1), 123–127.
Godfrey, G., Powell, W., 2001. An adaptive, distribution-free algorithm for the newsvendor prob-
lem with censored demands, with applications to inventory and distribution. Management Sci-
ence 247 (8), 1101–1112.
Huh, W. T., Levi, R., Rusmevichientong, P., Orlin, J. B., 2011. Adaptive data-driven inventory
control with censored demand based on kaplan-meier estimator. Operations Research 59 (4),
929–941.
Rudi, N., Drake, D., 2014. Observation bias: The impact of demand censoring on newsvendor
level and adjustment behavior. Management Science 60 (5), 1334–1345.
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