While you were advising BRRC on the management of suites refurbishment several weeks ago, your uncle introduced you to the Director of Procurement at the Singapore Metropole Hotel (SMH). The both of you started chatting and the Procurement Director was interested in getting your advice on the challenges that SMH faces, namely forecasting demand and ordering of consumables at the hotel. She said:
“SMH’s peak periods every year are the festive season from December to February, the Formula One week in September and the school holidays in June.
Our room rates were certainly affected by COVID-19, but occupancy wasn’t too bad as our hotel was used for quarantine and we also served long-stay guests. Occupancy has been steadily improving as we bring rooms that are mothballed or under refurbishment back into service.
Other than items related to dining and catering, the hotel’s largest spend on consumables are in bedroom slippers, towels, bedsheets. These items may appear to be generic but are of a high quality and are embroidered with the SMH logo, thus only available from a few suppliers. These items are regularly replaced, although consumption is also impacted by occupancy of rooms, wear-and-tear and nature of the item. For example, we replace slippers with brand new ones much more often than we do for bedsheets. However, my procurement analysts do not seem to have a good grasp of order quantities or replenishment frequencies.”

Question 1
Table 1 shows the past monthly consumption of the three items in 2021 and 2022.
Table 1: Consumption of Slippers, Towels and Bedsheets at SMH in 2021 and 2022

Month Slippers (Pair) Towels (Each) Bedsheets (Set)
2021 Jan 547 308 113
2021 Feb 757 287 113
2021 Mar 635 294 74
2021 Apr 548 275 82
2021 May 447 209 70
2021 Jun 552 319 90
2021 Jul 704 243 76
2021 Aug 723 233 95
2021 Sep 954 526 167
2021 Oct 681 213 60
2021 Nov 668 283 71
2021 Dec 1099 612 160
2022 Jan 846 403 122
2022 Feb 785 366 129
2022 Mar 645 354 100
2022 Apr 781 276 92
2022 May 791 230 79
2022 Jun 734 409 85
2022 Jul 721 345 88
2022 Aug 665 294 68
2022 Sep 1076 501 135
2022 Oct 658 285 78
2022 Nov 889 299 84
2022 Dec 1399 616 260

a) Forecast the consumption for each item type at SMH in 2023 using the following methods:
i. Enhanced exponential smoothing method with trend (assume 𝛼=0.2 and 𝛿 = 0.1)
ii. Decomposition method with trend and seasonality You may use a spreadsheet that should be submitted.
b) Between the above two forecasting methods, compare the back-tested Mean Absolute Error (MAD), Mean Absolute % Error (MAPE), Bias and Tracking Signals for the historical data set.
c) For January to March 2023, the actual consumption for items turned out to be as follows in Table 2. Given this new information, which one of the above two forecasting methods do you think performs better?

Table 2: Consumption of Slippers, Towels and Bedsheets at SMH in January to March 2023

Month Slippers (Pair) Towels (Each) Bedsheets (Set)
2023 Jan 1103 408 133
2023 Feb 787 449 142
2023 Mar 876 370 85

Question 2
The three items are currently procured from different suppliers that have different pricing schemes and delivery fees:
• The slippers cost $5 per pair and its supplier (Supplier A) imposes a fixed $100 delivery fee for every order, with no discount of any sort.
• The towels cost $10 each and its supplier (Supplier B) charges a $500 delivery fee. However, a shipping fee rebate of $0.20 per unit is offered for every order of 1,500 units and above, capped at $400.
• The bedsheets cost $50 per set and its supplier (Supplier C) imposes a $200 delivery fee for every order. The supplier occasionally offers limited time discounts whenever it needs to meet its quarterly sales target. Hence for the next week only, a one-time discount of 5% is offered for orders scheduled for delivery in the next quarter (April to June 2023).
Inventory holding cost is 2% monthly at SMH. SMH outsources its purchasing operations to an outsourced provider, who charges $50 to process a purchase order (PO).
Determine the optimal order quantities, order frequencies and relevant costs for each item in the next quarter. You may assume that monthly demand is based on the simple average of your forecasts for April to June 2023 from Question 1. (30 marks)

Question 3
The Director of Procurement has recently been contacted by another supplier (Supplier D) who can supply all three items. This supplier will match the “sticker prices” (i.e. before discount or rebates) of the existing Suppliers A, B and C, but will not offer discounts or rebates. Instead, Supplier D will charge a low $100 delivery fee per purchase order, plus packing fees of $30, 100 and $50 per order for slippers, towels and bedsheets respectively. Other costs not stated may be neglected.
SMH would like to explore an aggregate purchase of all three items from Supplier D in a single purchase order. Should SMH switch to Supplier D in the next quarter, rather than procure the items individually from Suppliers A, B and C? (30 marks)

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Answer 1: Exponential smoothing is an important method of forecasting that utilises time series data. This method of forecasting works by assigning exponentially decreasing weight for past observation. The application of exponential smoothing method in order to forecast the consumption at SMH is performed as follows:

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