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

MonthSlippers (Pair)Towels (Each)Bedsheets (Set)
2021 Jan547308113
2021 Feb757287113
2021 Mar63529474
2021 Apr54827582
2021 May44720970
2021 Jun55231990
2021 Jul70424376
2021 Aug72323395
2021 Sep954526167
2021 Oct68121360
2021 Nov66828371
2021 Dec1099612160
2022 Jan846403122
2022 Feb785366129
2022 Mar645354100
2022 Apr78127692
2022 May79123079
2022 Jun73440985
2022 Jul72134588
2022 Aug66529468
2022 Sep1076501135
2022 Oct65828578
2022 Nov88929984
2022 Dec1399616260

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

MonthSlippers (Pair)Towels (Each)Bedsheets (Set)
2023 Jan1103408133
2023 Feb787449142
2023 Mar87637085

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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