QUESTION $1[58$ MARKS$]$

Widgman manufactures widgets at two plants that supply three distribution centres

$($DCs$)$ from where it is distributed to their customers. The annual plant capacities are as

follows:

Capacity $($units$)$

Plant $1$

Plant $2$

$30000$

$40000$

The annual demand at DC$1$ for the following year has been estimated at $25000$ units.

However, the annual demands at DC$2$ and DC$3$ have not been finalized. However, the

annual demand at DC$2$ for the past ten years was as follows:

Year Demand $($units$)$

$123000$

$225100$

$323900$

$422500$

$523500$

$623700$

$723200$

$824700$

$924800$

$1024950$

In addition, management is of the opinion that a manufacturing index could be indicative

of the demand at DC$2.$ The index values have been recorded for a $10-$year similar

period as follows:

Year Index

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

$3\mathrm{.}4$

$3\mathrm{.}9$

$3\mathrm{.}6$

$3\mathrm{.}2$

$3\mathrm{.}6$

$3\mathrm{.}6$

$3\mathrm{.}5$

$3\mathrm{.}8$

$3\mathrm{.}8$

$3\mathrm{.}9$

In addition, the BER $($Bureau for Economic Research$)$ has estimated the index value for

the following year at $3\mathrm{.}9.$ It is believed that the demand forecast for the next year could

be obtained through the application of either trend or causal regression analysis.

The annual demand for widgets at DC$3$ was as follows over the past $8$ years:

Annual Demand $($units$)$

$11050$

$11150$

$13400$

$14100$

$15000$

$16950$

$17700$

$18700$

The company utilized a three$-$year weighted moving average $($weights $=0\mathrm{.}6,0\mathrm{.}3$ & $0\mathrm{.}1)$

and exponential smoothing method $(\backslash$alpha $=0\mathrm{.}7)$ to forecast demand for the next year and

obtained the following predictions of demand:

Year $3$WMA

ES

$(\backslash$alpha $=0\mathrm{.}7)$

$111050$

$211050$

$311120$

$41249012716$

$51359513684\mathrm{.}8$

$61457014605\mathrm{.}44$

$71608016246\mathrm{.}63$

$81720517263\mathrm{.}99$

The associated forecasts are as follows:

Forecast technique Forecast $($annual units$)$

$3-$month Weighted Moving Average

Exponential smoothing $(=0\mathrm{.}7)$

$18225$

$18269$

However, the company believes that the regression analysis approach should also be

investigated to forecast demand at DC$3$ for the following year.

The logistics manager has used a map of the area to find the locational coordinates of

the various facilities and these are shown in the table below:

Facility X coordinate Y coordinate

Plant $1$

Plant $2$

DC$1$

DC$2$

DC$3$

$3$

$4$

$9$

$8$

$10$

$2$

$5$

$7$

$4$

$2$

Note that each coordinate unit represents $10$ km$.$

The transport manager has estimated the transport rates from the plants to the DCs for

the existing network for the following year as follows:

Route

Volume

$($percentage of DC demand$)$

Transport Rate

$($cents$/$unit$/$km$)$

Plant $1$ to DC$2$

Plant $1$ to DC$3$

Plant $2$ to DC$1$

Plant $2$ to DC$2$

$40\%$

$100\%$

$100\%$

$60\%$

$60$

$65$

$65$

$70$

The logistics manager is of the opinion that the inbound transport cost $($plant to DC$)$

may be reduced through the following:

$$ Introducing a regional DC at location $(5$; $4)$ i$.$e$.$ ship $50\%$ of the total volume from

Plant$1$ to the regional DC$,50\%$ of the total volume from Plant $2$ to the regional

DC and from the regional DC to DC$1$ and new DC $($see below$)$

$$ Consolidating DC$2$ and DC$3$ into one DC at location $(9$; $5)$

These new facilities have been identified and have sufficient capacities based on the

total volume requirements.

The estimated transport rates from the plants to the proposed regional DC and from the

proposed regional DC to the DCs for the following year are as follows:

Facility

Transport Rate

$($cents$/$unit$/$km$)$

Plant $1$ to regional DC

Plant $2$ to regional DC

Regional DC to DC$1$

Regional DC to new DC

$50$

$48$

$55$

$45$

Based on transport costs only, which course of action would you recommend to the

company?

Random numbers

$0\mathrm{.}09$

$0\mathrm{.}64$

$0\mathrm{.}58$

$0\mathrm{.}74$

$0\mathrm{.}05$