In 1932 James Galloway founded Natural Home Brewers outside Dundee on the eastern coast of Scotland. At the time, all the local pubs were owned by three national brewers, but a small number of independent clubs sold speciality beer, mainly imported from Scandinavia and Germany. James founded Natural Home Brewers to sell his locally brewed beer to these clubs.
The local government encouraged new industries in the area and gave him a grant. He used this, together with a personal loan from the bank, to start his company. He did most of the work himself, with help from his brother and wife.
There was a clear demand for their beers, but James was more interested in traditional brewing for the local market than making large profits. By 1945 the company was brewing 1500 gallons a week and employed six people. Then there was a sudden surge in demand as new clubs opened in the area, and a number of pubs began selling Natural Home Brew as a special attraction. By 1955 Natural Home Brewers company was employing 120 people. At this point a national brewery made a generous offer and bought the company.
The new owners were keen to maintain the image of Natural Home Brewers and kept the name and brands. They started selling the products in their own pubs, as well as maintaining the original markets. By 1990 Natural Home Brewers employed 1500 people. During various expansions the brewing had been largely automated and although customers thought they were buying from a local brewery, they were actually buying a fairly standard product.
The brewery is now having trouble with its planning. Several of its most experienced production planners retired in the same year, and the current planning often seems haphazard. In particular, there are times when the brewery has trouble meeting demand. Management feels that it is the time to change their planning procedures, and find some way of guaranteeing reasonable schedules. Getting descriptions of the current procedures is the first step in computerising the whole planning process.
A sample of data was collected over eight months, and agreement was reached about a range of variables. Forecast demand for this period was found, in barrels, as follows:

Month                      Demand
January                     9,000
February                   8,000
March                        6,000
April                           4,000
May                            6,000
June                           8,000
July                            10,000
August                      10,000

Costs and manpower requirement were agreed. Although these are not necessarily exact figures they can be used for comparing plans. These include:

• Production cost of £200 a barrel
• Storage cost of 1.5 per cent of production cost a month
• Shortage cost of £10 a barrel a month
• Five-man hours to produce a barrel
• Direct labour force of 225
• Standard wage rate of £8 an hour
• Overtime wage rate of 1.5 times standard rate
• A standard working week of five days
• Hiring and training cost of £400 a person
• Lay-off cost of £500 a person
• Subcontractors can be used at an additional cost of £5 a barrel
• Opening stock is 2000 barrels
• A reserve stock is kept of 25 per cent of forecast monthly demand
• All shortages are back-ordered
• The main products are lager, bitter and mild which generally accounts for 50 per cent, 40 per cent and 10 per cent sales respectively.

Q.1. The management of Natural Home Brewers now wants your ideas about the plans. In particular, it wants you to design a set of alternative aggregate plans for the eight-month period, compare the costs for these plans and recommend the best.
Q.2. Then the management wants a master schedule for the period. For the longer term it wants a more formal procedure for designing reliable aggregate plans and master schedule. (20 marks)
Q.3. Consider an item with the following properties:
A = £20 c = £2 / unit i = 0.24 £/£/year

At time 0 the inventory has dropped to zero and a replenishment (with negligible lead time) must be made. The demand pattern for the next twelve months is:

Month j                      1    2    3      4      5      6
Demand (units) Dj    50   70 100 120   110 100

Month j                        7    8      9      10    11    12
Demand (units) Dj    100 80   120    70    60    40

All the requirements of each month must be available at the beginning of the month. Replenishments are restricted to the beginning of the months. No shortages are allowed. Using each of the following methods, develop the pattern of replenishments to cover the twelve months and associated total costs of each pattern (do not bother to count the costs of carrying D(j) during its period of consumption, namely period j). In each case, the size of the last replenishment should be selected to end month 12 with no inventory.

a) Fixed economic order quantity (rounded to the nearest integer number of months of supply; that is, each time the EOQ, based on the average demand through the entire twelve months, is adjusted so that it will last for exactly an integer number of months)
b) A fixed time supply (an integer number of periods) based on the EOQ expressed as a time supply, using the average demand rate for the 12 months.

Q.4. A company assembles three distinct finished SKUs, items F1, F2, and F3. The bills of materials for these items, their components, and quantities, are as follows:

Item F1: Composed of 1 unit of A1, A2, and A3 and 2 units of A4.
Item F2: Composed of 1 unit of A1, A2, and A4.
Item F3: Composed of 1 unit of A1, A2, and A4.
Item A1: Composed of 1 unit of A2, and B1.
Item A2: Composed of 1 unit of A4, B1, and B2.
Item A3: Composed of 1 unit of B1, B2, and 3 units of B3.
Item A4: Composed of 2 unit of B3.
Item B1: Composed of 1 unit of B3, and C1.
Item B2: Composed of 1 unit of C1, and C2.
Item B3: Composed of 1 unit of C1, C2 and C3.

Items C1, C2 and C3 are purchased parts. In addition, items A1 and A2 are sold directly to customers as spare parts.
Suppose that the offsets for the operations involved are as follows:

Assembly, Fabrication, or
Purchase of Item          Offset (weeks)
       F1                                  1
       F2                                  2
       F3                                  1
       A1                                  1
       A2                                  2
       A3                                  2
       A4                                  3
       B1                                  1
       B2                                  3
       B3                                  1
       C1                                  2
       C2                                  2
       C3                                  4
Considering only F1 and its components,
a) What minimum horizon should be used for the master production schedule?
b) If the only customer is for 10 units of item F1 in week 15 and there is no initial on-hand or on-order stock for any items, establish the procurement and production schedule for item F1 and all its components.

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